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ZTRANSVERSE

A simulation of a single-pass broad-band or functionally-specified transverse dipole 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?
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)
INPUTFILE   STRING NULL name of file giving impedance (BROAD_BAND=0)
FREQCOLUMN   STRING NULL column in INPUTFILE containing frequency
ZXREAL   STRING NULL column in INPUTFILE containing real impedance for x plane
ZXIMAG   STRING NULL column in INPUTFILE containing imaginary impedance for x plane
ZYREAL   STRING NULL column in INPUTFILE containing real impedance for y plane
ZYIMAG   STRING NULL column in INPUTFILE containing imaginary impedance for y plane
BIN_SIZE $S$ double 0.0 bin size for current histogram (use 0 for autosize)
INTERPOLATE   long 0 interpolate wake?
N_BINS   long 128 number of bins for current histogram
MAX_N_BINS   long 0 Maximum number of bins for current histogram
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
DX $M$ double 0.0 misalignment
DY $M$ double 0.0 misalignment

A simulation of a single-pass broad-band or functionally-specified transverse dipole impedance.
Parameter Name Units Type Default Description
FACTOR   double 1 Factor by which to multiply x and y impedances.
XFACTOR   double 1 Factor by which to multiply x impedance.
YFACTOR   double 1 Factor by which to multiply y impedance.
WAKES   STRING NULL filename for output of wake
WAKE_INTERVAL   long 1 interval in passes at which to output wake
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.





This element allows simulation of a transverse 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

\begin{displaymath} Z(\omega) = \int_{-\infty}^{+\infty} e^{-i \omega t} W(t) dt \end{displaymath} (34)

where $i = \sqrt{-1}$, $W(t)=0 for t<0$, and $W(t)$ has units of $V/C/m$. Note that there is no factor of $i$ in front of the integral. Thus, in elegant the transverse impedance is simply the Fourier transform of the wake. This makes it easy to convert data from a program like ABCI into the wake formalism using sddsfft.

For a resonator impedance, the functional form is

\begin{displaymath} Z(\omega) = \frac{-i\omega_r}{\omega} \frac{R_s}{1 + iQ(\frac{\omega}{\omega_r} - \frac{\omega_r}{\omega})}, \end{displaymath} (35)

where $R_s$ is the shunt impedance in $Ohms/m$, $Q$ 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.

next up previous
Next: Examples Up: Element Dictionary Previous: ZLONGIT
Robert Soliday 2007-04-02