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ATOMIC ENERGY COMMISSION
.SOME OPERATING PHENOMENA ASSOCIATED WITH THE 184-INCH CYCLOTRON
Do C. Sewell
Radiation Laboratory, Department of Physics
University of California
..ubdished for use within the Atomic Energy Commission, Inquiries for additional copies
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~Iate of Manuscript: June 13, 1947
loctument Declassified: July 9, 1947
This document consists of 5 pages.
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SOME OPERATING PHENOMENA ASSOCIATED WITH THE 184-INCH CYCLOTRON
By D. C. Sewell, L. Henri'ch and J. Vale
Radiation Laboratory, Department of Physics
University of California
June 13, 1947
The maximum energy to which particles can be accelerated in a cyclotron is limited
by the maximum value of H P, where H is the value of the magnetic field at a radius P .
i;THe maximum value of H P occurs at the radius where P dH +1= 0. If the
; H dP
quantity n P= is defined, then n = 1 at the maximum energy (Figure 1).
-The point n = 1 occurs in the 184-inch cyclotron, at a radius of 85 inches. It was ex-
pected, therefore, that the particles would continue to be accelerated until they reached
'his radius, but it was found that the beam disappeared at a radius of 82 inches. It was
...suggested that a rapid increase in the vertical oscillations of the ions at the 82-inch radi-
us caused the beam to hit the dee. This theory was checked by a series of experiments
i:: using special "c" shaped targets placed at different radii in the cyclotron (Figure 2). Ra-
dioautographs of these special targets were taken after they had been bombarded. They
*- : showed that at radii less than 82 inches the vertical beam spread was less than 2-1/2
inches and,therefore,was small enough to expand radially through the horizontal slot in
;: the target. However, the vertical spread at the 82-inch radius was large enough to cause
the ions to hit the top and bottom of the slot in the target (Figure 3). Also, a sharp peak
of radioactivity was found on the dee lip at the 82-inch radius, which gave additional ev-
idence that the beam was spreading vertically in this region. The energy to build up these
vertical oscillations seems to arise from the coupling between the vertical and the radial
oscillations. These two oscillations go through a harmonic resonance at a radius of 82
inches (Figure 4). The energy of these oscillations can be expressed as
mw a (Zmax)
d P (Apmax) m+ max)
At n= 0.2
2 .m .2 [4( max Zma)
W= wo2(0.2) +(z)2
Hence, if all the energy of radial oscillation is converted to that of vertical oscilation, the
i:: amplitude of vertical oscillation will be, at times, at least double that of the radial oscilla-
- 1 -
It must be kept in mind for systems having low accelerating voltages similar to the
184-inch cyclotron, that the ions will rapidly increase the amplitude of their vertical oscil-
lations at the point where n = 0.2. The solution of the problem of accelerating particles
past the radius where n = 0.2 in the 184-inch cyclotron has been postponed, since the avail-
able energy of the ions at this radius is within 5 per cent of the maximum of the system.
A number of studies have been made using a synchroscope to observe the time struc-
ture of the beam current collected by a current reading probe placed in the circulating
beam. As was expected, the beam arrives at such a probe in a series of pulses. These
pulses are due to the frequency modulation of the cyclotron, one pulse occurring each time
the cyclotron goes through an F. M. cycle. However, in addition it was observed that each
of these pulses showed a fine structure consisting of a series of amplitude modulated mi -
nor pulses (Figure 5). The frequency and number of these minor pulses was found to de-'
pend on the probe radius. This fine structure of the beam is apparently caused by the rad-
ial oscillations of the ions with respect to the probe. This net oscillation at the probe is
the result of two independent oscillations that the ions perform. First, the ions have a
radial oscillation, which is due to the center of rotation of the ions being displaced with
respect to the magnetic center of the system. These free radial oscillations cause a pre-
cession of the centers of rotation, which produces an oscillation of the beam with respect
to the probe. Second, the ion undergoes.a radial phase oscillation (Figure 6).
The frequency of the minor pulses in each beam pulse agrees quite well with the cal-
culated frequency of precession of the center of rotation of the ions about the magnetic
center of the system, which is given by the expression
wprec, = (1 1-n )w .
A further condition for the explanation of the fine structure seems to require that the cen-
ters of rotation of the ions be bunched azimuthally.
The modulation frequency of the minor pulses agrees quite well with the calculated
frequency of the phase oscillations, which is given by the expression
phase= eV cos 0 s K 1/2
SphaseEs 2 7r
where e = charge on ion
v = max. voltage available per revolution
f= phase of the synchronous orbit
Es = energy of the ion in the synchronous orbit
This work has been of aid in getting a better understanding of the motion of ions in the
- 2 -
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- 4 -
ION OF ENERGY E.
SYMMETRY i -p-
H,. MAGNETIC FIELD AT p.
p. EQUILIBRIUM RADIUS, OR RADIUS OF ION OF ENERGY EI,
IN MAGNETIC FIELD OF N.
EQUATIONS OF OSCILLATION :
d' = z I| z/ ,,idLH P dl
da w.2 (-n) ap + 2 : w. P +...
dt--T= ( 1-2 f Pd Z
pr Ef** J
HORIZONTAL OSCILLATION FREQUENCY ABOUT P0
VERTICAL OSCILLATION FREQUENCY "
vWHN n 0.2.: I. n f.r .
iW, f-- 0.2
W Ap- f W.
We '-- W.
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MAGNETT POLE PIECE
UNIVERSITY OF FLORIDA
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