10.126 ZTRANSVERSE—A simulation of a single-pass broad-band or functionally-specified transverse impedance.

A simulation of a single-pass broad-band or functionally-specified transverse impedance.
Parallel capable? : yes
GPU capable? : no
Back-tracking capable? : no






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∕mdouble 0.0

shunt impedance (Rs=Ra/2=Vˆ2  /(2*P))






Q double 0.0

cavity Q






FREQ Hz double 0.0

frequency (BROAD_BAND=1)






INPUTFILE STRINGNULL

name of file giving impedance (BROAD_BAND=0)






FREQCOLUMN STRINGNULL

column in INPUTFILE containing frequency






ZXREAL STRINGNULL

column in INPUTFILE containing real impedance for x plane






ZXIMAG STRINGNULL

column in INPUTFILE containing imaginary impedance for x plane






ZYREAL STRINGNULL

column in INPUTFILE containing real impedance for y plane






ZYIMAG STRINGNULL

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

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






ZTRANSVERSE continued

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






Parameter Name UnitsType Default

Description






DX M double 0.0

misalignment






DY M double 0.0

misalignment






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 STRINGNULL

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






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.






X_DRIVE_EXPONENT long 1

Exponent applied to x coordinates of drive particles






Y_DRIVE_EXPONENT long 1

Exponent applied to y coordinates of drive particles






X_PROBE_EXPONENT long 0

Exponent applied to x coordinates of probe particles






ZTRANSVERSE continued

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






Parameter Name UnitsType Default

Description






Y_PROBE_EXPONENT long 0

Exponent applied to y coordinates of probe particles






BUNCHED_BEAM_MODE long 1

If non-zero, then do calculations bunch-by-bunch.






ALLOW_LONG_BEAM long 0

Allow beam longer than covered by impedance data?






GROUP stringNULL

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 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

       ∫ +∞
Z(ω) =      e- iωtW (t)dt
        -∞
(166)

where i = √--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

       - iω        R
Z(ω) = ----r-------ωs---ωr-,
         ω  1 + iQ (ωr - ω )
(167)

where Rs is the shunt impedance in Ohms∕m, Q is the quality factor, and ωr is the resonant frequency.

When providing an impedance in a file, the user must be careful to conform to these conventions. In addition, the units of the frequency column must be Hz, while the units of the impedance components must be Ohms/m. At present, elegant does not check the units for correctness.

Other notes:

  1. The frequency data required from the input file is not ω, but rather f = ω∕(2π).
  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. Impedance data can be created from a wake function using the script trwake2impedance, which is supplied with elegant. This script also illustrates how to scale the data with the frequency spacing. The script uses sddsfft, which produces a folded FFT (f 0) from a real function. The folded FFT representation involves multiplying the non-DC terms by 2. elegant expects this and internally multiplies the DC term by 2 as well.
  4. 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.
  5. Wake output is available only in the serial 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 ZTRANSVERSE element is controlled using the BUNCHED_BEAM_MODE parameter.