By B. V. Chirikov (auth.), Acad B. B. Kadomtsev (eds.)
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The strongest difference is due to the phase shift tJ. in the last case. , the asymmetric configuration of the field relative to the singularity. )1: 8 0 (s = 0) -+ 8 ls = s 1)' where sl::::;-vLi/roo::::;-10/19. 38) Note that in both cases the shift is toward a smaller field gradient. 37) agrees with the results of [15], except for a constant phase shift 1111 148, which differs in [15] by +11/4. This difference is possibly due to the fact that in [15] the integration is over a contour in the complex plane of z and not 8 .
1) ] : (r X (p v2 + A»z = r (p1. :... l. 14) are equally valid during both half-cycles of the longitudinal oscillations. 4): Sp \' f (s) ds • e - e + coo, p-l ~1 where 8 1 = 8(Sl) and Sl have Sl -t: 0 (see below). 16) S (s) = Re (sp)' In the general case we For a short trap (see Subsection 2 of Section 3), f(s) = 1 + s2fL2 and sp = iL; Sl = 0; 8 1 = 8 0 , In the small~o approximation [8(S) .. 17) 3 Pm cos ~o The same expression is valid (with a certain effect Lef) also in the case of a multimirror trap (see Subsection 4 of Section 3).
10). Although we do not know the integrand as a function of t, we can express it in terms of the exactly known functions w(s) and R(s) (the specified configuration of the magnetic field) and, generally speaking, the (exactly) unknown function v(s). But the latter is needed only in the singularities, where w = w(sp) = 0 and VII (sp) = v; vJ.. (sp) = 0 in view of v 12 -= 211w. It is important that this result [Vl(Sp) = 0] does not depend on the corrections to 11, provided they are small, i. e. , at sufficiently low E.
