WAKE

Longitudinal wake specified as a function of time lag behind the particle.

Parameter Name	Units	Type	Default	Description
INPUTFILE		STRING	NULL	name of file giving Green function
TCOLUMN		STRING	NULL	column in INPUTFILE containing time data
WCOLUMN		STRING	NULL	column in INPUTFILE containing Green function
CHARGE	$C$	double	0.0	beam charge (or use CHARGE element)
FACTOR	$C$	double	1	factor to multiply wake by
N_BINS		long	128	number of bins for current histogram
INTERPOLATE		long	0	interpolate wake?
SMOOTHING		long	0	smooth current histogram?
SG_HALFWIDTH		long	4	Savitzky-Golay filter half-width for smoothing
SG_ORDER		long	1	Savitzky-Golay filter order for smoothing
CHANGE_P0		long	0	change central momentum?
ALLOW_LONG_BEAM		long	0	allow beam longer than wake data?

The input file for this element gives the longitudinal Green function, $W(t)$ versus time behind the particle. The units of the wake are V/C, so this element simulates the integrated wake of some structure (e.g., a cell or series of cells). If you have, for example, the wake for a cell and you need the wake for N cells, then you may use the FACTOR parameter to make the appropriate multiplication. The values of the time coordinate should begin at 0 and be equi-spaced. A positive value of time represents the distance behind the exciting particle.

A positive value of $W(t)$ results in energy loss. A physical wake function should be positive at $t=0$.

Use of the CHARGE parameter on the WAKE element is disparaged. It is preferred to use the CHARGE element as part of your beamline to define the charge.

Setting the N_BINS paramater to 0 is recommended. This results in auto-scaling of the number of bins to accomodate the beam. The bin size is fixed by the spacing of the time points in the wake.

The default degree of smoothing (SG_HALFWIDTH=4) may be excessive. It is suggested that users vary this parameter to verify that results are reliable if smoothing is employed (SMOOTHING=1).

The algorithm for the wake element is as follows:

1. Compute the arrival time of each particle at the wake element. This is necessary because elegant uses the longitudinal coordinate $s=\beta c t$.
2. Find the mean, minimum, and maximum arrival times ($t_{mean}$, $t_{min}$, and $t_{max}$, respectively). If $t_{max}-t_{min}$ is greater than the duration of the wakefield data, then elegant either exits (default) or issues a warning (if ALLOW_LONG_BEAM is nonzero). In the latter case, that part of the beam that is furthest from $t_{mean}$ is ignored for computation of the wake.
3. If the user has specified a fixed number of bins (not recommended), then elegant centers those bins on $t_{mean}$. Otherwise, the binning range encompasses $t_{min}-\Delta t$ to $t_{max}+\Delta t$, where $\Delta t$ is the spacing of data in the wake file.
4. Create the arrival time histogram. If any particles are outside the histogram range, issue a warning.
5. If SMOOTHING is nonzero, smooth the arrival time histogram.
6. Convolve the arrival time histogram with the wake function.
7. Multiply the resultant wake by the charge and any user-defined factor.
8. Apply the energy changes for each particle. This is done in such a way that the transverse momentum are conserved.
9. If CHANGE_P0 is nonzero, change the reference momentum of the beamline to match the average momentum of the beam.