Steady-state and time-dependent behavior of fusion-fission hybrid systems

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Title:
Steady-state and time-dependent behavior of fusion-fission hybrid systems
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xx, 423 leaves : ill. ; 28 cm.
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English
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Vernetson, William G ( William Gerard ), 1945-
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Subjects / Keywords:
Nuclear reactors -- Models -- Testing   ( lcsh )
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bibliography   ( marcgt )
theses   ( marcgt )
non-fiction   ( marcgt )

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Thesis:
Thesis--University of Florida.
Bibliography:
Includes bibliographical references (leaves 411-422).
Statement of Responsibility:
by William G. Vernetson.
General Note:
Typescript.
General Note:
Vita.

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University of Florida
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All applicable rights reserved by the source institution and holding location.
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Full Text







STEADY-STATE AND TIME-DEPENDENT BEHAVIOR OF
FUSION-FISSION HYBRID SYSTEMS






By


WILLIAM G.


VERNETSON


A DISSERTATION PRESENTED TO THE GRADUATE


COUNCIL OF


THE UNIVERSITY OF FLORIDA
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE
DEGREE OF DOCTOR OF PHILOSOPHY


























Dedicated to

Theresa

without whom this work

would have been impossible.













ACKNOWLEDGMENTS



The author would like to express his appreciation to his graduate


committee for their assistance during the course of thi


research.


Special


thanks are extended to Dr. H. D. Campbell, chairman of the author's super-

visory committee for providing guidance and encouragement throughout the


course of this work.


Dr. Campbell


many helpful comments and suggestions


have greatly aided the completion of this work


Thanks are also extended


to Dr. E. E


Carroll, Dr. R


. T. Schneider, and Dr.


L. Bailey who have


also served on the author's supervisory committee.

Special thanks are extended to Dr. M. J. Ohanian for the research and


teaching


assistantship opportunities presented which enabled the author


to pursue the doctorate.

The author's studies at the University of Florida have been supported,


in part, by a National


Science Foundation Traineeship and also by a one-


year Fellowship from the University of Florida and this support is grate-

fully acknowledged.

A large portion of the funds for the computer analysis were furnished

by the Northeast Regional Data Center on the University of Florida campus


through the College of Engineering.


difficult to obtain


Special thank


This help, though at times meager and


, is also acknowledged.

are due to Dr. N. J. Diaz without whose efforts and







Special thanks are also due to Dr. E.


T. Dugan whose knowledge of


computer analysis and nuclear reactor physics was of great


assistance


during much of thi


work.


In addition, thanks are extended to Mr


Maya for his aid with some of the plasma calculations and their impli


cations


of helpful


Thanks are also extended to Mr. B. G. Schnitzler for a number


consultations.


Finally, the author would like to extend his deepest appreciation to

his wife whose support and encouragement made it possible to complete this

work.














TABLE OF CONTENTS


?agfi


ACKNOWLEDGMENTS

LIST OF TABLES.

LIST OF FIGURES


ABSTRACT.


* a S S S S S S S S S S S S S S


S~~~ ~~ ~~~~~ 0 5 55 0 S S S S S S


CHAPTER


INTRODUCTION


Preliminary Concepts for Fusion-Fi
Review of Fusion Blanket Studies
Critical Review of Hybrid Blanket
Review of Controlled Thermonuclear
Stability Analyses .
Motivation for the Research. .
Summary of the Research. .


ssion Reactors


Studies.
Reactor


Thermal


* a a a a a
* S S S S S S
* S S S S S S S S S


THE PLASMA MODEL


Intro
The P
The L
Trans
Stabi


duction to
oint-Model
in ari 7PrH


fer F
lity


the Plasma
Plasma
P1 a~ ma Mnorl


Model


unction Representation of Plasma Character
Analysis of the Linearized Plasma Model.


istic


A HYBRID REACTOR ANALYTICAL MOD

Development of the Hybrid Model
Thp I inpAri pd Mvrid id Mndel


. . . . 116


S S S S a S S S S 5 116


Incorporation of Feedback Effects into the
Nonlinear and Linearized Hybrid Model Summ
Transfer Function Representation of the Hy
Stability Criteria for the Hybrid System

HYBRID PLASMA OPERATIONAL CONSIDERATIONS


. .
Hybr
ary.
brid


S . 1 31
id Model. 138
* 143
S . 147


* S S 5 5 5 1 60


* S S S S S S164.


T ~ ~ ~ L -l,, 4-, .4.,~, 3 4. 2 .I4. II 4 rl *'2f,... r-..


Irn







Diie


Uncontrolled Plasma Response to Perturbations.
Predicted Stability Versus Point-Model Response
Short-Term Plasma Transient Response .
Plasma Response With Feedback. .

HYBRID BLANKET ANALYSIS. .. . .


introduction .
lanket Calculations Using
homogeneous Diffusion Th
inetic Parameters
transport Theory Calculati
homogeneous Transport Th
ime-Dependent Blanket Con


or
ec
s-


* S S 181
.* S 196
.* S S 202
219


S258


25
Diffusion Theory . 26
3ry Calculations. . 30

ns. . 32
ory Calculations. . 34
iderations. . 34


CONCLUDING COMMENTS 356

Discussion and Conclusions . 356
Suggestions for Further Work . . 361


APPENDICES


GLOBAL


BLANKET


ENERGY MULTIPLICATION


HYBRID SYSTEM PHYSICAL CHARACTERISTIC


BURNUP AND
PLASMA


SENSITIVITY CONSIDERATIONS FOR THE HYBRID
S S S S S S S S 388


COMPUTER CODE DESCRIPTIONS


REFERENCES.


* 0 0 a a ..396


S S S S S S S S S S S S P S S S a S S S 4-1 1


BIOGRAPHICAL SKETCH


S 0 5 S S S P 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 4. 3


ec













LIST OF TABLES


Table


Paae


Fusion Reaction Parameters


1-II


, -III


Dependence of Tritium Breeding Ratios and Energy


Deposition Rates for Lee'


Summary Descriptions of ORN
Blanket Designs .


Fusion Blankets

L Ootimistic an


d Conservative


,-IV


Summary of


teiner's Tritium Breeding Calculations Per


Incident 14 MeV Neutron


Neutron Economy of Lidsky's Hybrid Blanket.


1-VI

1-VII


Lidsky'


Lee'


Hybrid Reactor Parameters.


Neutron Balance in Infinite Met


a S S


1-VIII


Subcritical Fast Fission Blanket Component


tudied by


Fast Fission Hybrid Neutron Economy Per 14 MeV Neutron
Calculated by Lee . .


Neutron Economy for Thorium-Fueled Blankets

Neutron Economy for Uranium-Fueled Blankets


1-XII


* S a *

* S a a a


Comparison of Best Natural Uranium-Fueled and Extrapo-
lated Thori um-Fueled Blankets . .


Earl


-XIV


y PNL Hybrid Neutron Balance.


y PNL Hybrid Specifications


PNL Hybrid Blanket Analysis


1-XVI


'-XVII


Critical Temperatures for D-T Fusion Reactors


Predicted Blanket Global Response per 14 MeV Neutron.


1-IX






Table

4-I


4-II


Page


Selected Spectrum of Equilibrium Operating Conditions
for the Hybrid Plasma With Constant Confinement. 173

Hybrid Plasma Equilibrium Operating Conditions for TEo
= 1.7 sec to Meet Required Power Production. ... 175


4-III


4-IV


4-V


Equilibrium Plasma Conditions Selected for Transient
Analysis With R = 2 and qPo = 1.41 x 1011 nts/cm3-se


c.


Final Uncontrolled Hybrid Plasma Equilibrium Conditions
Following a +5% Perturbation in the Temperature .

Final Uncontrolled Hybrid Plasma Equilibrium Conditions
Following a -5% Perturbation in the Temperature. .


. 178


.187


. 188


4-VI


Final Uncontrolled Hybrid Plasma Equilibrium Conditions
Following a 5% Step Increase in the Steady-State


Source Feedrate.


. . S . 0189


4-VII



4-VIII


4-IX


4-X



4-XI



4-XII


4-XIII


Final Uncontrolled Hybrid Plasma Equilibrium Conditions
Following a 5% Step Decrease in the Steady-State
Source Feedrate . . . .

Final Uncontrolled Hybrid Plasma Equilibrium Conditions
Following a +5% Perturbation in the Ion Density. .

Final Uncontrolled Hybrid Plasma Equilibrium Conditions
Following a -5% Perturbation in the Ion Density.

Final Uncontrolled Hybrid Plasma Equilibrium Conditions
Following a 5% Step Increase in the Steady-State
Injection Energy . .

Final Uncontrolled Hybrid Plasma Equilibrium Conditions
Following a 5% Step Decrease in the Steady-State
Injection Energy . . . .


Summary of Predicted Stabilization Requirements for
Instantaneous Temperature Feedback on the Feedrate

Comparison of Confinement Time Effects on Plasma
Temperature at 10 sec Following +5% Perturbation in
Feedrate versus +5% Perturbation in Temperature for
Six Hypothetical Hybrid Equilibrium States .


.190


. 191


. 192



. 193



. 194


. 197




. .218


Boundaries for Four-Group Critical i ty Calculation.


5-11


. 263


BRT-1 Cell-Smeared Thermal Constants for 1.35%
Fnrih Ped FIP. 264






Table


5-IV


Flux Dep
Lattices


ress


ion Factors for the 1.35% Enriched


Average Cros
Column. .


Sections for


23U and 238U in th


5-VI


Space Point Placement for BRT-1 Calculation Over Inner


Half of th


5-ViI


Hybrid Blanket.


Space Point Placement for BRT-1 Calculation Over Outer


Half of th
Refl sector


ssion Lattice and


nto the Graphit


VIII


Summary of PHROG Calculations by


Region


Resonance Region Scattering Cross
Nuclides. . . .


Sections


Four-Group, 13 Region Constants for 1
at 570K from BRT-1 and PHROG .


.35%


for Blanke


Enrichment


5-XI


PHROG-Generated Macroscopic Downscattering Cross


tions for 1.35% Enrichment, 5700K, and 1


Regions.


5-XII


Four-Group,


13-Region Constants for 1


.35%


Enrichment


at 9700K from BRT-1 and PHROG


5-XIII


PHROG-Generated Macroscopic Downscattering Cross


Sections for 1.35% Enrichment, 970K, and


5-XIV


Regions.


Results of Diffusion Theory Criticality Calculations.


Summary of Inhomogeneous CORA Calculations for
Variations in Enrichment and Temperature .


5-XVI


Yield Fractions for Si


Delayed Neutron Precursor


Groups.


5-XVII


Delayed Neutron Energy Spectrum Yield Fractions for
4-Group CORA Calculations . . .


5-XVIII


Blanket Kineti


Parameters


5-XIX


5-XX


Source Weighting Factors in Four Groups and Ten
Regions


Effectiveness of Uniform Volume Sources for Design
Power Level


Page






Table


5-XXIII


Effective Moderator Scattering Cros


Sections Per


Absorber Atom.


S S S S S S SS 5 327


5-XXIV


5-XXV


XXVI


Isotopi
NITAWL


Resonance Integra


Values Obtained from


SS SS S S S S S S S S SS S S 5 323


Hybrid Blanket Anal


S4 Quadrature Constants.


XSDRNPM 43-Group Energy Boundaries


330


S S S S S S S S 333


5-XXV II


XSDRNPM


Group and 11-Group Energy Boundari


. 335


XVIII


5-XXI


XSDRNPM 6-Group Cross Section Energy Boundari


XSDRNPM kef Results for a
edition at the Vacuum Wall.


* 337


Zero-Flux Boundary Con-
337


5-XXX


Transmission Ratio for 14 MeV Neutrons Through the


Hybrid Blanket


S S S S S S S S S S S S S S 34l6


Hybrid Blanket Equivalent Unit Cell Geometry


Fuel Column Spherical Micropartici


B -III


. . 375


Design Parameters.


377


Temperature-Independent Fuel-Pin-Averaged Nuclide


Number Density Variation with Enrichment


S. S 378


B-IV


Hybrid Blanket Shield Composition.


a S S S* S S 5 330


Helium and Natural Lithium Number Density Variation


with Temperature


B-VI


S S S S S S S S S S S S S S 381


Effects of Vacuum Wall Radius on Blanket Power


Requirements and Power Density


S. 5 S S S S S 384


Point-Model Comparison of Confinement Times and
Related Plasma Parameters in UWMAK-III and the Hybrid


Plasma


S S S S S S 5 5 5 5 S S S S S S 5 5 390


Page












LIST OF FIGURES


Figure


Page


The essential components of a Tokamak fusion reactor


Comparison of spatially-dependent heating rates for vacuum


wall regions in two designs .

Early PNL fusion-fission hybrid
configuration. . .


ubcritical blanket


Comparison of Lawson breakeven and plasma equilibrium


regions


Time variation of point-model plasma temperature and
density for constant confinement and charged particle
heating


Typical Lawson breakeven curve for a 50-50 D-T plasma and
33% overall efficiency showing relative position of hybrid
sys terns. . . . .


Predicted variation of blanket fusion neutron energy
multiplication with blanket effective neutron multi-
plication factor . .


Transfer function formulation for a point-model fusioning
plasma


Block diagram for the point-model plasma system.


Partially-reduced block diagram for the point-model
plasma system. . . .


Alternate block diagram for the point-model plasma system.

Partially-reduced block diagram for the alternate point-
model plasma system formulation. . . .

Reduced open-loop block diagram for the point-model plasma

Routh array for open-loop point model fusioning plasma


with burnuD


a a a a a a a - - - -






Figure


Page


Variation of F(T)


= nr with temperature


. .* .* 105


Block diagram for the point-model plasma with temperature


feedback to the feedrate.


.a.*.. . 5 ** 110


Block diagram schematic for point-model blanket kineti
retaining both source and reactivity perturbations .


cs
. 152


Block diagram of the
hybrid reactor model


inearized global fusion-fi


ssion


Partially-reduced hybrid block diagram with no artificial


feedback.


S S S S a S S S S S S S S S 5 156


Simplified reduced hybrid
artificial feedback


stem block diagram with no


Closed-loop block diagram for the linearized point-model


plasma with temperature feedback to the feedrate.


. . 159


Routh array for the cubic denominator for blanket effect


in the


overall hybrid transfer function


. . . 161


Equilibrium curves for various equilibrium plasma


conditions.


S S S U S S S S U S U S S SS U 174


Mills steady-state curves


including burnup for R


- 2.


. 180


Illustration of the feedforward effectiveness of the


feedrate and the injection energy on plasma
conditions and transient behavior .


Arbitrary equilibrium curve with a hypothetical


source


equilibrium
S . 184


stable


hybrid state at point A plus a possible equilibrium curve


containing a perturbed unstable


state at point B.


Variation of plasma temperature following a


step increase


in the temperature of the six hypothetical hybrid equilib-
ri um states . . .


Variation of plasma volumetric neutron production rate


following a


5% step increase in the temperature of the six


hypothetical hybrid equilibrium states.

Variation of plasma temperature following a


in the temperature of the si


rlum


step decrease


hypothetical hybrid equilib-


states


Variation of olasma volumetri


neutron production rate


S f f . 1541


200


o






Figure


Page


Variation of the heating rate in the first wall region of
the UMAK-III design. .


Variation of plasma temperature following a


step


crease


in the feedrates for the si


hypothetical hybrid


equilibrium states


Variation of plasma volumetri


following a


neutron production rate


step increase in the feedrates of the


hypothetical hybrid equilibrium states .

Variation of plasma temperature following a


decrease in the feedrates for the si


step


hypothetical hybrid


equilibrium states


Variation of plasma volumetri


following a


neutron production rate


step decrease in the feedrates for the six


hypothetical hybrid equilibrium states


Variation of plasma temperature following a


incr


ease


in the feedrate of an equilibrium


5% step
state at TE
-o


sec with delayed shutoff times


Variation of plasma volumetri


following a
equil ibrium
times.


neutron production rate


step increase in the feedrate of an


state at TEo
-o


sec with delayed shutoff


Variation of plasma temperature following a
increase in the feedrate of an equilibrium
1.7 sec with delayed shutoff times .


Variation of plasma volumetri


following a


5% step
state at TE
-o


neutron production rate


step increase in the feedrate of an


equilibrium state at TEo
ti mes


=117


sec with delayed shutoff


Variation of plasma temperature following a


crease


car (A'


step


in the feedrate of an equilibrium state at TE
444 rA/l c hnI nc Cki+n-FF + 0


3 C L l I LI I UC I UJ cU


.JU VI IULAJI U1111f


Variation of plasma volumetri


following a


neutron production rate


step increase in the feedrate of an


equilibrium state at Tr


sec with delayed shutoff


ti umes U

Variation of plasma temperature following a
decrease in the feedrate of an equilibrium
1 5 npr with dplavpd hutnff timp


5% step
state at TE
0


I I _ _







Figure

45. Variation of plasma temperature following a


decrease


in,' Ia


step


in the feedrate of an equilibrium state at TE
44h tin1- d l dr rk u4-nC 4-h-I f i


ace w e aye s uto f t mes


Variation of plasma volumetric neutron production rate


step decrease .in the feedrate of an


equilibrium state at rE_


- 1.7


sec with delayed shutoff


times. u

Variation of plasma temperature following a


decrease


CcaC I,!


5% step


in the feedrate of an equilibrium state at XE
S+fh aHol n aId ckh nff +4-mc o


.J'..t.. III LoE At. I UJ C 4 311U LAJ I II.IIC


Variation of plasma volumetric neutron production rate


fol lowina a
equilibri um
times.


step decrease in the feedrate of an


state at rEo
o


sec with delayed shutoff


Variation of plasma temperature with timperature feedback


following a 5%
1 c rr nt r'


step increase in the feedrate of the TE
i t l d l di;/-v/ h r' t4l rff f Ue o


sec equ r um s ate p us e aye s u o o


Variation of plasma temperature with temperature feedback


following a 5
1.7 sec equil


ih


step increase in the feedrate of the TE
v im cf+ nfine l aun chit+nt-Ff nC &R 0


P i uTi UL lui U3 U UU C 3IU3 IUV 4~IttI I 'U


Variation of plasma temperature with temperature feedback
following a 5% steo increase in the feedrate of the TE =
2.0 sec equilibrium state plus delayed shutoff of 6S .

Variation of plasma temperature with temperature feedback


following a 5
1.5 sec equil


ib


step decrease in the feedrate of the rt
rium state olus delayed shutoff of 6S


0


Variation of plasma temperature with temperature feedback


following a 5%
1 7 1 L


step decrease in the feedrate of the rE


1.7 sec equilibrium state plus delayed shu f


Variation of plasma temperature with temperature feedback


following a 5%


steo decrease in the feedrate of the TE
,1-,, -- .je o


2.0 sec equilibrium state plus delayed s f


Variation of plasma temperature with temperature feedback


following a 5%
1 -, *4 1 -1.


step decrease in the temperature of the Eo
*f a^ ***i r~* ^ ^'/ -


t~UL I et juI` I I u I .111 lLclLU


Variation of plasma temperature with temperature feedback


following a 5%
93


step increase in the temperature of the TEo


1 7 car annilibrium efate


following a


Page


r- ---J






Figure


Page


Variation of plasma temperature with temperature feedback


following a 5%
fl fl ^ ^. 1


step increase in the temperature of the TEo


2.0 sec equilibrium state.


Variation of plasma temperature with temperature feedback


following a 5%
r 1 L


step decrease in the temperature of the TE
U -o


c es e q u i l i b r i um s t a te.


Variation of plasma temperature with temperature feedback


following a
1.7 sec equ


step decrease in the temperature of the TEo
*o


m uirbili s t a t e.


Variation of plasma temperature with temperature feedback


following a
2.0 sec equ


5% step decrease in the temperature of the TE


bili r i u m s ta te.


Variation of plasma volumetric neutron production rate with


temperature feedback following a


step increase in


temperature of the TEo


= 1.5


sec equilibrium state


Variation of plasma volumetric neutron production rate with


temperature feedback following a


temperature of the XEo
0o


= 1.7


step increase in


sec equilibrium state


Variation of plasma volumetric neutron production rate with


temperature feedback following a


temperature of the rEo


step increase in


= 2.0 sec equilibrium state


Variation of plasma volumetric neutron production rate with


temperature feedback following a


step decrease in


temperature of the TEo


-'.5


sec equilibrium state


Variation of plasma volumetric neutron production rate with


temperature feedback following a


temperature of the TEo


step decrease in


= 1.7 sec equilibrium state


Variation of plasma volumetric neutron production rate with


temperature feedback following a


step decrease in


temperature of the TEo


= 2.0 sec equilibrium


state


BRT-1 thermal flux profiles across the equivalent unit cell


for 1


.35% enrichment at 290K, 5700K, and 9700K.


Typical paths for an unscattered neutron in an equivalent
unit cell and an actual unit cell of a nuclear reactor


BRT-1 thermal flux profiles across the inner half of the
hybrid blanket for 1.35% enrichment at 2900K, 570K, and
9700K with zero-flux vacuum wall boundary condition .


- "1 L-


*






Figure


Page


BRT-1 thermal flux profiles across the outer half of the
fission lattice out to 12 cm of graphite reflector for
1.35% enrichment and 2900K, 5700K, and 9700K .

Thermal flux profiles from BRT-1 calculations across the
outer 18 cm of graphite reflector and 30 cm of shield for
2900K, 5700K, and 9700K.


Four-group fundamental mode flux profiles from CORA for
the 1.35% enrichment at 2900K with zero-current vacuum
wall boundary condition. . . . .


Four-group fundamental mode flux profiles from CORA for
the 1.35% enrichment at 570K with zero-current vacuum
wall boundary condition. . .

Four-group fundamental mode flux profiles from CORA for
the 1.35% enrichment at 9700K with zero-current vacuum
wall boundary condition. . . . .

Four-group fundamental mode flux profiles from CORA for
the 1.35% enrichment at 9700K with zero-flux facuum wall


boundary condition


Variation of blanket effective neutron multiplication
factor with temperature for the 1.35% enrichment using
four-group diffusion theory. . . .


Four-group flux profiles from inhomogeneous CORA run
using group 1 surface source to generate 6500 MWth for
1.35% enrichment at 5700K. . .

Four-group flux profiles from inhomogeneous CORA run
using group 1 surface source to generate 6500 MWth for
1.35% enrichment at 9700K. . . .

Four-group flux profiles from inhomogeneous CORA run
using group 1 surface source to generate 6500 MWth for
1.50% enrichment at 570K. . . . .

Four-group flux profiles from inhomogeneous CORA run
using group 1 surface source to generate 6500 MWth for
1.50% enrichment at 9700K. . . .


Blanket power density variation for 6500 MWth for
enrichment at 5700K and 970K. . .


.35%


Blanket power density variation for 6500 MWth for 1.50
onrirhmpnnt at r700k ind Q700






Figure


Paqe
-.,,- .- -*..


Six-


group fundamental mode flux profile


from XSDRNPM for


1.35% enrichment at 9000K with zero-flux vacuum wall


boundary condition


Six-group flux profiles for a
10' nts/cmL-sec in group 1 t
enrichment and 900K .


surface source


of 1.336


o generate 6500 MWth at 1


x
.35%


Fractional transmit


on of 14 MeV neutrons through th


hybrid blanket


Power transient in th


hybrid blanket following a 5


step


increase in the neutron source for a forced-critical


sten


Hybrid blanket power transient derived for a subcritical


Conceptual Tokamak fusion-fission hybrid reactor


stem.


Overall hybrid blanket slab geometry used in neutronics
al culations


Selected PNL hybrid blanket module geometry for Tokamak
fusion-fission hybrid. . . .


Hybrid thermal fission lattice unit cell


Geometri


arrangement of the inner convertor with inner


breeder and outer breeder. . . . .

Reactivity and sensitivity variation with temperature for
the D-T fusion reaction. . . . .








Abstract of Dissertation Presented to the Graduate Council
of the University of Florida in Partial Fulfillment of the Requirements
for the Degree of Doctor of Philosophy


STEADY-STATE AND TIME-DEPENDENT BEHAVIOR OF
FUSION-FISSION HYBRID SYSTEMS

By


William G


. Vernetson


June 1979


Chairman:


Huah D. Campbell


Major Department:


Nuclear Engineering Sciences


study examined stability analysis of point-model systems repre-


sending pure fusioning plasmas as well as coupled fusion-fission


stems.


The stability criteria for these systems were derived for constant plasma

confinement conditions based on engineering perturbations of the system


feedrate.


The result


of linearized point-model plasma stability anal


ysis


of the thermal instability were shown to be applicable to hybrid plasmas

and to be attainable from considerations of engineering-related per-


turbations in the extrinsi


plasma feedrate variabi


A Tokamak fusion-fi


ssion hybrid design was


ected for further,


more specific analy


sis.


The modeled hybrid system in linearized form was


found to be stable provided certain hybrid plasma temperature and con-


finement time limits are met.

absolute stability is not suf


However, for realistic installations,


'ficient; nor is it guaranteed by linearized


anal


ysis.


Therefore, hybrid plasma behavior was examined under transient


and overpower conditions.


Time-dependent analysis


of a low reactivity hybrid plasma (8 keV






with perturbations to pure fusion plasmas with high plasma reactivity.


In addition


, the predictions of plasma stability ranges were verified


for various confinement times.


transients following -


The slowly developing hybrid plasma


temperature or feedrate perturbations were


found to be significant for the control of the power-producing hybrid.


Neutrons and their


associated energy are multiplied in hybrid


blank


ets;


therefore, the global equation in use to relate the blanket


energy deposition per fusion neutron to the blanket effect


multiplication factor was investigated.


indicate the oloba


neutron


Results were obtained which


approach supplies a poor estimate of blanket energy


multiplication for a fusion neutron source and an even poorer


estimate


for fission energy neutrons.


Although results


showed the blanket energy deposition per fusion


neutron to be some


below point-model predictions, the


selected blanket


is still a significant multiplier, by a factor of


25 or more, of th


neutron energy entering the blanket via fusion neutrons.


The documenta-


tion of the reduced worth of fusion neutrons, entering the blanket through

a convertor region, may be a significant factor in redesigning vacuum


wall


of hybrid reactors despite the advantages of reduced 14 MeV wall


loadings.


Diffusion theory and di


screte ordinates transport theory anal


ysis


were both applied to establish the relative importance of the inner con-


vertor region for power generation.


The results of the


calculation were used to determine the source


size


transport


required by volume


equivalence with the Tokamak geometry to produce 6500 MWth in the blanket.

The source value was used to establish the steady-state requirements on






Tokamak hybrid plasma volume involved.


In addition, the


calculation


was used to show that only about 6% of the 14 MeV fusion neutrons reach


the thermal fission latti


without a collision


These transmission


results indicate graphically why the blanket is less effective at energy


multiplication than

Finally, space


expected from previous reports.


-time kinetics calculations were performed on the


blanket to demonstrate the fast response of the blanket in keeping with


its millisecond prompt neutron lifetimes and subcriticality


Al though


no time-dependent feedback effects were examined, the speed of response

of the system was determined for typical transients and some character-

istics for hybrid operational controllability were established.












CHAPTER 1

INTRODUCTION


Preliminary Concepts for Fusion-Fission Reactors


The fusion-fission hybrid reactor concept is a combination of a


sub-Lawson


fusion reactor and a subcritical


ssion


reactor in a single


power-producing system.


Fiss


ion reactors are


"power rich" but


"neutron


poor," while anticipated D-T


fusion reactors will


"neutron rich" but


"power poor.


these


Hence,


two systems to u


the essential

se excess fus


hybrid feature


the combination of


;ion neutrons to breed fissil


fuel


while simultaneous


y sustaining and driving the


sys ten


for useful


power er


using fission energy multiplication of the fusion neutron source


~.ne rg:


Limited studies


, concentrating on blanket neutronics


have been


done on hybrid system


in parallel with pure fusion blan


t work


how-


ever


, no system dynamics or stability investigations


have been reported


for hybrids


Some research effort ha


been devoted to global


stability


anal


of th


plasma


in pure fusion device


present research


extends such pure fusion time-dependent studies


into the area of hybrid


systems.


continued development of the hybrid in parallel


with the


fast breeder reactor is supported by the hybrid's potential a


alternate and attainable energy and fuel


producing concept.


In fact,




-2-


Much research effort and capital investment have been committed to

the realization of a mixed burner-breeder nuclear reactor economy planned


for the end of this century.


This effort is justified by


expected con-


tinued growth of energy needs


sumption of fossil fuel


within the past few deca


des.


and by a marked shift from direct con-


secondary consumption of electrical energy


With the growth in nuclear generating capacity


limited fissil


fuel


reserves have caused the thrust of research and deve


opment in the


nuclear industry to shift to the fast breeder reactor


LHFBR)


Even with


the projected impact of the commercial LMFBR sometime after 1


siderabl


0, con-


additional enriching capacity and capital investment will be


required for fueling burner reactors.

Current emphasis on the safety and the environmental impact of


nuclear generating faci liti


as well


as certain technological and


political objection


make it increasingly unlikely that high gain breeder


reactors will make


a significant


rmpact prior to the mid-1990


s or later.


Even if the breeder i


introduced sooner, the relatively lono doubling


times under consideration (1


years or more


may not be adequate for


generation of sufficient additional fuel to support an


reactor economy


existing burner


IWith so much effort and capital investment committed


to the realization of the mixed burner-breeder economy planned for the

1990's, the availability of an effective alternate concept to produce


fissil


fuel


could be important.


One candidate for producing fissile fuel is the controlled thermo-


nuclear reactor utilizing the D-T cycl


C1


e. Deuterium resources are virtu-
7







fusion neutrons can be used to breed fissile material.


By diverting


neutrons from tritium production, the tritium supply can be maintained


reasonable


averted to fissi


evel while fertile

reactor fuel.


materials (238U and Th) are con-


Unfortunately the realization of pure


fusion power is too far removed and uncertain to be counted upon to pro-


duce fissil


fuel in the near term.


The alternative concept currently receiving renewed attention is the


coupled fusion-fission hybrid system combining a less than


self-sustaining


(energy) fusion reactor with a subcritical but power producing fission


reactor.


Although achievement of pure fusion power i


not yet possible,


recent advances indicate the plasma requirements for hybrids will be


reached while the fission power component of the


still increasing.


electrical economy i


9
Then, as an alternative to the LMFBR for fi


and power production, the hybrid can be very useful

The hybrid concept has many potential advantages over the LMFBR for


providing power and fissile fuel in the latter part of thi


century.


First, the hybrid reactor


possesses


great potential as a breeder of


fissil

be abl


fuel.


With its abundant supply of neutrons, the hybrid should


to produce fissil


material more rapidly than any of the current


breeder reactor concepts to keep pace with power requirements.


Second, the hybrid makes an alternative fuel cycle available for


existing burner reactors.


Reliance on the


U-239Pu fuel cycle with its


weapons grade plutonium can be reduced in favor of the


233U fue


cycle.


Third


, hybrid development allows early introduction of fusion


232Th_




-4-


hybrid system, current advanced reactor technology would require only

modest extensions to produce a hybrid system as a natural link in the


development leading from pure fission to pure fusion power.


Finally, the hybrid concept using


from a safety standpoint


subcritical blankets is attractive


since it would diminish the need for critical


nuclear reactors.


4.10


The current concern over reactor safety and


core meltdown could b


essentially eliminated.11


Past

hybrid ana


studies of the hybrid concept have been restrictive.


1


yses


Typical


limited to steady-state evaluation of the technical


characteristics of a concept with emphasis on the


neutron economy of the


conceptual blanket.


-3,12-14


Important features in such hybrid studies


parallel ordinary fusion reactor blanket


studies and include:


Tritium conversion ratio and doubling time.

Fissile breeding ratio and doubling time.

Energy production and multiplication in the blanket


Constraint


on the fusion plasma due to neutronics.


5. Vacuum wall loading and neutron energy transport.

The neutron economy and energy multiplication of the hybrid blanket


have been of primary interest in these initial studio


by fission events


both are enhanced


Little consideration has been given the fusioning


plasma in these hybrid designs beyond setting plasma characteristics


necessary to achieve the assumed blanket power performance.


Basic fusion


reactor blanket studies and hybrid blanket work to date are reviewed in


the next


section; the similarity of the two


remarkable despite the


increased importance of energy production in hybrid blankets.








factor, keff, less than unity)


as well


blanket, no time-dependent analysis


as the heat generation rates in the


has been considered; dynami


behavior


and associated safety of the hybrid fusion-fission system have been


ignored.


The effects of perturbations on the coupled system have also


been ignored.


Some studies on safety and control analysis


of pure fusion reactors


have been reported.1


5-24


Mills'


described the stability requirements


on a


state


teady-state,

(equilibrium


point model, fusioning plasma, and found the steady-


plasma unstable against various parameter fluctua-


tions below a critical


ion temperature.


The effects of artificial feed-


back were


simulated at lower temperatures to control this thermal


instability and maintain equilibrium operation below the critical


temperature.


The work of Mill


is a benchmark work in fusioning plasma


global dynamics and control


work on stability by


Ohta et al


18
is one of the most complete


thermal stability


studi


of point model thermonuclear plasmas.


Stability


criteria were established using linear analysis


energy balance plasma equations.


of coupled particle and


The thermal instability was evaluated


and suitable feedback control was implemented to allow stable operation

below the critical plasma temperature set by the stability criteria.


Stacey


as well as Usher and Campbell23'24 have reported extensions of


this work to more


sophisticated plasma model


Yamato et al


19,20 have
have


extended such stability studies to simpi


comparable e


i homogeneous plasmas with


results.


Since such time-dependent analysis was neglected in previous hybrid







of fusion energy blanket multiplication not previously considered.


much larger hybrid blanket energy multiplication demands a coupled time-


dependent analysis


establishment of specific safety and operating


character ri


stics


for a


coupled hybrid system is


necessary


for the con-


tinued development of the


concept into a viable energy alternative.


The effect of thermal instabilities in the fusioning plasma on the

fissioning blanket are analyzed in this work to establish hybrid system


interactions,

deficiency in


safety, and ea


existing studies


of control

of hybrid


This work


systems


eliminates a major


so that a decision can


be made on its pi


ace


in the power industry of this country in the last


decades of this century.



Review of Fusion Blanket Studies


The Fusion Process


Since hybrids depend on fusion neutrons to breed fissile fuel, at

least two fusion reactions have potential for use in a hybrid reactor.


These


are the deuterium-tritium and the deuterium-deuterium reactions


which have the following balances:


2 3D+
D + ,T
~1 1


He (3.52) + n (14
He (3.52) + n (14.06)
2 0


e (0.82) +
2He (0.82) + n (2.45)


(1 .01


+ p (3.03)


where the two D-D branches have nearly equal probabilities at energies


2 3
D D
1







The properties of the D-T fusion reaction are far superior to those


of the D-D reaction.


For energies below 200 keV the D-T reaction cross


section with its broad resonance at 110 keV i


nearly two orders of


magnitude above the D-D


cross


sections.


The probabili


for a fusion


reaction occurring i


characterized by the reactivity or rate coefficient,





, which i


an average of the product of the cross section


for the


fusion reaction in question and the relative speed


, v, of the reactants.


The reactivity can usually be approximated using a Maxwellian distribu-


tion of particle speeds.


With a broad resonance around 65 keV


the D-T


reaction rate coefficient i


much greater than the D-D reaction rate


coefficient below 100 keV


Finally


, the energy released per fusion reaction, QF


, is signifi-


cantly higher for D-T fusion events.


These comparative values are


summarized in Tabl


e -I25


and indicate why near term fusion reactors and


hence hybrids are limited to the D-T fuel cycle.



Table 1-I

Fusion Reaction Parameters


o (barns) (cm3/sec) Q (MeV
Reaction at 100 keV at 65 keV F '


0.46


x 10-16

x 10-15


3.65


17.6


As noted in Eq


1), the 17.6 MeV per D-T fusion reaction is divided




-8-


plasma, but the 14.06 MeV of neutron energy must be recovered in surround-

ing blanket regions.



Fusion Reactor Blanket Studies


Since only limited quantities of tritium occur in nature, sufficient

tritium must be generated through nuclear reactions to refuel operating


fusion devi


ces.


The 14.06 MeV fusion neutrons are used for this purpose


in two lithium reactions:


6
Li +
3


1
n (slow)


SHe + T3 + 4.8 MeV
2 1T


3Li + On (fast)


4He+?T+


- 2.82


where natural lithium has the composition:


7.56%


6Li and


92.44%


The exothermic reaction has a


thermi


2.9 b resonance at 0.25 MeV while


reaction, with its threshold at


the endo-


has a 450 mb resonance


at 8


.0 MleV.


For the usual toroidal fusion reactor using

for the magnetic confinement, the position of thj


superconducting coils


blanket used for heat


recovery and tritium generation is illustrated in Fig. 1.


This con-


figuration conforms to the Tokamak designs most often considered for


economic, power-producing fusion machines.


27-33


Refractory metals such


as vanadium, molybdenum, and niobium are usually postulated


as the vacuum


and structural material due to the hiqh heat and stress load as well


as the need for (n,2n) reactions to enhance tritium breeding


raphi te





-9-











































C-,

a)


LI




w Ad


o o c C


o Co -
(3 0
I-


0

4-,
a





a
E
0


C-)



a)
LI




E-



I-

1,

a)
I.-




-10-


tritium breeding are confined to the inner reflector/moderator regions

of the overall blanket, the outer regions shield the low temperature

superconducting magnets from the deposition of energy by high energy


particle


generated within the fusioning plasma and inner blanket region.


A typical thickness for the


total heat recovery and


shielding regions of


the blan


about two (2) meters with actual heat recovery and tritium


production confined to the first meter.


Many early studies were conducted to evaluate tritium breeding and


heat generation in idealized fusion blankets.


These initial studies in-


dictated that adequate tritium generation was possible but with severe


heat transfer requirements on the vacuum wall


This problem was partly


due to the fact that only the exothermic lithium reaction was known and


used in the earliest studi


Myers et a


>11


used diffusion theory to examine homogeneous cylin-


drica


blan


ts of varying thicknes


from 9 to 96 cm


Material


tested


included a lithium beryllium-fluoride

natural lithium metal and 6Li metal.


salt (LiF + BeF2) called "flibe,"

All but 6Li provided adequate


tritium breeding ratios above 1.45; the value of only 0.976 for "L

demonstrated the potential significance of 7Li breeding reactions.


Impink


and Homeyer


also examined the effects of blanket composi-


tion on tritium breeding and on spatial heating rates


, respectively


Graphite was used


the neutron moderator with molybdenum


as the vacuum


wall material because of its neutronic and refractory characteristic


The flibe coolant and tritium generation medium was

electromagnetic resistance to coolant circulation.


ected to avoid


For variations in





-11-


Since nuclear heating rate calculations showed extreme peaking near


the first wall based on 14 MieV neutron energy flux of only


MW/m


on the


vacuum wall, Homeyer concluded that cooling of the vacuum wall would be


most


severe heat removal problem in the blanket.


blanket energy was


calculated to be


The recoverable


17.4 MeV oer entering 14-MeV neutron.


used multigroup transport calculations to analyze an infinite


annular blanket and concluded that pure lithium is an attractive breeding

material but requires a thicker blanket than one containing beryllium.


Unfortunately beryllium is probably too


expensive to justify its large


volume usage in systems of the si


of power-producing fusion devi


ces.


Realistic blanket designs required more detailed neutron


studies


to consider structural and heat generation requirements as well as the


tradeoff between tritium breeding and energy generation


as shown in more


S8,27,38-43
recent, detailed calculations. '


used Monte Carlo theory to calculate neutronics results for


a three zone


spherical annular blanket with outer radii of


302 cm for a 100 cm radius plasma.


Structural effects were simulated


by homogeneous volume fractions of niobium chosen for its refractory,


fabricating, and welding characteristic


exce


llent results were obtained


for a structureless lithium blanket.


simulated by making Zone


in Zones


More realistic blankets were


(1 cm) all niobium and diluting the lithium


and 4 with increasing volume fractions of niobium structure.


Lee's results are


summarized in Table 1-II where the increase in energy


generation per fusion event i


due to Nb(n,y) reactions


Since


enrichment was found to be ineffective and only


5 to 6% niobium is




-12-


Electromagnetic resistance to lithium flow may


excessive


near the


vacuum wall where high coolant velocity


are needed.


Induced


currents


in the lithium act to retard lithium flow across magnetic field lines;


but such resistance


great


reduced in the outer blanket regions where


heating rates and hence flow rates are reduced.


Tabl


1 -Il


Dependence of Tritium Breeding Ratios and Energy Deposition


Rates for Lee'


Fusion Blank


Nb (Volume Per Cent)


QB (MeV)


1 .38
1.16
1.00


19.60
20.20
20.50


Steiner8'39


analyzed the neutronic behavior of two designs based on


the ORNL standard blanket configuration containing niobium structure,


coolant, and graphite reflector.


optimistic (D


These two blankets reflected an


esign 1) and a conservative (Design 2) outlook on the problem


cooling the


vacuum wall


Design 1 contained lithium throughout the


blanket


Design


assumed that flibe must be used to cool th


vacuum wall


with lithium elsewhere.


Steiner rejected flibe coolant throughout the


blanket since


it produced an inadequate


= 0.95) tritium breeding


ratio.


Neutron activation problems were also first revealed by Steiner.


Niobium was selected over molybdenum as the vacuum wall and struc-




-13-


lower sputtering ratio despite molybdenum's demonstrated


superiority for tritium breeding.

reflector in both designs. Summa


with


typical


Graphite was employed as the moderator/


ry descriptions of these two blankets


niobium structure are presented in Table 1-III to indicate


blanket model


Table


1-I''


Summary Descriptions of ORNL Optimistic (1) and Conservative (2)
Blanket Designs


Region
Number


Description
of Region


Thickness
by Region


Volume Composition by Region


Design 1


Design


Coolant


94% Li


94% Flibe


Structure


6% Nb


Second wall


Coolant


94% Li


94% Li


60.0


Structure


6% Nb


Moderator-
reflector


30.0


Gra white


Graphite


Coolant


94% Li


94% Li


Structure


6% Nb


The basic 100 cm Design 1 blanket with first wall at 200 cm radius
2A' n n + O rl a c *h n c+anA hl n n\ a* mn^al 3-a +ka MIa tI rn nar r c Zncc in c F


as well







44
National Laboratory (ORNL) in June 1971. This blanket has been frequently

used to check neutronics calculations.

Transport theory-was applied in slab geometry to obtain the tritium


breeding results listed in Tab


1-IV where the breeding ratio of 1.35 in


Design


is some 10% above the 1


value for Design


Slab geometry is


adequa


to th


large plasma radii


meters) for steady-state


fusion reactors.


33,45


Tabl


e 1-IV


Summary of Steiner's Tritium Breeding Calculations per Incident
14 MeV Neutron


Design T/n Neutron Leakage


0.023

0.020


If hypothesized low levels of tritium holdup


46,47


are realized, then


breeding rati


only slightly


above unity


.01) will be sufficient for


seven year doubling times.


Therefore, Steiner


s relatively low 1


breeding ratio i


sufficient to obtain the one month doubling time to


establish initial tritium inventories.


Steiner'


results for spatially dependent, nuclear-heating rates


were


based on a standard first wall energy transport of 10 MW/mn


due to


the 14 MeV neutron flux


Extreme peaking of nuclear-heating rates was


I,,,, :, 1,, ,, S


-n 4: n 4


-J


f


n,,:,, 1





-15-


---- DESIGN 1 (STEINER)


DESIGN


(STEINER)


170-

160 -

150 -

140-

1 30 -

1 20-


110-1



90-

80-

70-

60-

50

40-

30-


FIRST WALL


SECOND WALL


COOLANT & STRUCTURE


-- -


Distance from Vacuum iWal (cm


Figure


Comparison of


spatially-dependent heating rates for vacuum wall


*


200 -




-16-

heating rate peak at the vacuum wall will be 5-10% more extreme than in-


dicated


These extreme heating rates (power densities) near the first wall


along with the


excess


ve fusion neutron wall loading represent a major


technological problem for all Tokamak fusion power reactors.30,33,47


Steiner'


work


supported previous work


indicating that blankets employ-


ing lithium


the only coolant are superior to those employing flibe since:


Design 1 has a 10


higher tritium breeding ratio.


Design
since


has a 50


lower heat load in the niobium vacuum walls


high gamma cross section of flibe has been removed.


Neutron irradiation effects within the vacuum wall are essen-


tially the same in both designs along with


rates nea


excess


ive heating


r the first wall.


Blow et al.40 used Monte Carlo calculations in cylindrical geometry

with first wall at 150 cm to examine Steiner's two basic 100 cm thick


blanket model


with varying (


2-8%)


niobium structural content.


Good


breeding rati


cl usive


1.15-1.54) were reported for all


use of flibe


cases


except the


coolant in the entire blanket where T/n


= 1.027.


Blow reported additional good breeding results (T/n


= 1.58) for blankets


of Design


where niobium was replaced with


molybdenum.


Examination


of molybdenum was justified because the


Mo) has the neutronic characteristic


characteristics


alloy TZM (0


of pure molybdenum but welding


similar to niobium.


A modular blanket design using heat pipes has been proposed by


Werner et al


in which neutron


behavior was examined in a 100 cm


thick cylindrical annulus with 200 cm inside diameter.


n relocating the


"standard" vacuum wall of a thermonuclear reactor beyond the neutron-


moderatina. enerov-convertina blanket (at 320 cm). the entire moderator




-17-


to eliminate the neutronic losses and structural buckling problems of

previous designs.

The interlocking modular blanket units incorporated heat pipes which

remove radiant energy from the inner module surface and flatten the power


distribution in the blanket by moving


excess


energy outward to power-


deficient zones


WJerner's blanket model contained beryllium for neutron multiolica-


tion


, lithium for tritium breeding, sodium for energy generation


niobium for structural strength.


The 100 cm moderator section of the


blanket was divided into two zones


Zone 1 contained


Li and


wh i e


Zone


contained varying volume percentages of Be, Na, and Li


Both


zones contained


% 20%


volume for heat pipe voids.


Zone 1 was used to


buffer the energy density in the fluid so that all nuclear and radiant

heating energy could be removed by convective heat-transfer through the


heat pi

densiti

Thi


resulting in power flattening and increased average power


tradeoff between tritium breeding and energy multiplication


through use of beryllium or

tions in a 90 cm thick Zone


neutron up to


odium was examined for varying volume frac-


Increased energy generation per fusion


.0 MeV for beryllium and 26.05 MeV for sodium was obtained


but with a reduction in the tritium breeding ratio.


Unless maximum energy


is very important, Werner recommended maintenance of tritium breeding--

probably because of beryllium costs and sodium activation.


Struve and Tsoulfanidi


used Monte Carlo methods to calculate


tritium breeding ratios and heating rates for two proposed blanket designs





-18-


The two blanket configurations included a basic Steiner-type

the vacuum wall surrounds the plasma and a Werner-type where the


where


vacuum


wall surrounds the blanket.


To avoi


the problem of


coolant flow,


Struve proposed a heat transfer fluid such


as helium which would be un-


affected by magnetic field lines and transparent to neutron


It was


simulated by


volume void in the lithium.


Breeding ratios


above


were obtained and agreed


areas


onably


well with previous blanket


studio


using niobium structure.


8,40,42


The use of helium


as a fusion blanket


coolant has


been


investigated by Hopkins and Mlelese-d'Hosoital and


others at Genera


patiall


Atomic Company.31


dependent nuclear-heating rates for the two blankets


showed high vacuum wall heating and agreed with previous results.


Steiner's


generally


higher calculated heating rates


were


caused by niobium blanket


structure.

These detailed neutronic studies of fusion blankets indicate ample


tritium breeding


possible in realistic blankets.


The inability to


breed tritium is not a problem in fusion designs


The real problems in-


clude providing adequate heat removal for the first wall and protecting

and designing the vacuum wall to withstand the required 15 MeV neutron


fluxes.


These fusion reactor blanket


scoping studies have formed the basis


for a number of design studies for Tokamak fusion power reactors of


either full commercial scale or demonstration


size


28-32


various


oure fusion Tokamak blankets use either flibe, natural lithium


as coolant and flibe, natural lithium, or


or hel ium


ome lithium-bearing medium




-19-


of flibe.


All blankets are on the order of 100 cm thick and some


20-25


MeV are deposited in the blanket per 14 MeV neutron entering the blanket


with extreme peaking of heating rates near the first wall


are not expected then to be


The blankets


significantly energy multiplying.


In genera


the tendency i


toward more compact fusioning plasmas with


an associated reduction in the first wall neutron flux to well below 10


NiH~/r


of 14 lMeV neutron energy transport.


28-33


The basis for such reduc-


tions is the extreme technological problems of designing a first wall


which will function for at least two years or more.


If such cannot be


accomplished, then fusion power plants that are viable in other respects


are likely to be


too limited in outage maintenance


time to compete


economically


with other


electrical power sources.


33,49


Critical Review of Hybrid Blanket Studies


Overview of Hybrid Blanket Studies


Fusion blanket designs attempt to maximize energy generation while


maintaining the tritium breeding ratio.


The inclusion of fissionable


materials in the blanket is an obvious possibility for achieving signifi-


cant power and neutron multiplication.


Such a hybrid blanket must still


meet the basic fusion blanket requirements of adequate tritium breeding,

heat transfer, and magnet shielding as well as produce energy multipli-


cation and/or fissile material


As with pure fusion systems,


previous


evaluations of hybrid concepts have been based primarily on the cal-

culated neutronic behavior of the conceptual blanket as reflected in the




-20-



Fusion plasma characteristics.

Neutron first wall loading.


The tritium breeding ratio must be


sufficient to refuel operating


hybrid


systems


and fuel new on


As for pure fusion


systems, adequate


values are in the range T/n


- 1.1


and are relatively


y easy


obtain.


Simultaneously, a hybrid may also be required to produce or


even breed significant amounts of fissile fuel


,3,6


Energy deposition in the blanket per fusion event i


a very important


hybrid criterion.


Usually


D-T fusion


systems assume a blanket energy


deposition, QB

neutron and th


of about 20 MeV per fusion to account for the 14.1 MeV


MeV per


6)3T reaction.
Li(n, a) T reaction.


Fusion blanket studies


show thi

position


energy deposition is relatively insensitive to design or com-


with calculated values per fusion neutron ranging from a


maximum of


26 MeV for Werner's41 best design down to 18.


MeV evaluated


by Leonard


for the ORNL standard design.


Although fusion blankets are limited in their energy multiplication


capabil iti


this is not the


case


for hybrids which are evaluated for


significantly increased blanket energy deposition per fusion event


through fission energy multiplication.


Interest in subsystem interactions


and dynamics studies of such a coupled hybrid system is certainly justi-

fied when the potential for energy generation through energy multiplication


in the


subcritical blanket i


considered.


The third area of technical assessment of hybrids involve


fusion plasma characteristics


required to achieve the assumed blanket


Th' ic fnr nm a ic cc cm n cmn+t da c iro-l ma i-n f-ho hin.nL'ot onnn nv/


nn rf:n mi ~ n r a




-21-


to reach overall breakeven in energy production or scientific breakeven.

The breakeven nT-value varies inversely with the total energy generated


per fusion event.


Therefore


, the potential value of a hybrid system is


characterized by its ability to relax the Lawson condition through effec-


fission increase of energy released per fusion event.


Finally


, the required transport of neutron energy through the fi


vacuum wall


an important figure of merit.


Previous projections of 10


MW/m


impose


stringent material problems so more recent designs attempt


to achi


eve


val 1 loadings in the range 0.25 to


MW/m


1,3,13


hybrid relaxation of first wall


pure fusion


oadings is a technical advantage over


systems


Such potential for breeding fissile fuel with fission energy multi-


plication of the fusion neutron source


strength to sustain and drive the


coupled


stem h


been examined by many researchers.


Early concepts


were summarized adequately by Leonard and have little more than historical

significance.1



Lontai Attenuator Model


The first detailed calculations on the neutron economy of hybrid


blankets


were


performed by Lontai in 1965.10


He assumed a


steady-state,


D-T clyindrical plasma with a 5.0 MW/m


energy transport of 14 MeV


neutrons but performed the neutron balance calculations for an infinite


slab source geometry.


Lontai's results were based on blanket configura-


tions using flibe coolant channelled in a graphite matri


Neutron


iI *





-22-


ratios


Such a


scope of study and results reported set the stage for


most of the hybrid studi


Lontai


which followed.


s best results were reported for a blanket concept consisting


of a


cm molybdenum vacuum wall


, 1.5 cm coolant (flibe) region, and 49 cm


attenuator region containing 21


graphite by volume with 70


salt bearing


uranium (LiF


- BeF2


- UF4)


natural lithium


case


had insufficient


tritium breeding.


Adequate tritium breeding was calculated only by using


lithium


salt enriched to 50% Li and varying composition.


The fi


ssion


energy multiplication increased by nearly a factor of two over non-fissile


blankets with better heat transfer characteristics.


Similar calculations


for 90% enriched 6Li resulted in much lower fissile fuel production with no


increase in energy multiplication.


Plasma requirements are not relaxed much


by such small amounts of fission energy deposition; however, Lontai opti-


mistically labeled th


6Li attenuator practical because of possible


reduced plant


Lontai'


capital


costs


hybrid feasibility


study currently has little more than


historical


significance because of inherent deficiencies:


Faiure to consider values of plutonium production.


Failure to consider cost of maintaining high


6Li enrichment.


Failure to


consider


U present in depleted uranium.


Use of obsolete computer


Lidsky


codes and poor cross section data.


Symbiosis Concept


A novel approach to the fusion-fission hybrid concept was proposed


-* .a I- *tJ- b j. S




-23-


feature of this symbioti


tritium and fissile nuclei


device such


scheme was a fusion system breeding sufficient

to fuel itself and a power-producing fission


as an MSCR.


A cylindrical


m radius torus of D-T plasma


was used in the


symbiosi


The basi


duplex blanket configuration contained a thorium-


bearing blanket fl i be


salt composed of LiF


:SeF2:


ThF4 in the ratio


71:0O


2:27


and lithium depleted in


Th


neutron


properties of pure


molybdenum with


ts large Mo(n,2n) cross section, were utilized in the


TZM structural alloy


Since Lidsky'


s fusion reactor was designed for


, not power production, a graphi


moderating region was used to


prevent thorium fission products from poisoning the blanket during opera-


tion.


only


p055


ibie at initial operation until fissile


233 is
U ls


produced which impli


which Lidsky ignored.


frequent refueling and possible cost penalties


Lidsky used SN transport theory to evaluate the


neutron


this


economy of th


hybrid blanket configuration


as well as variations in the base design are


results for


shown i n Tabi


,-V.


Since


simultaneous production of fissile nuclei and tritium


be attainable


system can be


over a range of production ratios


optimi


found to


each component of the


for power or fuel production to utilize the strong


points of both fusion reactors (neutron rich) and fission reactors (power

rich).


The reactors in the symbiosi


were coupled by the production of fuel


for th


ssion reactor by the fusion reactors


Lidsky6


also analyzed


equations for the time dependence of the fuel inventori


of the two


rPacrtnrR in thp fuiinn-nficinn




-24-


Tabi


Neutron Economy of Lidsky' s Hybrid Blanket


Events per 14-neV Source Neutron


Calcul ated


Range


Tritium production


Thori u
Total


captu


covers


1.126
0.325
1.451


0.05-0.50


2 1.40


Lidsky


results demonstrated that the fuel doubling time of such a


balanced hybrid


system


determined entirely by the neutron-rich fusion


reactor component.


Lidsky


power production analysis


indicated further


that the net


power production in such a dual system i


determined pri-


marily by the fission reactor component since the fusion power reactor


is onl


y a small perturbation on the net power


r of real


systems.


Thus each


symbiosis can theoretically be optimized for its


respective primary purpose of fuel or power production. T

important point to remember with respect to hybrid reactor


Lidsky


his i


system design.


selected a CTR-MSCR power plant with 1500 MWe output and a


10 year doubling time for symbiosis study


MSCR was rated at 4450


14JMWth with a fuel conversion ratio of 0.96 operating on the


cle.


Lidsky calculated a 10 year fissile doubling time with a tritium


linear fuel doubling time of 0.113


years.


For a 40% thermodynanmi


efficiency the fusion reactor would be a net consumer of


the overall


MWe while


stem was calculated to be able to provide 1690 fWe net


subsystem in


233U_23~Th





-25-


Required plasma characteristics were encouraging since the vacuum

wall loading due to 14 IMeV neutrons was only 1.00 MW/m --well below that


necessary to assure technological feasibility in pure fusion plants


In addition, there was no energy multiplication in the fusion reactor

blanket of the symbiotic scheme; this assumption was clearly not accurate


as soon


as some fissile fuel breeding has occurred.


Plasma parameters


are near Lawson conditions as indicated by the hybrid parameters summary


in Table 1-VI and the fact that only


MWth was required to support


the fuel-producing fusion system.



Table 1-VI


Lidsky


Hybrid Reactor Parameters


= 1014 ions/cm


= 0.625


sec


0 keV


Wall loading
233
U production


=1 MIW/r


= 1.1 kg/day


The symbiosis has a number of advantages.


simplify


First, this scheme


construction of power plants capable of breeding and


processing all requisite fuel in situ.


Second


, the lessening of fuel


cost constraints makes the modifications of existing reactors possible

to avoid thermal pollution. Finally, by developing this concept, the




-26-


In addition to the symbiotic hybrid concept and the usual power-

producing hybrid concept, Lidsky has also formalized consideration of a


third hybrid concept called the augean concept.


concept involves


using the hybrid blanket to burn the actinide waste from fission


reactors.


augean concept is of little interest for dynamic


consideration.



Lee's Fast Fission Hybrid Concept


eliminated Lidsky'


separate fusion and fission reactors in


favor of the so-called subcritical fast fission blanket.


Monte Carlo


Transport theory was used to perform neutron balance calculations in


infinite media of pure thorium, pure

the breeding potential of hybrid blan

1-VII are in good agreement with expe


Weal


238U, and natural uranium to verify

kets. The results shown in Table


measurements done by


51
et al


Table 1-VII

Lee's Neutron Balance in Infinite Media


Blanket


QB (MeV)


Breeding Reactions
per 14-MeV Neutron


Thorium


2.7 [232Th(n,y)]

4.4 [23U(n,y)]

5.0 [238U(n,y)]


Natural Uranium




-27-


sperhical annulus having an inner radius of 200 cm and an outer radius of


300 cm with composition as listed in Table 1-VIII.


For constant blanket


qeometry and material volume fractions, the following optimum results

were obtained for depleted lithium (4% Li) and depleted uranium (0.04%


U) per 14 MeV neutron:


= 103 MeV


= 0.986;


U(n,y) reactions


- 1.


Because of the 1.68 239Pu breeding reactions per D-T fusion


event, Lee chose


Pu as the fissile fuel.


Tabl

Subcritical Fast Fi


e 1-VIII


on Blanket Components


Studied by Lee


Element


Volume Fraction


Zone 1
(30 cm thick)


0.95
0.05


Zone


cm thick)


Nb
Heavy Element


0.30
0.05
0.65


Lee also studied the neutronics effects of changes in the thickness


of Zone 1 and material volume fractions in Zone


for the composition


shown in Table 1-VIII results were reported for the following heavy

element material variations:


Depleted uranium versus


U content.


Metallic and oxide mixtures of plutonium and uranium versus 239p




-28-


Best energy generation with


sufficient breeding was reported for


the metallic uranium blanket with 4% plutonium.


poisoned with


case


fission products are summarized in Table


and one

-IX.


Tabl


e 1-IX


Fast Fission Hybrid Neutron Economy per 14 MeV
Neutron Calculated by Lee


Plutonium
Tritium Conversion B
Material Production Ratio (MeV) eff

4% Pu-U 1.38 3.14 431 0.84

4% Pu-U + 8% FP 1.18 3.03 306


The usefulness of a hybrid concept is contingent upon a short


ssile fuel doubling time


. Lee estimated a very high 14 MeV neutron


wall loading of 12.


MW/m


to obtain a


year plutonium doubling time


for the


Leonard la


FP blanket but reports no fusion plasma characteristics.

ter claimed that the 306 MeV blanket energy release per fusion


neutron


n Lee's


8% FP model would lead to a three-fourths reduction of


the usual Lawson breakeven condition.


However, current engineering con-


siderations indicate that such first wall power loadings will almost

certainly make fusion power unrealistic due to the need for frequent


first wal


Since hi


times over non-fissil


replacement


results indicated energy production increases of 10 to 20


blankets with simultaneous adequate tritium and




-29-


advantage over other concepts except as a fuel producer.


Considerabi


additional research has been reported on blankets and hybrid systems


using the fast fission concept.


All have emphasized fuel production versus power production and


have


worked with reduced first wall neutron loadings of 1-5 MW/m


advantages of using fusion neutrons for fast fission as well as breeding


fuel in situ


are probably only applicable in the true symbiotic conceptS


where the hybrid is not a system energy producer but a fuel producer,


since blan


fission.


multiplication


Hence, th


lowered for low enrichments with fast


fast fission hybrid is of little interest in this


current study.



Texas Fast Fission Hybrid


Parish and Draoer


presented extensive hybrid neutronics results


for their no


del which


was also a fast fission design.


They investigated


the potential of 14 MleV fusion neutrons to fission fertile material


(232


Th and


U) while


maintaining adequate fusion blanket performance.


Parish and Draper based the a

tive abundance of such fertile


attractiveness of this concept on the rela-


fuels and the elimination of dependence


on breeding fissil


fuel for hybrid usage.


The large fission energy


multiplications obtained in other studi


1,3 were not paralleled in thi


hybrid; however, the potential of both thorium and natural uranium-fueled

fast fission blankets to produce both fission power and fissile material

was demonstrated.
.. /L .. .




-30-


various calculational methods.


To verify methods of analysis


Parish and


Draper calculated the neutronic and photonic characteristic


standard fusion blanket model using ENDF/B-III cross


of the


section data in the


ANISN5


code for a P3-S4 transport approximation.


The resultant standard


blanket neutron


economy compared wel


with Steiner


s latest results on


the same standard.59


Good agreement was obtained for breeding


1.445


versus T/n


= 1.452) and (n,2n) reactions as well as neutron leakage


despite Steiner's use of pre-ENDF/B-III cross section data


hybrid was one of the first hybrid studies to account for (n,3n


s Texas


reactions


which become very important in such poorly multiplying blankets.


Since high energy neutrons are needed to fission fertile fuels


fission material regions in this concept were placed as


as possibi


to the vacuum walls.

offset by (n,2n) and


Low energy neutron absorption was only


n,3n


partially


reactions.


The volume fractions of fuel, clad


niobium)


and coolant (lithium)


in the model


tively


were


maintained constant at 0.45, 0.15, and 0.40,


, to approximate fuel regions


n a LMFBR


respec-


The tritium breeding


fissil

region


breeding, fission power, and spatial heat deposition by


were presented in the T


blanket


exas study for various blanket fuel thick-


nesses.


blank


The results of these calculations for two thorium-fueled


and four uranium-fueled blankets are presented in Tabi


and 1-XI.


The calculation of


spatial heat deposition rates in the standard


and fertile fueled blankets in this work emphasized the problems with


ow mul tipli


cation hybrid blankets.




-31-


Table 1-X

Neutron Economy for Thorium-Fueled Blankets


Thorium Fue


Reactions/Fusion Event


Region Thickness


2Th(n,f)


232Th(n,)
Th(n, )


6 cm


.3012


.0310


.1326


13 cm


1.0964


.0472


.3118


Table


U "LXI


Neutron Economy for Uranium-Fueled Blankets


Natural Uranium


Reactions/Fusion Event


Region Thickness


U(n,f)


235U(n,f)


Total
Fission


238U(ny)


10 cm


1.3252


.133


.0133


.1463


.2487


1.2694


20 cm


1.0865


.0161


.0259


.2024

.2096


.3818

.5320


0.9614


.1986


.0315


.2301


.6654


For the large 10 MW/m


first wall neutron loading limit, the two


thorium-fueled blankets showed peak power densities of 200 W/cm


3
For


the 1


wall


of 20


cm natural uranium case


ranged from 510 to 364 W/cm


to 146 W/cm


, the power density between the niobium


the related thorium case had a ranqe


Fuel was eliminated in the 3 cm region between


----1


L~.......-ll -11


-1




-32-


density, Parish and Draper have claimed these hybrid blanket power den-


siti


are acceptable.


This is doubtful because of the


ow power den-


siti


at blanket positions removed from the vacuum wall and the resultant


unit cost of


electrical and fusion power produced.


The superiority of natural uranium to thorium as a fast fission


hybrid blanket fuel because of its larger fast fission cros


illustrated in Parish


presented in Tabl


section is


s comparison of the best case for each fuel

II.


Table 1-XII


Comparison of Best Natural Uranium-Fueled and
Extrapolated Thorium-Fueled Blankets


Uranium


Thorium


Tritium Breeding Ratio
Fusion Blanket Energy Multiplication
Fissile Nuclei Produced per Fusion Event
Peak Power Density at Nb First Wall


1.09
, 20


'"" 3
409 W/cm3


1.15
0.5
0.31
S200 W/cm


However, the low return of the fissioning blanket renders this concept

uneconomical versus other concepts relying on better fissile blankets.

Increasing fuel costs could make this concept more attractive at some

future date but others seem more appropriate.



Light Water Hybrid Reactors


The feasibility of fusion-fission hybrid reactors based on breeding




-33-


Princeton Plasma Physics Laboratory.60 Emphasi


was placed on fuel


-self-


sufficient (FSS) hybrid power reactors fueled with natural uranium.


Light Water Hybrid Reactors (LWHR) considered included FSS-LWHR'


Other


fueled


with spent fuel from Light Water Reactors (LWR's), and LWHR's to sup-

plement LWR's by providing a tandem LWR-LWHR power economy that would be


fuel self-sufficient


similar to Lidsky


symbiotic concept


Nuclear


power economies based on any of these LWHRs were found to be free from


the need for uranium enrichment and for the separation of plutonium.


They


offer a high utilization of uranium resources (including depleted uranium)

and have no doubling-time limitations.


study investigated the property


atti


of subcritical thermal


for hybrid applications and concluded that light water is the


best moderator for FSS hybrid reactors for power generation.


latti


Several


geometries and compositions of particular promise for LWHR'swere


identified with thicknesses up to 250 cm.


The performance of several


conceptual LWHR blankets was investigated and optimal blanket designs


were identified for natural uranium-fueled lattices.


The effect of


blanket conversion efficiency and the feasibility of separating the

functions of tritium breeding and of power generation to different


blankets were investigated.


Optimal iron-water shields for LWHR


were


also determined.

The evolution of the blanket properties with burnup was evaluated


along with fuel management schemes.


The feasibility of using the lithium


system of the blanket to control the blanket power amplitude and


was also investigated


shape


A parametric study of the energy balance of LWHR




-34-


with critical systems and delineated the advantages of such hybrids in

alleviating nuclear technology problems relating to resource utilization,


prol iferation


and safety issues.


In general


, this study reported the


same types of


information as previous studio


but for a different blanket


design.



PNL--Thermal Fission Hybrid


Pacific Northwest Laboratories (PNL)1'61 initially studied a hybrid


fusion reactor utilizing a subcritical thermal fission latti


around the


usual


cylindrical D-T plasma


The four distinct regions of the hybrid


blanket configuration are illustrated in Fig.


cm thick neutron convertor region was filled with niobium-clad


pins of both depleted uranium carbide and natural lithium.


Niobium


structure


walls are used along with helium coolant.


The 150 cm thick


thermal fission lattice, consisting of a graphite-moderated, natural


uranium-fueled, helium-cooled matrix,


was designed for fi


ssion power


generation.


The last 50 cm of blanket thickness are filled with graphite


reflector and natural lithium absorber


, respectively


The ENDF/B III cross section data were used in the HRG362


Revised-Thermos (BRT-1)63


and Battelle-


cross section codes to obtain fast and thermal


broad group data

trained using a P


, respectively


The final neutron balance results ob


transport calculation in ANISN58


are summarized in


column


of Table 1


-XII I.


Neutronic effects from slight enrichment of


the uranium in the fi


ssion lattice are also shown in the neutron balances


I-~~ -5- II tt-


r I





-35-


S'- 4
A 4


~C~L~ll*ll~:
t
I~ ,&




-36-


Table 1-XIII

Early PNL Hybrid Neutron Balance


Events per Source 14-MeV Neutron


235
U Atom Percent Enrichment


0.7196


0.80


0.90


Tritium Production


0.956

0.019


1.188

0.019


1.763

0.020


Total Tritium Production


0.975


1.207


.783


Fissions


0.234


1.936


U Captures


1.121


0.251


.776


0.988


.292


4.863

0.853


U Absorptions


Estimated kff
eff


0.84


0.884


0.928


1050


Based on their composite behavior with fi


enrichment, an


enrichment was predicted


0.77 atom


) for which both the tritium and


fissile conversion ratios could be optimized to


excee


d unity.


The cal-


culated energy deposition in the blanket for the best case was calculated


to be about 500 MeV per


pl ication of about


significantly 0.7


source neutron corresponding to an energy multi-


This PNL optimum hybrid is attract


nce


enriched uranium can be produced than the higher




-37-


reactor capabilities which is very low.


This power density was used to


determine the plasma and blanket specifications shown in Table I-XIV where

the plasma requirements are substantially less than for a nonmultiplying


blanket and the vacuum wall loading i


Tabl


very low.


e 1-XIV


Early PNL Hybrid Specifications


Blanket


Plasma


Specific power
Thermal power
Vacuum wall loading


keV)


0.75 W/cm3
20 MW/m
0.05 MW/m2


nT (steady


tate) (sec/cm3)


x 1013
x 1013


Since a non-negligible fraction of the thermal energy produced in the

blanket must be used to sustain such a plasma, the need for investigation


of controls i


tion i


justified, especially since the fission energy multiplica-


predicted to be so high.


This preliminary PNL hybrid design was faced with drawbacks such


as large


(2 m thick blanket) and low power density


0.75 W/cm3).


However,


it was favored with low wall loading and plasma conditions re-


duced to


S1/6 Lawson Criterion value.


Since the hybrid objective


energy multiplication with adequate breeding of tritium and fissile fuel

are attainable, the PNL concept appeared to be a promising competitor for


the LMFBR program.


Much additional work has been performed including




-38-


studies have identified and delineated the merits of the helium-cooled,

thermal fission hybrid fueled with natural or slightly enriched uranium


moderated with graphite, and cooled with helium.


In addition, the


optimal use of lithium for breeding has been delineated.


This PNL concept of a fusion-fission


system has been developed to a


considerable


degree


as reported by many studio


64-67


The most complete


results on blanket parameters were reported by the combined efforts of


Lawrence Livermore Laboratory and Pacific Northwest Laboratories.


Although thi


hybrid blanket design was intended for use in the spherical


geometry of Livermore'


mirror (Yin-Yang) fusion reactor


concept, the


basic blanket geometry is very similar to that shown in Fig.


modul


Blanket


of varying composition were analyzed using a fuel pin lattice


geometry similar to that used in High-Temperature Gas-Cooled Reactors.


Results reported for th


hybrid blanket analysis are included in Table


1-XV showing seven (7) different


cases


analyzed, all of approximately


200 cm thickness.


The inner convertor region was closest to the plasma


and contained helium coolant and stainl


steel structure as well as


depleted uranium to enhance neutron multiplication.


The inner thin


breeder contained lithium for fast neutron tritium breeder while the

thicker outer lithium breeder contained lithium for thermal neutron


breeding of tritium.


The reflector, where used


was composed of graphite


and the thermal fission latti


was composed of hexagonal unit cell


slightly enriched (as noted) fuel pins in a helium-cooled graphite matrix.


The fuel pin geometry and


cell pitch were optimized using


transport


calculations.




-39-


Tabi


1-XV


PNL Hybrid Blanket Analysis


Tritium Fissile Blanket
Case Blanket Breeding Breeding Fusion Energy
Arrangement Ratio Ratio Multiplication

1 8.5 cm convertor
1.5 cm breeder
150 cm lattice (1.0%)* 0.766 1.59 18.9
20 cm reflector
15 cm breeder


2 10 cm convertor-breeder mix
150 cm lattice (1.0%) 0.725 1.57 19.8
20 cm reflector
15 cm breeder


3 10 cm convertor-breeder mix
180 cm lattice (1.0 %) 0.365 1.62 25.2
10 cm breeder


4 8.5 cm convertor
1.5 cm breeder
0.737 1.55 20.0
180 cm lattice
10 cm breeder


5 8.5 cm convertor
1.5 cm breeder
1e 0.893 1.22 31.8
180 cm lattice (1.25%)
10 cm breeder


6 8.5 cm convertor
1.5 cm breeder
15cbed 41.26 0.984 59.6
180 cm lattice (1.50%)
10 cm breeder


7 8.5 cm converter
1.5 cm breeder
n 00 1. 11 39 .8
180 cm lattice (1.35%)
10 cm breeder




-40-


unity


In addition, the energy multiplication of the fusion power was


found to be very large for thi


best case (MB


= 39.8).


This energy multiplication was claimed to be related to the effec-


neutron multiplication of the


blanket and the neutrons produced per


fission in the blanket by the following global parameter equation:


200 MeV 1)
14 MeV


eff


- kff
eff


where 200 and 14 represent the energy deposited due to fission reactions


and fusion neutrons, respectively,


v is the number of neutrons released


per fission and


tion factor.


keff i


usual blanket effective neutron multiplica-


this equation related global parameters and


since


4 MeV source i


introduced inhomogeneously, the current work was


partially directed at determining if this equation might be inadequate

despite its frequent use in describing and analyzing results from cal-

culations performed on hybrid blankets.



Review of Controlled Thermonuclear Reactor


Thermal Stability Ana


yses


Fusioning Plasma Operational Criteria


The first determinations of operational criteria for thermonuclear

reactors were performed using global or point-model reactor parameters.


Rigorous descriptions of comply


plasma dynamics with attendant spatial


variations were usually beyond the scope of such criteria development.

The first attempt to soecifv fusion reactor operational criteria




-41-


uniform temperature, T, and confined for a time, r, after which cooling


was allowed.


Conduction losses were entirely neglected.


This initial


work established values of temperature and the product of ion density


and confinement time, nr, for a zero-power but

nuclear system. A system energy balance was u


self-sustaining thermo-


sed in which the energy to


heat the plasma, E and the energy to overcome bremsstrahlung radiation


losses

energy


, Eg, were


upplied


supplied to produce fusion reaction energy


as well


as the fusion reaction energy, was assumed to be


recoverable


and converted to useful output energy at


some efficiency, n.


The minima


condition for breakeven is simply defined as follows:


[EF + E + Ep]n


EB + Ep


where n is the overall system energy conversion efficiency


For a D-T fusion system as described above, the so-called Lawson

Criterion for breakeven becomes simply:


( )p(l


- p)QFDT


where


= fuel ion density (ions/cm3 )

= plasma temperature (keV)


DT


= reactivity of D-T plasma (cm


3/sec


n = overall


system energy conversion efficiency


= proportionality constant for bremsstrahlung radiation

= tritium fraction of ion density
r.. ./i.. \


- bT1/2




-42-


The Lawson Criterion for the pure D-T fuel cycle is represented


by a series of parametri


spectrum of curves in Fig.


curves in the efficiency as shown in the lower


Points on such parametric curves represent


minimum nr and T values for breakeven fusion energy production


no net


fusion energy i


produced.


If the energy per fusion event can be aug-


mented by fission reactions in the hybrid blanket, then the requirements

on the plasma can be significantly relaxed.

Cyclotron or impurity radiation losses are not considered in Lawson-


type anal


yses.


No stability i


considered


since the conditions quoted


from such analyses refer to minimum requirements for overall breakeven.


Another


early study of the reactor energy balance was done by


Jensen et al


Again the


D-T reaction was of primary concern though


subsidiary fusion reactions were also treated.


Jensen reported on the


effects of finite energy transfer rates and found self-sustaining

reactors were possible over an increased parameter range, although all


ion speci


were treated at a uniform temperature.


The major


shortcoming


of Jensen


energy balances was its failure to consider particle confine-


ment times of diffusion losses.


Additional energy balance


considerations


were reported by Woods.


Horton and Kammash


have also considered energy balances and


operating conditions for the D-T fusion cycle.


since alpha particles are


a significant plasma heating mechanism, energy and particle conservation

equations were introduced for the alphas created in D-T fusion reactions.


Both bremsstrahlung and synchrotron radiation 1


losses


were treated along


with the effects of cold and energetic fuel injection.


This work was




-43-


temperature and density, some of which were applied in the later stability


work of Mill


15-17


and Ohta et al


A similar but more realistic condition than the Lawson Criterion

for minimal operation has been developed by Mills for a system using only


the D-T reaction.


15,16


This model i


based upon continuous injection of


cold fuel where fusion temperatures are assumed to be supported by alpha


heating.


Mills used particle


and energy conservation equations for the


ion density


follows:


dt


- n/T


d 3
dt 2


+ Te)]


= p(1l


- p)n 2 DTCQ


S(T. + T )
1 e'


where


= fuel ion density (ions/cm")


= fuel ion injection feedrate


nuclei/cm3-sec)


= tritium fraction of ion density

= confinement time against all plasma losses including
fusion (sec)

= alpha particle energy from D-T fusion events (3520 keV)

= fraction of alpha energy retained in the plasma for
heating


i,e


= temperature for ion and electron


species respectively (keV)


DT


= D-T fusion reaction reactivity or rate coefficient
(cm3/sec)


For steady-state operation with this model


Mills found that the


following equilibrium condition must be maintained if operating charac-




-44-


2p(1


+ T )


- p)DTcQ


This result is similar to the Lawson condition but more conservative


since only a fraction of th


alpha particle energy i


retained to sustain


the plasma while none of the neutron kinetic energy is retained.


addition, the Mills


condition i


a steady-state condition based only on


the plasma while the Lawson Criterion attempts to account for all in-


fluences on


losses


tem efficiency.


The constant, c, accounts for energy


due to bremsstrahlung and synchrotron radiation.


feature of thi


work i


An important


the temperature difference allowed between the


ion and electron speci


in general, Mill


s found that the electron


temperature is elevated due to preferential alpha heating


Figure 4


illustrates the Lawson breakeven region for


to 45% efficiency


com-


pared to the Mill


' equilibrium region


= 0.8, p


= 0.25 and 0.50)


Since Mills' model i


concerned only with alpha heating and radia-


tion 1


losses


within the plasma, energy release to neutrons was not con-


sidered.


Though actual power generation capabilities were not considered


by Mills, comparison with the zero power condition developed in Lawson

model does indicate net overall power production as expected for

equilibrium operation.


Fusion devices producing values above Mills


equilibrium region in


Fig.


4 can be operated only in the pulsed mode.


similarly, devices pro-


viding ni-values below the Lawson region can never operate


as power-


producing reactors, while those falling between the two criteria will


4tn, l nnvn 4n4r4n,,n C; .; n a n 1, n n + I I


r.. c.,ll ..,.+., cn inhn ; $





-45-


10"15


PLASMA EQUILIBRIUM


REGION (c


= 0.8)


p = 0.25


- 0.50


n = 45%
n = 40%
n = 35%


LAWSON BREAKEVEN REGION


20 40 60


Ion Temperature (keV)


I,


t~


14
10


13
10




-46-


Plasma Thermal Stability Considerations


Plasma global thermal stability studies were initiated by Mills


based on the operational equilibrium


studies.15-17
studies


Mills demonstrated


that the equilibrium condition is equivalent to requiring the constancy


of a function


follows:


= STr2p(


- p)S


where the so-called stability function,


cm2/keV-sec)


varies with ion


temperature Ti


as S


" cT~ which exhibits a broad resonance
%CT1


peak around


In the


first approximation Mills treated the alpha energy re-


tention fraction


as a constant.


For stable equilibrium, the


ogarithmic


variation of i(S,T,p,T.) must vanish.


Therefore, Mills found that the


operational equilibrium i


unstable


against fluctuations in the fuel


feedrate


th


confinement time, the


fuel mixture (unl


), and


the ion temperature except when the


exponent in Ta falls to zero above
1


28 keV.

Although the exact behavior of the confinement time with ion tem-

perature was not known (nor is it known today), the p-function formaliza-


tion showed that if t i


nuclear reactor below


s independent of T.


keV is impossible without


stable operation of a thermo-


some form of control.


Below


, departures from equilibrium are supported due to the posi-


tive


slope of the


stability function.


It is not until the negative


slope


region of the


stability function i


reached above


keV that the in-


herent instability against fluctuations in T. is controlled and the
1
+ maarnnr s -I I r t i -u h3Pfn4 annII 1i h nr I~ +n ar,4 km




-47-


In fact, most fusion reactor


system design studies currently


operating temperatures below 20 keV


28-32


But at temperatures below


keV, Mills showed that control i


extreme departures from equilibrium.


necessary to avoid the predicted

This control can be implemented


via the feedrate, the fuel mixture, the confinement time, or radiation


losses


dependent on injection of impurities.


Initially, Mill


favored


control via the confinement time


5,17 but later work has emphasized


feedrate control


More recent studio


by Ohta et al.


18 have confirmed


the use of feedrate as a viable method by which to control stability.


If the confinement time i


temperature-dependent


, then it may be


useful for inherent control by introducing temperature dependency into


the p-function.


Mills hypothesized Bohm-type diffusion (r


ST-1) as a
CLT) as a


possible inherent control to allow stable operation below the 28 keV


cutoff indicated for constant confinement operating conditions.


fixed feedrate and fuel mixture, Mill


used the p-function variationa


method to demonstrate inherent stabilization of plasma equilibria for


this Bohm-type diffusion for temperatures in the 7 to


keV range.


analyzing the dynamic behavior of thermonuclear plasmas, Mills

lished the self-stabilizing influence of Bohm diffusion below


estab-


temperatures


as the perturbed plasma temperatures (ion and


electron)


and ion density were shown to approach equilibrium with time.


Mill


In this


justified operation near the 12 keV temperature to take ad-


vantage of the optimal D-T reaction rate73 without the necessity of

introducing artificial control.


Mills17


also presented details on calculations to evaluate the time




-48-


exchange between ion species


as an instantaneous process.


Results were


reported only for plasma time behavior for attempted initial equilibrium

operation about a temperature of 11 keV with 50% deuterium and 50% tritium


fuel injection


leading to ion densiti


x 10 ions/cm


stability of plasma operating conditions in thi


region was verified for


constant confinement and shown to result in rapid plasma runaway in less


than three seconds


The plasma temperatures (T. and T ) were shown to
1 e


runaway above or below ignition depending to extreme acc


uracy on whether


or not the constant plasma confinement time was too


ong or too


short


artificial control was found to be essential below


Mills17


also investigated feedback control via the fuel mixture


using the monitored plasma electron temperature.


When the


ectron tem-


perature was set below a preselected control temperature, the injected


fuel mixture was maintained at the original 50


D, 50


T; when the tem-


perature exceeded the control temperature, tritium injection was replaced


with pure deuterium.


effect of stopping tritium injection was to


reduce fusion events and lower temperature


the stabilizing effect of


this mixture control feedback was achieved by making the time average of


p(l-p) low enough to compensate for


excess


ive confinement time.


Control


to a temperature that was too low to provide the nr-equilibrium condition


was found to result in the reacting plasma


extinguishing itself.


Mill


also noted that


excess


ive confinement time will result in severe initial


temperature overshoot.


These investigations by Mill


constituted the first efforts to


study the dynamics and control of thermonuclear reactor plasmas. The




-49-


incomplete stability criteria development in Mill


work is its most


significant deficiency.

The same stability problems of point model D-T plasmas have been


investigated in more detail by Ohta et al


18 but using the following


global nonlinear balance equations for plasma density and temperature

(energy):


- n/T


n (


d(nT) n2f)
dt


- nT+ ST


(13)
s


where


DT


f(T)


- 1.12


-1015 1/2
x 10 T


= plasma ion density (ions/cm3)

= uniform plasma temperature (keV)

= particle and energy confinement times (1/sec)


= fuel injection feedrate (ions/cm


DT


-sec


= fuel ion inject energy (keV)

= alpha particle energy from D-T fusion events (3520 keV
3
D-T fusion reaction rate coefficient (cm /sec).


Ohta addressed only the D-T reaction; the fusion reaction was not

considered an important loss mechanism in the particle conservation equa-


tion in essential agreement with Mills.


and the bremsstrahlung energy 1


Both the fusion energy source


terms were included in f(T) but


dn
dt




-50-


No temperature difference was allowed between the electron and ion


species which is a limitation in contrast to Mill


attempt to treat


differing temperatures


The advantages of Ohta'


model include accounting


for energy diffusion with particles and energetic ion inj


section as well


as including an explicit expression for bremsstrahlung radiation.


obtained the following form of th


state subscriptt o)


Ohta


Mills equilibrium condition for steady-


evaluation of the balance equations:


oEE


T
E
_o


0
(14)


f(T


which indicates the reduction in required nT-values by the inclusion of

Ohta's injection heating option.

Efforts by Ohta to examine steady-state plasma stability can be

categorized into two areas:


Linear analysis establishing temperature-dependent stability
criteria in possible operating regions for future fusion
plasmas, and


Nonlinear dynamic


subject to


simulation of the plasma balance equations


small perturbations with and without feedback


effects to verify agreement with linear stability analysis


and control possibility


in unstable operating regimes


Linearized analysis


will usually predict stability regimes.


If a


system is not


stable, linearized analysis will not predict true con-


sequences of the


unstabi


situation--hence


the need for dynamic simula-


tions.


ability criteria to predict whether small plasma perturbations


will grow or diminish with time were developed by Ohta from linearized


forms of the density and temperature balance


Pouations.


The elimination




-51-


and small temperature perturbations, 6T(t), which Ohta assumed to vary

exponentially with time.

Stability is assured provided the real part of the growth rate is


negative.


Ohta obtained general stability criteria by solving for the


growth rate after substituting the density and temperature variations into

the linearized density and temperature equations.


To proceed beyond such general stability criteria


, the functional


dependence of both the particle and energy confinement times were re-


Because the exact density and temperature dependence of confine-


ment time was uncertain, Ohta based the analy


functional dependence of confinement time on density and temperature


T n Tm

this genera


upon the following


It is the derivation of stability criteria on the basi


diffusion model that represents the major contribution of


Ohta


s stability analysis.


To obtain useful stability criteria, Ohta


used three diffusion models to get specific values for


and m:


Constant confinement


T % constant (z


= 0, m


= 0).


Bohm confinement:


T T-l (e


Classical confinement:


= O, m


T % n-'T1/2 (A


= -1)


= 1/2).


The minimum temperature satisfying the stability criteria for each


confinement model is known as the critical temperature, T

temperature above which operating conditions are predicted


that is, the


d to be stable


as described by Mill


s' work.


Representative temperature results pre-


dicted by these stability criteria are listed in Table 1-XVI for both

charged particle and injection heating for all three diffusion models.

Ohta also dynamically simulated the balance equations to check the


quired.




-52-


densities, however, were perturbed a small amount above and below


equilibrium and th

and temperature ca


effect on the temporal behavior of the plasma density


culated as presented in Fig. 5.


Table 1-XVI


Critica


Confinement Model


Temperatures for D-T Fusion Reactors


c (keY)
C


Charged particle Heating


Injection Heating*


(*n E/


= 10)


(n /TE


- 1)


T = constant

T T-


T fl


*Ion Injection Energy:


For the c

which the


ase


= 150 keV.


of constant confinement and charged particle heating for


critical temperature T


keV was found also by Mills.


Ohta's results are depicted in Fig. 5 for three initial equilibrium tem-


peratures of 10 keV


30 keV


and 50 keV.


For equal magnitude density


perturbations, equilibrium density is always approached with time which

indicates plasma stability under isolated density perturbations.


Similarly


, temperature transients resulting from the density perturbations


out for ca


30 keV to 50 keV) where T


However, for the


subcritical 10 keV initial temperature, the time evolution of temperature

is unstable as shown in Fig. 5 and predicted in Table 1-XVI.




-53-


From Ohta et al


T = 10 keV
ST = 30 keV
T = 50 keV


0 2 4 6 8 10


Time


sec)


= 10 keV
= 30 keV


T = 50 keV


0 2 4 6 8 10


Time (sec)


Figure


Time variation of point-model plasma temperature and density
for constant confinement and charged particle heating.




-54-


general, the quick plasma response on the order of a few seconds was


found for all these anal


yses


of unstable plasma variations in pure fusion


plasmas.


Ohta'


s behavior agreed with previous fusion plasma analyses.

results demonstrate the need for stabilizing control to allow


fusion reactors to operate below the critical


temperatures


as planned by


current fusion reactor design studies.


stabilization for the


Ohta et al


balance equation


The case of feedback


constant confinement model was also examined by


Stability criteria were again derived from linearized

ns. Density feedback control was introduced by adding the


term,


6n(t)


, but was not able to stabilize the system because the


balance equations are stable for isolated density perturbations.


since


temperature instabilities can grow independently, various types of tem-

perature feedback were introduced by adding the stabilizing feedback term,


6T(t)
a T
T
0
tions.


, to either one or both of the perturbed linearized balance equa-

New stability criteria were derived dependent on the value of the


feedback coefficient,


in implementing control

ferred by Ohta et al. i


. Although many parameters are possible for use

, feedback via the injection feedrate was pre-


n agreement with Mills.


Ohta demonstrated control of the temperature instability through

dual temperature and density feedback which was introduced through the

injection rate and its "small" variation about equilibrium as follows:


an


S(t)


+65S


T


- At)


where


a is the feedback coefficient and At is the delay time between a




-55-


applicable to realistic control situations.


The effectiveness of feedback


stabilization was found to be dependent on both feedback parameters:


and At.


For the applicable plasma model Ohta found a stabilized region


in the aAt-plane from the linear stability analysis


of thi


s feedback


effect.


In general larger negative feedbacks and


shorter delay times


were found to yield more effective stabilization.


At or small


subcritical (T


For sufficiently large


feedback stabilization was found to be ineffective in all


cases.


As expected, Ohta found the unrealistic case of


zero delay time to be


the most effective


feedback.


However, when the delay time and feedback


coefficient were within the stability region predicted by linear analysis,

an equilibrium temperature was always approached; however, the amplitude

of oscillations was found to increase with delay time as the limits of


the stability regime were neared.


Since delay times of


to 3


seconds


are outside the


linear stability regime predicted for this case, extreme


amplitude of oscillation for these delays


was found as


expected


Usher and Campbell23'24 extended point-model thermal stability


analyses to other fuel cycle


and other plasma diffusion models with


similar results and


speeds of response.


In addition burnup was treated


in this extension of Ohta


s analysis with essentially similar results for


the D-T fuel cycle.


Stacey'


point model plasma


stability analysis of the D-T fuel cycle


extended point model plasma


stability analysis of the D-T fuel cycle to


include more detailed plasma behavior including four balance equations


to represent the following plasma parameters:




-56-


Alpha particle density.

Electron energy density.


Again the temperature instability was found in certain regimes.


Effective


stabilization to control operation about an unstable equilibrium point


through use of controlled ion injection rate as well


as controlled D-T


fuel mixture was demonstrated


temperature instability has


also been examined for radially


homogeneous D-T fusion plasmas by Yamato, Ohta


and Mori


, using partici


and energy balance equations.


19-21


The results of thi


s inhomogeneous


anal


ysis


support the validity of decoupling


excursions in the overall


particle densities and temperatures from excursions in the spatial density


and temperature distributions.


When the injection of fuel is uniform


the temperature instability can develop only in the zero order mode.

Stability criteria were developed similar to those for the uniform plasma


with similar results


, including feedback stabilization through temperature


to allow operation below the critical temperature.

There have been no investigations of hybrid plasmas to examine the


temperature instability discussed in thi


review.


an area that


requires study because large hybrid blanket energy multiplication values

coupled with large plasma transients and neutron release could have con-


as wel


as safety significance.


Motivation for the Research


As is evident from the preceding critical review of hybrid studies,


- hn rn vmn m v n \F r r P vnn 4n 4 nncn n# i An ct M c n h r


hlar c f I I rl; o c n n h ~rh ri rl c r ;I n







the dynamic interaction of the two components of the hybrid system.


investigations have not been reported in the literature to date.


Such


Thus,


the objective was not to devi


a new system but to take the


somewhat


arbitrary approach of selecting a previously establi


shed hybrid concept


with necessary adjustments.


Many different types


of hybrid machines have been proposed with many


different methods of application.


Power-producing


Tokamak hybrids are of


most interest for


control


and dynamic


considerations


and so such a model


was selected for thi


work.


entially thi


hybrid design is compatible


with various hybrid advantages


Laboratory


delineated in the recent Princeton Plasma


tens study of Tokamak fusion-fission hybrid


reactors which concluded that the most economical mix of power- and


fuel-producing hybrids should emphasis


power production


An optimized


hybrid machine should be a substantial


power producer with a by-product


of fissionable fuel,


the optimum ratio of fuel


production to power pro-


duction being determined by economics.

An early demonstration of hybrids could allow a very reassuring


program for future development of the utility industry.


A guarantee of


future reasonable fuel costs could promote the accelerated installation


of current LWR plants


straints on all


to fill


sectors of th


near-term power needs while


United States energy economy


loosening con-


subsequent


commercial


development of hybrids could supplement LWR's,


provide them


with fue

eventual


1, and take up the load of retired power stations followed by

introduction of the pure fusion reactor sometime in the coming


century.




-58-


enrichment operations run for nuclear power plants and defense purposes.


The hybrid may be a better way to burn


U reserves with possible elimina-


tion of some enrichment requirements and perhaps elimination of plutonium


separation if bred plutonium i


burned in situ.


scenario i


especially important in


eight of the continuing breeder controversy


the recent Three Mil


Island accident ,74


which will undoubtedly delay


introduction of the breeder still longer due to safety considerations.

Since the hybrid represents an alternate concept for power production

and orderly progression to long-range utility application of pure fusion,


its characteristics require analysis

central station power production.


scribe hybrid


prior to its being approved for


One parameter frequently used to de-


characteristics is the global relationship for the blanket


neutron energy deposition per fusion neutron


QB, derived in Appendi


f
=--- [-
v
-Li


kff
eff


]+E


- keff


where


= blanket energy deposition per entering fusion neutron


= fission energy deposited in the blanket per fission event
(192.9 MeV)75

= average number of fission neutrons produced per fission
event


keff


= effective blanket neutron multiplication factor

= energy of the fusion neutron (14.06 PMeV)


= addition
due, for


energy generated and deposited in the blanket


example, to exothermi


neutron absorption


reactions


+ 6E




-59-


Several forms of the global relationship of Eq. (16) have been used


tensively to describe hybrid blankets.


1,64,76,


However, no results have


been reported on its validity.


If the parameter is to be used as a


figure of merit characterizing the multiplicative capabilities of hybrid

blankets, then its applicability must be verified and its limitations

established.

Hybrid blankets are expected to have substantial energy deposition

per fusion event so it becomes imperative that safety studies be undertaken


to examine the implications of this characteristic.


For non-multiplying


pure fusion blankets, the energy deposition per fusion event is


to be about 20 MeV.


expected


For hybrid blankets, even extremely modest ones


with keff = 0

fusion event.


.8 are predicted by Eq


. (16) to have 316 MeV deposited per


energy deposition and fusion energy multiplication


predicted by Eq. (16) for possible blanket keff values are listed in

Table 1-XVII.


Table 1-XVII

Predicted Blanket Global Response per 14 MeV Neutron


Effective Blanket Blanket Energy Blanket Fusion Neutron
Neutron Multiplication Deposition* Energy Multiplication
keff QB (MeV) MB


0.80
0.85
0.90


0.94
0.95
0.98
0.99


439
687
872
1181
1429
3654
7364


ex-




-60-


The accepted variation of blanket fusion neutron energy multiplica-


tion with blanket values of keff i


depicted graphically in Fig. 6 to


demonstrate the hybrid capability for high energy multiplication with in-


creasing but still far subcritical blanket systems.


Despite the impossi-


ability of reaching a critical fi


ssion reactor state


in such


stems,


variations in the plasma operating conditions could cause blanket energy


production rates beyond the technical limitations or the technical


fications of the design.


speci-


Even with no danger of supercritical behavior,


large uncontrolled thermal instabilities in the plasma could


ead to


cess


ive energy deposition


in the power-producing hybrid blanket.


In addi-


tion, there is the possibility of criticality at low temperatures prior to


power startup.


If plasma


startup is very quick, then the plasma neutron


production may drive the blanket to large overpower ratings before the

temperature defect can reduce the effective blanket neutron multiplication

factor, keff


Although relatively small quantities of therma


energy are contained


in the plasma a full-scale hybrid system generating 6500 MWth of steady-


state thermal power will require large numbers of 14 MeV neutrons.


a far-subcritical blanket (keff


tion of the fusion neutron


fission neutrons in the blanket.


Even


Z 0.9) can cause considerable multiplica-


available as an external source for providing


The component interactions as well a


the control and stability of such power-producing hybrid systems must be

well-understood.

The Lawson Criterion for hybrid reactors is modified as follows to

account for fusion and fission sources of thermal power with zero energy




-61-


x 1014


1012


LAWSON BREAKEVEN CURVE


Temperature (keV)


Fioure 6.


Tvoical Lawson breakeven curve for a 50-50 D-T plasma and


14
10


13
10




-62-


12 T


l-fl DT(Q


- 4bT1/2


where QB is the blanket energy deposition per fusion neutron and n i


usual overall


system efficiency defined for the Lawson Criterion.


50.69


Obviously


f significant energy is produced in the fissile blanket, the


requisite hybrid plasma parameters can be relaxed to allow earlier utili-


zation of fusion power in


combination with a subcritical fission reactor


to take full advantage of inherent hybrid safety features.

The typical effect of hybrid operation with blanket energy multipli-


cation is a reduction in the required


n product is depicted in Fig. 7.


The production of fission energy effectively reduces the need for fusion-


produced energy.


The hybrid-revised Lawson Criterion of Eq. (18) is


greatly relaxed because QB is on the order of hundreds of l1eV versus the


usual QB used for pure fusion systems which i


s limited to about


0 [IeV


including exothermic blanket reactions.


As noted, this interactive multi-


plication demonstrates the need to examine the dynamics and controllability

of hybrid systems.

Previous studies have been restricted to steady-state neutron


balance calculations and associated technological limitations.


There


has been no analysis of the time-dependent behavior associated with

hybrids, when subjected to reasonable perturbations in the characterizing


parameters


In addition, there have been no reports of analysis of hybrid


plasmas in the reduced reactivity regions where plasmas are not self-


sustaining.


The development of a model to describe the dynamic


S Sl -I I I .4 I r I


nT-


+ Q,)


F





-63-


PREDICTED: MB vs. k ff


0.80


0.85


0.90


0.95


Effective Neutron Multiplication Factor


Figure 7.


Predicted variation of blanket fusion neutron energy
multiplication with blanket effective neutron multiplication




-64-


hybrid system must be established when subjected to effects


due to the thermal instability analyzed by Mills15-17


such as those


and by Ohta et al


for pure fusion plasmas.


The desired result was a hybrid


system model whose analysis


would


yield useful operational characteristic


then enabi


of hybrid machines which could


the hybrid to make a contribution to power production before


the turn of the century


These


various investigations will only be possible


if both the plasma and blanket components are modeled and coupled to allow

dynamics and stability analysis to be performed.



Summary of the Research


The research reported here began with the Ohta plasma model18


burnup effects included after Campbell and Usher


with


and developed plasma


stability criteria based upon source feedrate perturbations and other

engineering considerations for plasma changes affecting the output neutron


production rate.


Essentially, an effort was made to develop an analytical


model for pure fusion plasma


stability and control based on a global


parameter treatment of a linearized fusioning plasma model using concepts


of classical control theory and transfer functions.


Feedback effects


were also incorporated into the model which was kept independent of


specific


design concepts.


The analytical model and its stability pre-


dictions were compared with Ohta 's results to develop an engineering-


oriented mode


which could have broad application to more sophisticated


plasma models in the future.


Perturbations causing plasma transients


r' II .1 ... I I J -




-55-


With the completion of this plasma stability and transfer function


analysis, the effort was extended to develop a


simplified hybrid model


from which general stability criteria were developed for the interacting


components of a hybrid system.


Again, the model was kept independent of


specific hybrid concepts except that the plasma confinement time was


assumed to be a constant


The model was


, independent of plasma temperature and density.


specifically developed and related to engineering con-


iderations of hybrid system perturbations


as well as dynamic


imulation


and control


Inherent as well as artificial feedback effects were in-


corporate where appropriate


The entire effort was directed to develop-


ment of a


simple, linearized


closed-loop model in transfer function


format which could be used for future extensions of this work on dynamic


and stability characteristic


of hybrids.


Of course the nonlinear form


was retained for dynamic


simulations.


The hybrid analytical model was then used to examine the properties


of a particular hybrid system.


The various augean and symbiotic concepts


and variations proposed by Lidsky2and analyzed parametrically in the


Princeton Study


were rejected for this research since they are not


primarily intended for power production.


s left essentially two


choices:

the possib


a fast fission blanket or a thermal fission blanket.


1


need for


To avoid


significant enrichments and to take advantage of


expected higher multiplication factors, a thermal fission concept was


selected.


The most advanced and promising design was reported by PNL


and Livermore workers under Wolkenhauer


This PNL blanket design was based primarily on existing technology




-66-


severely power-limited, the only substantive change for this research wa


the conversion to a Tokamak-driven hybrid versus the mirror-device hybrid

to promote larger power output and allow consideration of thermal in-

stability effects.

Since the physical arrangement of the hybrid blanket selected cor-


responded to the


reported PNL concept as nearly as possible, the results


of oreviousl


performed parametric anal


yses


of optimized region width


ordering of


zones, and region material constituents were used as the basis


for extending steady-state neutronic analysis


Tokamak-driven blanket design used is described


Detailed neutroni


of the blanket.


n Appendi


claculations were performed on the blanket for


selected design whose thermal lattice unit cell enrichment and global


temperature were the only varied parameters.


The cell enrichment was


varied from natural uranium up to 1 .50% enriched while the temperature


was varied from 2900K up to 970K


BRT-16


This work was performed using the


(one thermal group) and PHROG79 (three fast groups) codes to get


4-group constants.


The 4-group CORA diffusion theory code80 was then


used for criticality calculations and acquisition of fundamental flux


shapes.


The doppler defect was also calculated as a function of the


blanket operating temperature.


Only the more promising blankets with


keff


0.90 at elevated temperatures were considered


n detail.


This


limitation minimized blanket dependence on the fusion component of the

hybrid system.

Adjoint and perturbation calculations were performed on the system


to provide parameters to characterize the kinetic property


of the




-67-


source weighting factors,


of the hybrid blanket were calculated using


diffusion theory


Additional


inhomogeneous calculations for blankets driven by planar


sources of group


mate the fi


fast neutrons (10 MeV


ssion energy source size


- 0.821 MeV) were used to approxi-


required to produce a nominal design


power of 6500 MWth.


Volume source calculations were also run to investi-


gate the difference in the worth of the diffusion theory group 1 source

neutron power production depending on the point of introduction into the


blanket


This investigation was accomplished to analyze the validity of


global parameter relationship for the blanket energy deposition per


fusion neutron presented in Eq. (16).


relationship was expected to


yield reasonable


agreement with diffusion theory


simulations since the


source neutrons were introduced at nearly fission spectrum energy


The series of diffusion theory results were used essentially as


scoping


calculations to


select the best enrichment for further, more


detailed and exact


transport theory analysis using the AMPX code


package


available from ORNL


The blanket neutronic analysis


performed


with the XSDRNPM


code82 from AMPX was the first reported application of


the ORNL-developed AMPX package to such hybrid studies.


using the AMPX package


In P2-S4 analysis


, the fusion neutron source energy was treated more


nearly


as a true 14 MeV source.


The required


source strength for pro-


during the 650 MW


design power was determined for the toroidal


to establish finally the applicable degree of validity


expected in cal


culating or predicting the blanket energy deposition per entering fusion


neutron using Eq


(16).


The flux


hapes were also investigated again but




-68-


On the basis of the XSDRNPM-predicted fusion neutron source strength

required for a 6500 MWth hybrid plant, the required plasma conditions were


estimated.


The corresponding plasma temperature, density, constant con-


finement time, source feedrate, and injection energy characteristics were

then parametrically varied to establish reasonable hybrid plasma operating


conditions.


Perturbations in various parameters with emphasis on plasma


feedrate and temperature were then


simulated to investigate the thermal


instability of the hybrid plasma and the results compared with stability


predictions and expected dynamic behavior under transient conditions.


way the plasma component of the hybrid plant was examined with


respect to the thermal instability to establish operational characteristics

necessary for planning proper deployment of hybrid power plants.


Finally


transient phenomena,


time variations

driving the bla


since hybrid plasmas are expected to be subjected to various


especially thermal instability-driven transients,


n the design magnitude of the 14 MeV neutron source


nket were considered on the basis of those transients


resulting from the perturbed behavior of the hybrid plasma examined pre-


viously.


Kinetics calculations representing the effects of plasma-caused


perturbations on the fusion neutron source driving the blanket were run


and changes in power level were examined for one


patial dimension and


six delayed neutron groups


These kineti


calculations were performed


using the space-time kinetics code GAKIN II83


with si


neutron groups


whos


group constants were obtained from the previous XSDRNPM, P2-S4


calculations.


Although no time-dependent feedback effects were examined,


the speed of response of the system was determined for typical transients













CHAPTER


THE PLASMA MODEL



Introduction to the Plasma Model


First generation fusion power plants are expected to utilize the

basic deuterium-tritium (D-T) fuel cycle


2 3
D + T


S-


4He (3.52 MeV) + 1
2He (3.52 PMeV) + On (14.06 MeV


(19)


Because of its large cross section and reactivity, its minimized plasma


temperature requirements and its relatively large energy rel


ease


reaction, no other fuel cycle is given serious consideration for use in


early pure fusion power reactors.

and demonstration fusion power syst


Certainly the near term experimental

ems are expected to use D-T fuel 29,32,84


The United States Department of Energy effort toward implementation of

central station fusion power plants has clearly recognized the superiority


of this fuel cycle in the overall development programs


85-87


Even the utility industry has recognized the need for future choices


in types of power generating


systems and is supporting the effort to


develop fusion reactors using the D-T fuel cyc1


The major magneti


confinement efforts to produce fusion power in other countries have also


been directed toward the D-T fuel cycle.


89,90


Even so, D-T fueled fusion




-70-


The complexity and difficulty involved in achieving fusion power is

amply demonstrated in full scale commercial fusion power plant design


studies.


28-30


Because economic fusion power is such a large


made the


technological challenge, no factor can be dismissed which wil


development proceed more easily.


designs


The one common factor in different


for fusion power plants in a closed, steady-state mode of opera-


tion (Tokamak) has


been the universal selection of the D-T fuel


Hence, although the D-T fuel cycle has the drawback of producing high


energy, penetrating neutrons


serious choi


Mill


, its other advantages make it the only


for fusion fuel for many years.


demonstrated that the fusion reaction rate and fusion power


production are maximized for thermonuclear plasmas which have a 50%


deuterium-50% tritium fuel ion composition.


the most favorable fuel cycle


This 50-50 D-T mixing ratio


for the production of fusion energy.


With thi


cycle, not only i


the demonstration of scientific breakeven


in a


self-sustaining fusioning plasma more easily accomplished but the


steady-state production of net energy in a fusion power plant can be


accomplished at minimized


evel


of plasma particle density, temperature,


and confinement time.


These inherent advantages


of the D-T fuel


cycle in reducing plasma


requirement


have been


illustrated in various analyses of equilibrium


requirements and conditions including those of Lawson in which the


criterion for energy breakeven was first presented.50


of the 50-50 D-T fuel


The superiority


cycle for reaching and maintaining thermonuclear


power-producing conditions has been uniformly demonstrated in extensive




-71-


Because fusion-fission hybrids are expected to serve


as an inter-


mediate energy-producing stepping block between current LWR plants and

the eventual development of pure fusion power, the usual 50-50 D-T fuel


cycle


was logically sel


ected for this hybrid analysis.


This choice was


aimed at optimizing the time


scal


for th


implementation of the hybrid


power-producing concept.


The Point Model Plasma


In this work


, time-dependent point model balance equations were first


established for the plasma ion density, n(t), the plasma energy density,


3n(t)T(t), and the volumetri


plasma neutron production rate, qp(t)


these three balance equations for the plasma ion (particle) density,

temperature, and neutron production rate state variables are presented

as follows:


Plasma Ion (Particle) Density:


dn(t
= S(t)


n(t)


t)DT


Plasma Energy Density:


d[3n(t)T(t)]


n2 (t)DT Q+
=---D + T(t)


3n(t)T(t)
t) -


- bn(t)T1/2(t)


Plasma Volumetric Neutron Production Rate:


n (t)DT


t4-"




-72-


Conventional definitions for symbol


equations are listed below:


n(t)

T(t)


used in these nonlinear point model


-3
= plasma ion density for 50-50 D-T plasma (ions/cm3 )

= plasma temperature (keV)


= external fuel volumetri


injection rate


ions/cm


sec)


= volumetri


Ts(t
7


fusion neutron production rate (#/cm


sec)


= external particle (ion) injection energy (keV)

= particle confinement time (sec)


= energy confinement time


DT


sec)


= completely plasma confined fusion-produced alpha particle
energy (3520 keV)

= D-T fusion reaction rate coefficient (cm3/sec)


= proportionality coefficient for plasma energy loss rate via
Bremsstrahlung radiation (3.36 x 10-15 cm3 keV1/2/sec)18


the plasma in this analysis was treated


as a global system,


only a


single average plasma temperature was


considered


that i


distinction was made between ionic species or between ion and electron


temperatures.


The inclusion of the burnup term in the plasma ion density


equation i


an improvement to the model used by Ohta


corporate by others


23,24,95


18 that has been in-


In stability studies on pure fusion devices


this burnup term and its effects have frequently been neglected because


burnup causes small


changes in the


stable


e temperature operating regimes of


D-T fusion systems.


This analysis was intended for application to a


hybrid system where most of the energy would be produced in the blanket


so burnup predictions were


even lower than in pure fusion devices


that


, plasma temperature and plasma density are both expected to be lower




-73-


burnup increases due to temperature increases


will be directly respon-


sible for lowering neutron yields which are proportional to the square


of the ion density


All of the alpha particle energy produced in fusion


was assumed to be deposited within the


plasma to help heat the system.


Others have


assumed fractional deposition,


but there is no loss of


applicability in assuming full alpha energy deposition.


For this initial analysis


of point model kineti


the plasma volume,


, was treated as a constant; for linearized stability analysis, thi


adequate because only small plasma system perturbations were considered.

For time-dependent, nonlinear analysis energy and neutron production are

overpredicted by the assumption of constant volume since both are pro-


portional to the square of the ion density.


More detailed anal


yses


the future will incorporate temperature-dependent as well as magnetic


and other dynamic


conditions that can affect the volume occupied by the


plasma independent of whether the plasma density has changed.


liminary global analy


Some pre-


of such plasma volume variations have been


19-21,96
reported for pure fusion models


and additional work is under-


97,98The analysis was directed ultimately to the kinetic behavior


of the hybrid so the inclusion of the added complication of a variable

plasma volume in this initial treatment of the plasma neutron source

driving a power-producing blanket was not justified.


The inherent behavior and characteristic


of the point model fusion-


ing plasma used for analysis


in thi


study i


completely described by


Eq. (20), Eq. (21), and Eq.


In fact


, the plasma response to any


input perturbation


as well as its equilibrium characteristic




-74-


with the driven nature of the hybrid subcritical blanket, the third

equation for the specific neutron production rate was also necessary;

without neutrons produced in and hence output from the plasma, no inter-


action i


possib


between the two component halves of the hybrid system.


Note that these neutrons are produced in the plasma and inherently drive


the blanket; however, there i


plasma is affected by the neutrons themsel


no inherent reverse effect whereby the


or by the blanket itself.


The neutrons and their effects are strictly feedforward in nature.


The volumetric neutron production rate


q (t), is an intrinsic


variable--characteristic of the condition of the plasma represented by


the state variabi


of ion density and temperature only.


The volumetric


neutron production rate was multiplied by the effective plasma volume,


V to obtain the


total plasma neutron production rate, Q (t


follows:


Qp(t)


= q (t)
'p


p (23)


where the total neutron production rate is an extrinsic variable charac-


teristic of a


specific plasma with constant effect


volume, V


other words, Q (t) is


characteristic not of all plasmas in a state de-


scribed by an ion density and a temperature


but only of those specific


plasmas whose


volumes satisfy Eq. (23)


This extrinsic variable could


useful for relating specific


blanket; however, for this genera


plasmas to the corresponding hybrid


development, the volumetric neutron


production rate was more useful


since it is the intrinsic variabi


from


which any specific pure fusion or hybrid plasma can be analyzed.


Indeed,




-75-


constant volume will be simply multiplicative--the larger the plasma,

the greater the system power production.

The density equation was rewritten in the following simplified form:


dn(t)= S(t)
=S(t)


- n(t) f2
nf (T)n (t
n


where the temperature-dependent coefficient, fl(T), was defined as follows


to simplify the burnup


term:


f,(T)


Similarly, Eq


DT
2


1) for the plasma energy density was also simplified


preparatory to linearization by rewriting it in the following form after


Ohta:


d[n(t)T(t)]
dt


f,(T)n


n(t)T(t) +
fE


TsS(t)


where the temperature-dependent coefficient, f2(T), was used to account

for charged alpha particle heating and bremmstrahlung radiation,


respectively


CclV>D T~c


fo(T)


(27)


bT32
3


Although it was not so complicated, the equation for the volumetric

neutron production rate was also redefined as follows:


qn(t)


= g(T)n2(t)


(28)


v




-76-


It is noteworthy that g(T) in the neutron production equation and


fl(T) in the burnup term of the particle


a factor of two (2)


density equation differ only by


follows:


= 2fl(T)


which simply means that two (2) ions must undergo fusion burnup for each

neutron produced.


The Linearized Plasma Mode


The global plasma equations were linearlized in order to facilitate


analysis of stability regimes in the frequency domain.


At this point


contrary to previous work


3,24,95


specific perturbations were intro-


duced into the point model plasma equations


Since the feedrate,


is the only external influence appearing in both the density and tem-

perature point model equations, the feedrate was chosen as the typical


source perturbation for the


choice was logical


examination of global plasma stability


the driving force for the entire fusioning energy


producer is ultimately supplied by


the plasma feedrate.


The same depen-


dence on feedrate is applicable for the hybrid


stem, since the hybrid


will be entirely dependent for energy production on the plasma-produced


neutrons because of the blanket subcriticality.

neutrons is ultimately governed by the state of


But the production of


' the plasma (ion density


and temperature) which itself i


driven and sustained by the


feedrate of


energetic fuel ions.


Therefore, examination of the hybrid system response


.. -~ L. -.1
fl 5" J*% .n S in L.. 5 S La - S -.
j**. ri .,. S. -. n .. -d 4- 1 -


S(t),




-77-


For inherent stability and control analyses, the system response to


small external or internal perturbations was a primary concern.


Depen-


dent variable perturbations about steady-state values were used to generate


a dynamic variation in the point model equations.


the following necessarily small variabi


For linear analysis


perturbations were used:


n(t)


T(t)


+ 6n(t)


(31a)


+ 6T(t)


(31b)


+ 6S(t)


(3)


qp(t)


= qPo


+ 6qp(t)


(31d)


where the subscript "o" was used to designate a system variable at an


initial


steady-state equilibrium value about which a small perturbation


in the variable, represented by


6-terms was


introduced so the system could


subsequently examined for stability in linearized form.


In other words,


the time-dependent arbitrary perturbations in ion density, 6n(t), plasma


temperature, 6T(t)


source feedrate


(t), and volumetric neutron pro-


duction rate


6qp,


were required to be small to validate the lineariza-


tion of the point model equations.


These perturbed variable


were sub-


stituted into the point model dynamics equations along with first order

linear expansions for all the density- and temperature-dependent coeffi-


clients in these equations.


The objective was to obtain linearized


perturbed equations from the three original nonlinear plasma dynamics

equations for the plasma ion density, temperature, and volumetric neutron




-78-


The inverse confinement time coefficients were examined using pro-


cedures from previous analyses of global plasma behavior.


15,16,23,24


Both the particle and energy confinement times were assumed to depend


exclusively


y on the plasma ion density and temperature state variabi


= F(n,T)


Therefore


, fo


owing the


example of Ohta


both inverse confinement times


were


expanded about an initial steady-state in first order Taylor series


in the dependent density and temperature variables as follows:


Tn(t)


5T(t)


6n(t) 1 6T(t)
n T, T


(33a)


1~


1
-~ -


The constants 1/1,nl


1

6n(t) + E
0


6T(t)


6n(t) + 1 6T(t)
n E,, T


ITT,


, 1/nl, ,and


(33b)


/rT1 were used to reduce


complexity of analytical manipulations.


to denote quantiti


The subscript "o" was used again


in an initial steady-state condition about which the


system was somehow to be perturbed and subsequently examined for stability


- +


*1


1
T




-79-


Each of the other three temperature-dependent coefficients (no


density dependence) was also


From the particle


expanded


expanded in a simple linear Taylor series.


equation the temperature-dependent coefficient was


as follows:


6T(t)


The temperature-dependent bremsstrahlung and alpha heating coefficient


in the energy density equation was expanded


af2(T)


fjTi


Finally


similarly:


6T(t)


, the temperature-dependent coefficient in the equation for the


volumetric neutron production rate becomes:


g(T)


= g(To) + aT)
yv 4


6T(t)


(36)


A linearized system of plasma equations can now be produced by substitu-

tion of the perturbed variables from Eq. (33) and the various coefficient

expansions into the plasma model equations.

Substitution of the first order variable and coefficient expansions


into the plasma particle


equation yields the following equation:


+ 6S(


- [+
1
C +
n
0


,..r\


n( t) 1 i 6T(t)
n -- ---]no


+ an(t)]


dan(T)
dt


fl


f2(T~)+




-80-


The steady-state condition in the expanded particle equation was eliminated

using the steady-state equilibrium condition.

Two additional coefficients were defined from the effect of including


burnup via fl (T) in thi


model


specifically, the


effective confinement


time for particle


burnup effects.


due to any 1


Certainly


mechanisms is reduced by including


, fusion of particles is a loss mechanism.


subscript "b" was used in defining inverse confinement time terms to

account for the increased loss of plasma ions by fusion as follows:


S= 2n f
T. o0 1


af, (T


= n T
o o


(39)


By eliminating the steady-state solution and neglecting all terms above

the first order in the perturbed variables and coefficients, the following

linearized equation for the perturbed plasma ion density was obtained:


d6n(t)
dt


6S(t) 1_ +
n T


+ 1 n(t) 1 6T(t)
b, o T1 b, o


.(40)


The inclusion of burnup results in an additional burnup-dependent

inverse confinement time term as well as the usual density- and


temperature-perturbed terms. This dual effect fc

the dependence of burnup on both state variables.


allows directly from


Note that the addition


of inverse confinement time terms results in lowered overall particle