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| Subject | ： Re: SAD Update. V1.0.10.3a Fringe of K0 in MULT |
| Date | ： 2008/12/05(Fri) 20:43:50 |
| Contributor | ： K. Oide |
Dear Users,
I think nothing has been wrong on the tracking of fringe, for Kn, n>= 1.
One can sill argue on the fringe of K0, though. The fringe field of K0 can
include arbitrary sextupole component which is proportional to f''(z),
where f(z) is the longitudinal profile of the dipole filed, without violating
the rotational symmetry. In the case of higher poles, such arbitrariness
appears only in much higher order (e.g. K5 for K1), so they should be
omitted. Actually the tracking routine up to now has chosen the
generating function of the frringe of K0 as
G = B/8/p (-2 py1 x y + px1 (x^2+3y^2))
which is different from usual form
G' = B/2/p ( px1 y^2)
by
dG = G - G' = B/8/p (-2 py1 x y + px1 (x^2-y^2))
that corresponds to a particular choice of the arbitrary sextupole component.
Actually G is derived from a general expression for any n.
As the model magnet wants to simulate a horizontally flat magnet, one should
use G' instead of G, I think G' is more natural than G in most cases. Therefore
the next version of SAD will change the tracking routine for K0 fringe to use G'.
>
> 1. The next version, V1.0.10.3a will include the edge forcus due to K0 of MULT in emittance and calculate optics. It has been included only intracking for many years, but not in EMIT and CALC. It will be able to disable it by setting DISK0FR=1 in each MULT element. The default is DISK0FR=0, which includes the edge effect. Also the fringe effects of Higher Kn (n>1) in MULT have been included in tracking only, but they are not installed neither in emittance nor calc yet.