WIGGLER

Parameter Name	Units	Type	Default	Description
L		double	0.0	length
RADIUS		double	0.0	peak bending radius
K		double	0.0	Dimensionless strength parameter. Ignored if radius is nonzero.
DX		double	0.0	Misaligment.
DY		double	0.0	Misaligment.
DZ		double	0.0	Misaligment.
TILT		double	0.0	Rotation about beam axis.
POLES		long	0	number of wiggler poles

This element simulates a wiggler or undulator. There are two aspects to the simulation: the effect on radiation integrals and the vertical focusing. Both are included as of release 15.2 of elegant.

If the number of poles should be an odd integer, we include half-strength end poles to match the dispersion, but only for the radiation integral calculation. For the focusing, we assume all the poles are full strength (i.e., a pure sinusoidal variation). If the number of poles is an even integer, no special end poles are required, but we make the unphysical assumption that the field at the entrance (exit) of the device jumps instantaneously from 0 (full field) to full field (0).

The radiation integrals are computed by summing the contributions for a series of half-poles. The integrals for a single half-pole were computed analytically using Mathematica, using a sinusoidal field variation. The horizontal beta function and dispersion are propogated correctly for these computations. Of course, the beta function propagates as in a drift space.

The vertical focusing is implemented as a distributed quadrupole-like term (affecting ony the vertical, unlike a true quadrupole). The strength of the quadrupole is (see Wiedemann, Particle Accelerator Physics II, section 2.3.2)

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The wiggler field strength may be specified either as a peak bending radius (RADIUS parameter) or using the dimensionless strength parameter K (K parameter). These are related by

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