RFDF basic question

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PCaminal
Posts: 15
Joined: 02 Nov 2017, 12:26

RFDF basic question

Post by PCaminal » 14 Nov 2018, 21:15

Hi,

I'm implementing a RFDF element in a diagnostics section beamline. For optimization purposes the structure was divided into two pieces (of half the total length each) in order to put a marker in between. Now, when I simulate a typical time calibration that one would perform experimentally with a LOLA type structure to get the streak parameter and the time resolution, I got different results if I use a single piece of length L or two consecutive pieces of length L/2 (in the second case I get a streak twice as large as in the first case).

My understanding is that this shouldn't make any difference - unless the thin-lens approximation for the RFDF is used. So I am not sure if I am defining the element properly or if I am missing any parameter that could change the behavior of the cavity... Below the definition in the lattice file:

a) divided into two pieces
"TDS.U": RFDF, L=0.4, TILT=1.570796326794897, FREQUENCY=11988000000, N_KICKS=101, VOLTAGE=27000000
"TDS-C": MARK, FITPOINT=1
"TDS.D": RFDF, L=0.4, TILT=1.570796326794897, FREQUENCY=11988000000, N_KICKS=101, VOLTAGE=27000000

b) one single piece:
"TDS": RFDF, L=0.8, TILT=1.570796326794897, FREQUENCY=11988000000, N_KICKS=101, VOLTAGE=27000000

Thanks a lot in advance for your help!

Best regards,
Pau

PCaminal
Posts: 15
Joined: 02 Nov 2017, 12:26

Re: RFDF basic question

Post by PCaminal » 15 Nov 2018, 05:54

Hi again,

I forgot to mention that the result obtained with a "single element" RFDF agrees with the analytically calculated Streak parameter and time resolution, for instance:

Streak = sqrt{beta_at_TDS*beta_at_SCREEN}*e*V*k/E,
Res_z = bs_SCREEN/Streak
Res_t = Res_z/c

where:
beta_at_TDS = beta in the RFDF structure
beta_at_SCREEN = beta in the monitoring screen where the measurement is performed
V = voltage applied to the RFDF
k = wavenumber of the structure (= 2*pi*frequency/c)
E = energy of the electron bunch
bs_SCREEN = beam size in the monitoring screen without the RFDF streaking effect
e, c -> usual physical constants for electron and velocity of light

Again, thanks a lot in advance for your help,
Pau

PCaminal
Posts: 15
Joined: 02 Nov 2017, 12:26

Re: RFDF basic question

Post by PCaminal » 16 Nov 2018, 05:59

Hi,

in case this helps: I printed the individual matrices of the TDS as a single element and as two elements of half the total length. My understanding is that the product of the two matrices with half the length should result in the same matrix as the one for the TDS as a single element... but that's not the case with the matrices given by &matrix_output setup/action namelist...

Here I just print the {y, y', s, d} coordinates, since the streak is in the Y direction:

TDS matrix in one piece of length 0.8 m:

1.000 0.800 -2.713 0.000
0.000 1.000 -6.784 0.000
-0.000 -0.000 1.000 -0.000
6.784 2.713 -6.136 1.000

Half a TDS with length 0.4 (called either TDS.U or TDS.D in the lattice file):

1.000 0.400 -1.357 0.000
0.000 1.000 -6.784 0.000
-0.000 -0.000 1.000 -0.000
6.784 1.357 -3.068 1.000

Product of TDS.D * TDS.U:

1.000 0.800 -5.427 0.000
0.000 1.000 -13.568 0.000
-0.000 -0.000 1.000 -0.000
13.567 5.427 -24.544 1.000

Best regards,
Pau

Björklund
Posts: 84
Joined: 19 May 2016, 07:14

Re: RFDF basic question

Post by Björklund » 29 Nov 2018, 03:22

Hi!

I think your problem is related to your voltage, you have set the integrated voltage in the half-length structures to be the same as for the full-length one.

Best regards
Jonas

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