BEVATRON RESEARCH MEETING III - BEVATRON THEORY Page: 4 of 5
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() UClt 2384
during the accoloration. At the and of tho inoe tion cycle the instantaneous
circle rill be at the center of the vacuum chamber, and Betatron oscillations iill
fill the entire ohambr. If the acceloration voltazQ is turned on at that instant,
the maximum portion of the boam uill be caught in tho synchronous orbit. if however,
the voltage is turned on earlier or later, the corresponding portion of the beam
will b: scraped off on tho tank valls. Phaso oscillations which begin at the
moment tho R-F is turned on 'ill causo perhaps 25 porcont loss of the boam uhon
the amplitude adds to the Botatron oscillations which already fill the tank.
Another source of boam losa is tho finite simc of the infloector, uhich ill obstruct
ions, particularly thoso injected oarly. A 25 percent loss of boam might bo
oxpectod from this effort. An ostimato of the good injected beam in terms of the
acceptance timo of tho machine is perhaps that 250 p.soc of tho 500 izsec theoretical
acceptanef tino till be useful, Assuming that 30 micro ampcros of protons leave
tho linear acoolorators, 2 x 1010 particles por pulse should be attainalo. This
should be contrasted with the coamotron shcro only 50 iJsoc of acceptanec timo
results fron the theoretical 250 tsoe. That acceptance time is understandable by
the abovo arguments, but their losses in the nxt 100 milliseconds arc not explained.
c.'aeqncToloranu Accclration
Ihstoad of interpreting equation (1) in terms of radial errors one can determine
the pormissablo frquoney errors in torms of tho available radial width of the field.
Roforring to equation (4) and using tho expression of oncrgy in equation (9), ono
has
- (1-n) e l+ n . 1 (13}
r L1-n 7/
- n jj4 02 (b1_
It should be roTaarked at this point that all tho abovo derivations havo
nogleoted the effect of straight sections, so that (16), for example, is not quite
correct. Hovover, the effects are not very important in terms of frequoney
toleranco, :to. In equation (18) assuming a radial width of field of the ordor of
4 feat, the frequency must always bo held closer than + 4 percent. Actually vo
mould liko to achicvo tho tolerance at the ordor of .1 percent, to avoid appreciable
loss at injection and later ,hon the good field width shrinks with increasing
saturation.
Rosonanco Effects
Choice of n value at 0.6 resulted from a caroful study of the possible resonances
in tho ion orbit. JRosonanco growth of the phase oscillations may result from field
ripple. Theao Mould bo duo to the iacasurod 20 rilligauss ripple at 1,440 cycles
and would occur a fow tenths of a second aftor injection. There is reason to bo-
live that the fact that phase oscillation frequoney doponds on phase aplitudo will
prevent any savero trouble.
Thore are a number of random effoets rhich could conceivably causo boam loss.
During the long acceleration tiac, thero is no asimuthal damping of phaso oscillation.
Thus any random changes of frequency, accelerating Voltage, and Mgnctic perturbations
incroases the asimuthal spread of the beam. Those effects add up as in a random valc
problo; the phase amplitude due to a succession of random impulses during tho
ac coloration period iill bo proportional to the square root of the number of impulso.i.
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Smith, Lloyd. BEVATRON RESEARCH MEETING III - BEVATRON THEORY, report, October 20, 1953; Berkeley, California. (https://digital.library.unt.edu/ark:/67531/metadc1015303/m1/4/: accessed April 24, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.