Performance Analysis Using Genesis 1.3

1
Performance Analysis Using Genesis 1.3

• Sven Reiche
• LCLS Undulator Parameter Workshop
• Argonne National Laboratory
• 10/24/03

2
Overview

• Modeling in Genesis 1.3
• SASE - Performance
• Undulator Taper
• Tolerance Study

3
Modeling - Electron Beam

• Using Design Parameter
• Flat profile (70 mm FWHM)
• Current of 3.4 kA
• Normalized emittance of 1.2 mm.mrad
• RMS energy spread of 5.5 MeV
• No variation of beam parameters along bunch
• No runs with start-end distributions
• Correct bunching statistic up to 3rd harmonics
• Up to 20000 Slices à 32000 macro particles for
  full bunch ( 700 million macro particles)
• 2 weeks of CPU time on single node 1.7 GHz
  processor

4
Modeling - Undulator

• For SASE simulations (Dz8.lu)
• Module length 112.lu
• Quadrupole length 8.lu (gradient 12.74 T/m /
  -12.59 T/m)
• Drift length 16.lu (no super-period)
• Energy loss by SR and taper excluded.
• For taper simulations (Dz4.lu)
• Similar as above but with super-period
• Drift length 16/16/20.lu
• Stepwise taper (constant field per module)
• For field error simulations (Dzlu/2)
• Steady-state simulation only
• For simpler analysis no drift spaces

5
Modeling - Wakefields

• 3 mm bore radius
• Copper plated chamber
• 100 rms roughness with 5001 aspect ratio

Transient amplitude reduced from 250 keV/m to 180
keV/m, but longer transient region (20 mm)
Flat current profile
6
Modeling - FEL Process

• SASE Process at Ångstrom level very CPU
  intensive. Full bunch simulation only for 1.0,
  1.5 and 15 Å, with and without wake fields.
• Subsection of about a third of full bunch length
  used for tapered SASE FEL at 1.5 Å.
• Dependence on emittance, energy spread, beam
  offsets and field errors in steady-state mode
  (FEL amplifier). Change in saturation power,
  saturation length or gain length with respect to
  ideal case.

7
SASE-Results
Wavelength Sat. Power Sat. Length Gain Length Trans. Coh.
1.0 Å 1.5 GW 122 m 10.96 m 96 m
1.5 Å 2.9 GW 103 m 7.38 m 65 m
15 Å 8.3 GW 35 m 1.95 m 17 m
Wakefields included. Gain length determined by
linear fit to exponential growth of radiation
power. Transverse coherence obtained from
statistic of instantaneous power.
15 Å
1.5 Å
1.0 Å
8
Wakefield Impact

• Reduction of up to 50
• 25 by gap in profile due to transient in wake
  potential
• 25 by slight energy loss of 30 keV/m at core
  of bunch

1.0 Å
15 Å
1.5 Å
9
Quantum Fluctuation

• Lower undulator parameter and beam energy reduce
  impact of quantum fluctuation, although not a big
  effect even for the old design.

Increase of Dsg of 0.9 over 80m for 1.0 Å case.
15 Å
1.5 Å
1.0 Å
10
Profile and Spectrum at 1.0 Å

• Gap in profile and shift in resonant wavelength
  due to wakefields.

11
Profile and Spectrum at 1.5 Å

• Gap in profile and shift in resonant wavelength
  due to wakefields.

12
Profile and Spectrum at 15 Å

• Impact of wakefields strongly reduced.
• Strong sideband instability in deep saturation
  regime.

13
Bandwidth

• Growth of bandwidth for 15 Å case by factor of 3
  in deep saturation regime.

15 Å
1.0 Å
1.5 Å
14
Bunching

• New shot noise algorithm in Genesis
• Growth of bunching at higher harmonics does not
  agree with theory at short wavelength (needs
  investigation)

15 Å
1.5 Å
1.0 Å
15
Bunching Statistic at 1.0 Å
16
Bunching Statistic at 1.5 Å
17
Bunching Statistic at 15 Å
18
Taper

• Taper required to compensate for losses due to
  the spontaneous radiation.
• Additional taper can be applied to increase
  performance.

SASE-run of 20 mm subsection of bunch at 1.5 Å
(wakefields excluded).
No SR no taper Taper compensating SR Additional
taper after 90 m
19
Taper (cont)
Wavelength Taper Gradient Post Saturation
1.0 Å -1.15.10-5m-1 -
1.5 Å -9.27.10-6m-1 -9.76.10-5m-1
Taper for 1.5 Å SASE run
Steady-state model
Blue - 1.5 Å / Red - 1.0 Å Solid - taper
optimized Dot - optimized for other
wavelength.
20
Emittance Dependence

• Most Sensitive Parameter!
• Saturation beyond LCLS undulator length of 120 m
  for 1.0 mm.mrad at 1.0 Å and 1.4 mm.mrad at 1.5 Å.

1.0 Å
1.5 Å
15 Å
21
Energy Spread Dependence

• Rather weak dependence (phase spread is dominated
  by emittance effect).
• 1.0 Å case does not saturate for any value of the
  energy spread.

1.0 Å
1.5 Å
15 Å
22
Field Errors and Related

• Field errors effects the FEL process by
• Degraded synchronizations between electron beam
  and radiation field (phaseshake)
• Exitation of trajectory distortion (overlap)
• Both effects are coupled by are differently
  exited, depending on the cause (pole field
  errors, quadrupole misalignment, undulator
  misalignment, initial offsets and angle).

Overlap
Phaseshake
Initial Offsets
Correlated Errors
Uncorrelated Errors
Undulator Misalignment
Quad Misalignment
23
Offset Tolerances at 1.5 Å

• Due to large period length of betatron
  oscillation, an initial offset has almost no
  impact on the longitudinal synchronization except
  for a constant slow-down, which is compensated by
  a higher energy (or self-adjustment for SASE FEL).

No Saturation
24
Phaseshake

• Ponderomotive phase q(kku)bzt-wt depends
  implicitly on the undulator field and residual
  betatron motion. The collective change in the
  phase is given by

Daw 1 rms Dxlt100 nm rms (correlated errors)
A linear change in Dq is compensated by a change
in the mean energy. After subtracting the linear
fit the phase shake is obtained.
25
Phaseshake (cont)

• Saturation power and length difficult to estimate
  for large field errors. Use integrated gain
  length instead.
• Results for correlated errors with a trajectory
  distortion below 100 nm rms.

1
0.1
0.01
26
Tolerance Summary
Values indicate a successful operation to reach
saturation within the 125 m of the LCLS
undulator.
Wavelength 1.0 Å 1.5 Å 15 Å
Emittance lt 1.1 mm.mrad 1.4 mm.mrad gt 2.1 mm.mrad
Energy Spread 0.02 0.04 gt 0.15
Orbit - 17 mm -
Phaseshake - 1.2 rad -
27
Summery

• Saturation of SASE FEL at 15 and 1.5 Å, close to
  saturation for 1 Å
• Compared to old design saturation length
  increases by 20m and power drops by 50
• Degradation of up to 50 by wakefields
• Additional tapers after saturation push output
  power to 20 GW. Maximal change of field due to
  extra taper is 0.3
• Tighter tolerances for emittance, energy spread,
  but reduced for beam orbit
• Start-end simulation not done yet.