Elements/DECA

DECA †

A decapole magnet.

DISFRIN: If nonzero, the nonlinear Maxwellian fringe is suppressed.
DISRAD: If nonzero, the synchrotron radiation in the particle-tracking is inhibited.
DX: Horizontal displacement of magnet. This applied before the rotation by ROTATE.
DY: Vertical displacement of magnet. This applied before the rotation by ROTATE.
K4: The normal 10-pole magnetic field component (times the length L).
where L is the length of the component. Positive sign means horizontal focusing.
L: Effective length.
ROTATE: Rotation in x-y plane. After displacing the magnet by DX and DY, rotate the magnet around the local s-axis by -(amount given by ROTATE), then place the component. At the exit rotate back the magnet around the local s-axis at the exit, then take out displacement.
transformation: The transformation in a DECA is given as
where L and H4 are Hamiltonians of a drift of length L and a thin decapole kick of integrated strength K4:
respectively. The coeffients are and b = 1/2 - a. Terms and are transformations for entrance and exit nonlinear fringes. The term exp(:V4:) is a correction to adjust the third-order terms in L:

  V4 = (SUM over j=(x,y), k=(x,y)) [
             - beta/2 (H4,k)^2 
             + gamma (H4,j H4,k H4,j,k)] ,

where ,i represents the derivertive by x or y. We have also introduces two coefficients a math image and .