ZLONGIT

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

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
WAKES		STRING	NULL	filename for output of wake
WAKE_INTERVAL		long	1	interval in passes at which to output wake
AREA_WEIGHT		long	0	use area-weighting in assigning charge to histogram?
INTERPOLATE		long	0	interpolate wake?
SMOOTHING		long	0	smooth current histogram?
SG_ORDER		long	1	Savitzky-Golay filter order for smoothing
SG_HALFWIDTH		long	4	Savitzky-Golay filter halfwidth for smoothing
REVERSE_TIME_ORDER		long	0	Reverse time-order of particles for wake computation?
FACTOR		double	1	Factor by which to multiply impedance.

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

$$Z(\omega) = \int_{-\infty}^{+\infty} e^{-i \omega t} W(t) dt$$ (11)

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

$$Z(\omega) = \frac{R_s}{1 + iQ(\frac{\omega}{\omega_r} - \frac{\omega_r}{\omega})},$$ (12)

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.