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WIGGLER

A wiggler or undulator for damping or excitation of the beam.
Parallel capable? : yes
Parameter Name Units Type Default Description
L $M$ double 0.0 length
RADIUS $M$ double 0.0 Peak bending radius. Ignored if K or B is non-negative.
K   double 0.0 Dimensionless strength parameter.
B $T$ double 0.0 Peak vertical magnetic field. Ignored if K is non-negative
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
FOCUSING   long 1 If 0, turn off vertical focusing (this is unphysical!)
GROUP   string NULL Optionally used to assign an element to a group, with a user-defined name. Group names will appear in the parameter output file in the column ElementGroup





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 were computed analytically using Mathematica, including the variation of the horizontal beta function and dispersion. For an odd number of poles, half-strength end-poles are assumed in order to match the dispersion of the wiggler. For an even number of poles, half-length end poles are assumed (i.e., we start and end in the middle of a pole), for the same reason.

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)

\begin{displaymath}
K_1 = \frac{1}{2\rho^2},
\end{displaymath} (96)

where $\rho$ is the bending radius at the center of a pole. The undulator is focusing in the vertical plane.

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

\begin{displaymath}
K = \frac{\gamma \lambda_u}{2 \pi \rho},
\end{displaymath} (97)

where $\gamma$ is the relativistic factor for the beam and $\lambda_u$ is the period length.
next up previous
Next: ZLONGIT Up: Element Dictionary Previous: WATCH
Robert Soliday 2014-06-26