Possible low-pass filter

[headdoggy64]

Dear all elegant users,

Are there any low-pass density modulation filters built in elegant lattice element DRIFT and/or distribution generation routine?


Thanks,
Alex

[michael_borland]

Alex,

No, this has to be done ahead of time. There's a script called smoothDist6 that does it.

--Michael

[headdoggy64]

Thanks, Michael!

I meant a different thing. If I compute bunching factor and plot it versus energy, I persistently see a cut-off at a given frequency (see attached). This exists with both LSC on and off and also does not change for different bunch parameters. To me it looks like there is a limiting low-pass filter of some sort or round-off issue. By the way, does elegant use full 64-bit double precision everywhere? Can you please comment on this?

Here is the script I am using to generate data file for the plot attached.

Thank you for your time!

Code: Select all

#!/usr/bin/tclsh
set i 14
set input [lindex $argv 0]
set output [lindex $argv 1]
exec rm -rf $output
while {$i < 16} {

for {set j 1} {$j < 100} {incr j} {
set logw [ expr $i + log10($j/10.0)];
exec echo -n $logw  >> $output
exec echo -n " " >> $output
set pcentral [exec sddsprintout $input -par=pCentral -noLabel -notitle -formatDefaults=double=%16.16e | grep .]
exec echo -n $pcentral >> $output
exec echo -n " " >> $output
set w [ expr $j/10.0*pow(10,$i)];
exec sddsprocess $input -pipe=out "-redef=parameter,omega,$w" "-redef=col,CosWt,omega t * cos n_rows /" "-redef=col,SinWt,omega t * sin n_rows /" "-process=CosWt,sum,ReB" "-process=SinWt,sum,ImB" "-redef=par,bfactor,ReB ReB * ImB ImB * +" | sddsprintout -pipe -parameter=bfactor -noTitle -nolabel -formatDefaults=double=%16.16e  >> $output | grep .
}

    incr i
}

Output format: log(w) | beta*gamma | n(w).
Then all output files are combined together and plotted in gnuplot.

[headdoggy64]

I made another scan for higher beta*gamma values to further illustrate the issue.

[michael_borland]

Alex,

I'm looking into this but might not get back to you for a week because of travel.

--Michael

[headdoggy64]

Thanks, Michael!
I have been struggling with this for a long time and your help will be very appreciated.

Alex

[michael_borland]

Alex,

I'm looking at it today. While elegant does all computations in double-precision floating point, the random number generator is limited to 48 bits. Whether that affects the results I don't know. Hope to have more later today.

--Michael

[michael_borland]

Alex,

I've done simulations with various numbers of particles, just taking the t coordinates from the bunched_beam command without any tracking. The bunching factor gets noisy above a certain frequency, which increases slowly as the number of particles increases. Better results are obtained using Halton sequences (i.e., "quiet start").

Here's my result when I use the random number generator

Bunching factor using random number generator.

Here's my result when I use Halton sequences

Bunching factor with Halton sequences.

I'm uncertain still if the cause of the problem is the use of 48-bit random numbers. I'd need to implement a new set of random number generators to test this.

--Michael

[headdoggy64]

Michael,

Thanks for the reply!

I included these lines in my bunched_beam section

Code: Select all

  halton_sequence[0] = 1,
  halton_sequence[1] = 1,
  halton_sequence[2] = 1,

and ran the same configuration again. I am still running into the issue.
Can this come from the implementation of the longitudinal space-charge algorithm?
Is the wavenumber k in the impedance Z(k) limited from above by some large value?

Thanks for your help!

P.S. The plot represents the bunching factor n(w). Y-axis is beta*gamma and X-axis is log w.

[michael_borland]

Alex,

I think you need to give a few more parameters for the Halton sequence to work. I suggest adding

Code: Select all

	symmetrize = 0,
        enforce_rms_values[2]    = 0
        halton_sequence[2] = 1,
        halton_radix[4] = 2,3
        optimized_halton = 1

This isn't going to cure the problem but may extend the smooth region of the spectrum out to slightly higher frequencies.

--Michael