10.23 CWIGGLER—Tracks through a wiggler using canonical integration routines of Y. Wu (Duke University).

Tracks through a wiggler using canonical integration routines of Y. Wu (Duke University).
Parallel capable? : yes
GPU capable? : no
Back-tracking capable? : no

Tracks through a wiggler using canonical integration routines of Y. Wu (Duke University).

Tracks through a wiggler using canonical integration routines of Y. Wu (Duke University).

This element simulates a wiggler or undulator using a modified version of Ying Wu’s canonical integration code for wigglers. To use the element, one must supply an SDDS file giving harmonic analysis of the wiggler field. The field expansion used by the code for a horizontally-deflecting wiggler is (Y. Wu, Duke University, private communication).

(37)

where is the peak value of the on-axis magnetic field, the C_mn give the relative amplitudes of the harmonics, the wavenumbers statisfy k_ym² = k_xl² + k_zn², and θ_zn is the phase.

The file must contain the following columns:

• The harmonic amplitude, C_mn, in column Cmn.
• The phase, in radians, in column Phase. The phase of the first harmonic should be 0 or π in order to have matched dispersion.
• The three wave numbers, normalized to k_w = 2π∕λ_w, where λ_w is the wiggler period. These are given in columns KxOverKw, KyOverKw, and KzOverKw.

In Version 17.3 and later, for matrix computations elegant uses a first-order matrix derived from particle tracking when it encounterse a CWIGGLER. Tests show that this gives good agreement in the tunes from tracking and Twiss parameter calculations. For radiation integrals, an idealized sinusoidal wiggler model is used with bending radius equal to Bρ∕(B₀ ∑ C_mn) for each plane. Energy loss, energy spread, and horizontal emittance should be estimated accurately.

elegant allows specifying field expansions for on-axis B_y and B_x components, so one can model a helical wiggler. However, in this case one set of components should have θ_zn = 0 or θ_zn = π, while the other should have θ_zn = ±π∕2. Using Wu’s code, the latter set will not have matched dispersion. Our modified version solves this by delaying the beginning of the field components in question by λ∕4 and ending the field prematurely by 3λ∕4. This causes all the fields to start and end at the crest, which ensures matched dispersion. The downside is that the (typically) vertical wiggler component is missing a full period of field. One can turn off this behavior by setting FORCE_MATCHED=0.

Additional field expansions

Y. Wu’s code included field expansions for a vertically-deflecting wiggler as well as the horizontally-deflecting wiggler given above. In both cases, these expansions are suitable for a wiggler with two poles that are above/below or left/right of the beam axis. They are not always suitable for devices with more complex pole geometries.

Another geometry that is important is a “split pole” wiggler, in which each pole is made from two pieces. Such configurations are seen, for example, in devices used to produce variable polarization. In such cases, the expansion given above may not be appropriate. Here, we summarize the form of the various expansions that elegant supports. For brevity, we show the form of a single harmonic component.

Horizontal wiggler, normal poles, produces B_y only on-axis. Specified by setting BY_SPLIT_POLE=0, and giving BY_FILE or SINUSOIDAL=1 with VERTICAL=0.

Experimental feature: Horizontal wiggler, normal poles, with transverse gradient, producesB_y only on-axis. Specified by setting BY_SPLIT_POLE=0, SINUSOIDAL=1, TGU=1, VERTICAL=0. The TGU normalized gradient is given using the TGU_GRADIENT parameter. Taking a as the normalized gradient, the fields are[54]

Horizontal wiggler, split poles, produces B_y only on-axis. Specified by setting BY_SPLIT_POLE=1, and giving BY_FILE or SINUSOIDAL=1 with VERTICAL=0.

Vertical wiggler, normal poles, produces B_x only on-axis. Specified by setting BX_SPLIT_POLE=0, and giving BX_FILE or SINUSOIDAL=1 with either VERTICAL=1 or HELICAL=1.

Vertical wiggler, split poles, produces B_x only on-axis. Specified by setting BX_SPLIT_POLE=1, and giving BX_FILE or SINUSOIDAL=1 with either VERTICAL=1 or HELICAL=1.

Splitting wigglers

The CWIGGLER element supports a limited ability to split a long element into parts using the element_divisions command or the divide_elements pararameter of the run_setup command.

In addition, if contiguous CWIGGLER elements are seen in a beamline, they will be treated as part of the same element. That means that the pole factors will be ignored except at the ends of the sequence. For this purpose, CWIGGLER elements separated only by MARK or WATCH elements are considered to be contiguous.