Transcript Effect of Wake Field on SASE Numerical Results

Effects of AC Resistive-Wall Wake
Upon LCLS SASE Performance:
Numerical Simulation Results
William Fawley - LBNL
Sven Reiche – UCLA
7 April 2005 – LCLS FAC Meeting
April 7. 2005
LCLS FAC
Wm. Fawley
[email protected]
Sven Reiche
[email protected]
Talk Outline
 Summary of simulation method and wakefield algorithm
 Simulation results for 1-nC “sloppy taco” case
 Simulation results for 200-pC “El Chargito” case
 Comparison with predictions of Huang and Stupakov
April 7. 2005
LCLS FAC
Wm. Fawley
[email protected]
Sven Reiche
[email protected]
Simulation Description
ELEGANT dump of the 6D phase space distribution of
LCLS start-end simulation at the undulator entrance.
Distribution re-matched to the undulator lattice including
breaks (provided by H.-D. Nuhn).
Current profile extracted to calculate wake potential
Ginger/Genesis runs with reconstruction of the 5D phase
space and I(t)
Shot-noise added (SASE runs).
Slice spacing of about 11 as => 20K slices for 220-fs bunch length.
Runs for copper and aluminum vacuum chambers and various
compensating gradients (via K taper).
April 7. 2005
LCLS FAC
Wm. Fawley
[email protected]
Sven Reiche
[email protected]
Wakefield Algorithm
Current profile extracted from particle distribution with
a 1-fs smoothing window
Effective wake potential calculated with two different
programs (H.-D. Nuhn and S. Reiche)
Resistive wall wakefield using the AC model for copper and
aluminum
Geometric wake with an effective gap of 0.18 m and a module
length of 4 m
Surface roughness wake (inductive model and synchronous mode)
with an rms roughness of 100 nm and a period of 30 microns.
Constant gradient added to wake potential to simulate the
real-life effects of tapering undulator K to compensate wake
losses.
April 7. 2005
LCLS FAC
Wm. Fawley
[email protected]
Sven Reiche
[email protected]
Characteristics of 1-nC “Sloppy Taco” pulse
April 7. 2005
LCLS FAC
Wm. Fawley
[email protected]
Sven Reiche
[email protected]
Wake Components for the 1-nC Case
April 7. 2005
LCLS FAC
Wm. Fawley
[email protected]
Sven Reiche
[email protected]
Simulation Code Predictions for P(t) in
Cu & Al Pipe without Compensation Field
Time (fs)
Data is smoothed from raw ~12 as resolution to ~1 fs resolution
Note that GENESIS data is 30 m upstream of GINGER data
For Cu case, agreement between the codes is extremely good, both where
there is lasing and in the actual coarse-grained P(t) amplitude
Lasing appears strongest around +100 kV/m for this untapered case
April 7. 2005
LCLS FAC
Wm. Fawley
[email protected]
Sven Reiche
[email protected]
Optimal Lasing occurs at ~+100 kV/m net field
GINGER
1-nC
1-nC
Characteristics of 200-pC “El Chargito” pulse
April 7. 2005
LCLS FAC
Wm. Fawley
[email protected]
Sven Reiche
[email protected]
200-pC wake: More constant in time, lower
amplitude than 1-nC “sloppy taco” case
200-pC
1-nC
• Lack of high current head spike and longer rise time both contribute to lack
of strong temporal oscillation in wake field for 200-pC case
• Nearly all of pulse wake lies within +/- 50 kV/m of mean => easy
compensation by undulator taper (300 kV/m over 130 m ~ 0.3% taper in K)
April 7. 2005
LCLS FAC
Wm. Fawley
[email protected]
Sven Reiche
[email protected]
GINGER Results for 200-pC Pulse Energy vs. Z
•
•
•
•
Uncompensated 200-pC Cu & Al wake lower power ~8-10X
Gain length increased ~15% but sat. point unaffected
External field of ~150 kV/m makes up for wake
Increasing ext. field to +300 kV/m nearly doubles power over no
wake case – agreeing with Huang and Stupakov prediction
April 7. 2005
LCLS FAC
Wm. Fawley
[email protected]
Sven Reiche
[email protected]
Code Comparison for 200-pC Case
Reasonably good agreement between
codes, given complexity of calculation.
1 mJ = 7.5E11 photons @ 0.15-nm
April 7. 2005
LCLS FAC
GINGER typically shows 25-50%
more power, post-saturation
Unclear why --- algorithms, grid
resolution, physics ???
Wm. Fawley
[email protected]
Sven Reiche
[email protected]
Output Power vs. Time @ z=130m
200pC - Cu Pipe
GINGER
• Data is smoothed from raw ~12-as resolution to ~1-fs resolution
• For 300-kV ext. field + Cu wake case, agreement between the codes is good
in overall temporal dependence with GINGER showing ~1.5X greater power
• Compared to 1-nC “sloppy taco” case, lasing occurs over full 200-pC pulse
April 7. 2005
LCLS FAC
Wm. Fawley
[email protected]
Sven Reiche
[email protected]
Summary & Comparison to Theory
No
wake
LG (power) (m) 5.17
PSAT (GW)
7
Cu –Wake Cu – wake Cu – wake Al – wake
Al – wake
0 kV/m
200 kV/m
300 kV/m
200 kV/m
300 kV/m
6.4
5.19
5.18
5.10
5.25
1.8
6
12
8
10
If r = lw/8pLG ~ 2.3E-4 (probable underestimate by 1.5X),
then Huang and Stupakov predict an optimal energy taper
(ignoring wake) of 2rE/LSAT ~ +40 kV/m
Range of 40-80 kV/m above wake compensation
probably works well for 200-pC case
Saturation power of ~8 GW agrees well with rEI = 10 GW
(factor of 1.5 included here)
April 7. 2005
LCLS FAC
Wm. Fawley
[email protected]
Sven Reiche
[email protected]
Conclusions
1-nC case yields more energy (2 mJ for Al pipe
and optimum taper), but…
Temporal radiation profile is very non-uniform
Only partial compensation by field taper due to strong
transient in wake potential
200-pC case gives 1.5 mJ output
Pulse duration ~half of 1 nC case
(=> ~100% larger brightness)
Almost complete compensation of wake fields
(continuous radiation profile) possible via taper.
Performance independent of vacuum chamber
material (i.e., Al and Cu are comparable)
Good agreement between theory and simulation.
April 7. 2005
LCLS FAC
Wm. Fawley
[email protected]
Sven Reiche
[email protected]