By Thomas P. Wangler
The 1st ebook that offers a unmarried resource of introductory details an all linear accelerators, together with electron and ion accelerators.
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Additional info for RF Linear Accelerators (Wiley Series in Beam Physics and Accelerator Technology)
8) is an important result that we will use frequently. The phase @ = 0 if the particle arrives at the origin when the field is at a crest. It is negative if the particle arrives at the origin earlier than the crest, and positive if it arrives later. Maximum energy gain occurs when 4 = 0 , which is often the choice for relativistic electrons. But we will see later that for nonrelativistic particles, where longitudinal focusing is important, it is necessary to operate with negative phases for the particles in the bunch.
Gough, W. T. Weng, and A. J. Jason, presented at the 5th European Part. Accel. Conf. Barcelona, Spain, June 10-14, 1996. H. R. Haseroth, Proc. 1996 lnt. , Geneva, August 26-30, 1996, p. 283. l 7 Compendium ofScienti$c Linacs, 18th Int. , CERN-PS 96-32 (DI), Geneva, August 26-30, 1996 l X The Stunford Two-Milr Accelerator, ed. R. B. Neal, W. A. Benjamin, New York, 1968; W. K. H. Panofsky, Proc. 18th Int. Linear Accel. , August 26-30, 1996, Geneva, ed. C. Hill and M. Vretenar, CERN 96-07, Geneva, November 15, 1996, p.
1. This is a more realistic approximation, because it constrains the field to vanish only at the bore radius inside the conductor rather than on the axis at the end of the gap. Thus we require that From Eq. 19), this leads to 1. VilT(o,k)-1 2E, . 38) -X From Eq. O) = ST'dzE(O,z) = Vo, or T(0) = T(O,O) = 1, and at k and r = a, Eq. 25) gives T(a,O) = Jo(Koa),where Ko = 27r/h. Then =0 RF ACCELERATION IN LINACS For p 5 1 we obtain from Eqs. 43) It is usually a good approximation that Jo(27ra/h) z 1.