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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 9223372036854775807 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.
BUNCHED_BEAM_MODE   long 1 If non-zero, then do calculations bunch-by-bunch.
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

\begin{displaymath}
Z(\omega) = \int_{-\infty}^{+\infty} e^{-i \omega t} W(t) dt
\end{displaymath} (98)

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

\begin{displaymath}
Z(\omega) = \frac{R_s}{1 + iQ(\frac{\omega}{\omega_r} - \frac{\omega_r}{\omega})},
\end{displaymath} (99)

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.
  3. Using the broad-brand resonator model can often result in a very large number of bins being used, as elegant will try to resolve the resonance peak and achieve the desired bin spacing. This can result in poor performance, particularly for the parallel version.

Bunched-mode application of the impedance is possible using specially-prepared input beams. See Section 6 for details. The use of bunched mode for any particular ZLONGIT element is controlled using the BUNCHED_BEAM_MODE parameter.





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.


next up previous
Next: ZTRANSVERSE Up: Element Dictionary Previous: WIGGLER
Robert Soliday 2014-06-26