ZLONGIT

A simulation of a single-pass broad-band or functionally specified longitudinal impedance.
Parallel capable? : yes

Parameter Name	Units	Type	Default	Description
CHARGE	$C$	double	0.0	beam charge (or use CHARGE element)
BROAD_BAND		long	0	broad-band impedance?
RA	$Ohm$	double	0.0	shunt impedance
RS	$Ohm$	double	0.0	shunt impedance (Ra=2*Rs)
Q		double	0.0	cavity Q
FREQ	$Hz$	double	0.0	frequency (BROAD_BAND=1)
ZREAL		STRING	NULL	$<$filename$>$=$<$x$>$+$<$y$>$ form specification of input file giving real part of impedance vs f (BROAD_BAND=0)
ZIMAG		STRING	NULL	$<$filename$>$=$<$x$>$+$<$y$>$ form specification of input file giving imaginary part of impedance vs f (BROAD_BAND=0)
BIN_SIZE	$S$	double	0.0	bin size for current histogram (use 0 for autosize)
N_BINS		long	128	number of bins for current histogram
MAX_N_BINS		long	0	Maximum number of bins for current histogram
WAKES		STRING	NULL	filename for output of wake
WAKE_INTERVAL		long	1	interval in passes at which to output wake
WAKE_START		long	0	pass at which to start to output wake
WAKE_END		long	2147483647	pass at which to stop to output wake
AREA_WEIGHT		long	0	use area-weighting in assigning charge to histogram?
INTERPOLATE		long	0	interpolate wake?
SMOOTHING		long	0	Use Savitzky-Golay filter to smooth current histogram?
SG_ORDER		long	1	Savitzky-Golay filter order for smoothing
SG_HALFWIDTH		long	4	Savitzky-Golay filter halfwidth for smoothing

A simulation of a single-pass broad-band or functionally specified longitudinal impedance.

Parameter Name	Units	Type	Default	Description
REVERSE_TIME_ORDER		long	0	Reverse time-order of particles for wake computation?
FACTOR		double	1	Factor by which to multiply impedance.
START_ON_PASS		long	0	The pass on which the impedance effects start.
RAMP_PASSES		long	0	Number of passes over which to linearly ramp up the impedance to full strength.
HIGH_FREQUENCY_CUTOFF0		double	-1	Frequency at which smoothing filter begins. If not positive, no frequency filter smoothing is done. Frequency is in units of Nyquist (0.5/binsize).
HIGH_FREQUENCY_CUTOFF1		double	-1	Frequency at which smoothing filter is 0. If not given, defaults to HIGH_FREQUENCY_CUTOFF0.
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 allows simulation of a longitudinal impedance using a ``broad-band'' resonator or an impedance function specified in a file. The impedance is defined as the Fourier transform of the wake function

$$Z(\omega) = \int_{-\infty}^{+\infty} e^{-i \omega t} W(t) dt$$ (91)

where $i = \sqrt{-1}$, $W(t)=0 for t<0$, and $W(t)$ has units of $V/C$.

For a resonator impedance, the functional form is

$$Z(\omega) = \frac{R_s}{1 + iQ(\frac{\omega}{\omega_r} - \frac{\omega_r}{\omega})},$$ (92)

where $R_s$ is the shunt impedance in $Ohms$, $Q$ is the quality factor, and $\omega_r$ is the resonant frequency.

When providing an impedance in a file, the user must be careful to conform to these conventions.

Other notes:

1. The frequency data required from the input file is not $\omega$, but rather $f = \omega/(2 \pi)$.
2. The default smoothing setting (SG_HALFWIDTH=4), may apply too much smoothing. It is recommended that the user vary this parameter if smoothing is employed.

Explanation of $<$filename$>$=$<$x$>$+$<$y$>$ format: Several elements in elegant make use of data from external files to provide input waveforms. The external files are SDDS files, which may have many columns. In order to provide a convenient way to specify both the filename and the columns to use, we frequently employ $<$filename$>$=$<$x$>$+$<$y$>$ format for the parameter value. For example, if the parameter value is waveform.sdds=t+A, then it means that columns t and A will be taken from file waveform.sdds. The first column is always the independent variable (e.g., time, position, or frequency), while the second column is the dependent quantity.