Performance Analysis Using Genesis 1.3 Sven Reiche LCLS Undulator Parameter Workshop Argonne National Laboratory 10/24/03.

Performance Analysis Using Genesis 1.3

Sven Reiche

LCLS Undulator Parameter Workshop

Argonne National Laboratory

10/24/03

ANL - 10/24/03Sven Reiche - Analysis with Genesis 1.3

Overview

Modeling in Genesis 1.3

SASE - Performance

Undulator Taper

Tolerance Study


Modeling - Electron Beam

Using Design Parameter Flat profile (~70 m 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


Modeling - Undulator

For SASE simulations (z=8.u) Module length: 112.u

Quadrupole length: 8.u (gradient: 12.74 T/m / -12.59 T/m)

Drift length: 16.u (no super-period) Energy loss by SR and taper excluded.

For taper simulations (z=4.u) Similar as above but with super-period Drift length: 16/16/20.u

Stepwise taper (constant field per module)

For field error simulations (z=u/2) Steady-state simulation only For simpler analysis no drift spaces


Modeling - Wakefields

3 mm bore radius Copper plated chamber 100 rms roughness with 500:1 aspect ratio

Transient amplitudereduced from 250 keV/m to 180 keV/m, but longer transient region (20 m)

Flat current profile


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.


SASE-Results

15 Å1.5 Å

1.0 Å

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.


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

15 Å

1.5 Å

1.0 Å


Quantum Fluctuation

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

15 Å

1.5 Å

1.0 Å

Increase of of 0.9 over 80m for 1.0 Å case.


Profile and Spectrum at 1.0 Å

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


Profile and Spectrum at 1.5 Å

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


Profile and Spectrum at 15 Å

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


Bandwidth

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

15 Å

1.5 Å

1.0 Å


Bunching

New shot noise algorithm in Genesis Growth of bunching at higher harmonics does not agree

with theory at short wavelength (needs investigation)

15 Å1.5 Å

1.0 Å


Bunching Statistic at 1.0 Å


Bunching Statistic at 1.5 Å


Bunching Statistic at 15 Å


Taper

Taper required to compensate for losses due to the spontaneous radiation.

Additional taper can be applied to increase performance.

SASE-run of 20 m subsection of bunch at 1.5 Å (wakefields excluded).

No SR & no taperTaper compensating SRAdditional taper after 90 m


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

Steady-state model

Blue - 1.5 Å / Red - 1.0 ÅSolid - taper optimizedDot - optimized for other wavelength.

Taper for 1.5 Å SASE run


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


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


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

Undulator MisalignmentQuad Misalignment

Uncorrelated Errors


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


Phaseshake

Ponderomotive phase =(k+ku)zt-t depends implicitly on the undulator field and residual betatron motion. The collective change in the phase is given by

€

d

dzΔθ = −k

aw

γ 2Δaw +

1

2′ x cen2

⎛

⎝ ⎜

⎞

⎠ ⎟

A linear change in is compensated by a change in the mean energy. After subtracting the linear fit the phase shake is obtained.

aw = 1% rms x<100 nm rms (correlated errors)


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%


Tolerance Summary

Wavelength 1.0 Å 1.5 Å 15 Å

Emittance < 1.1 mm.mrad 1.4 mm.mrad > 2.1 mm.mrad

Energy Spread 0.02 % 0.04% > 0.15%

Orbit - 17 m -

Phaseshake - 1.2 rad -

Values indicate a successful operation to reach saturation within the 125 m of the LCLS undulator.


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.

Performance Analysis Using Genesis 1.3 Sven Reiche LCLS Undulator Parameter Workshop Argonne National Laboratory 10/24/03.

Documents

sven reiche analysis

performance analysis

simpler analysis

bunch length

processor slide

u module length

flat current profile

u quadrupole length