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Beam Optimization with
Fast Particle Tracking (FPT)
LCLSII Physics Meting, 10/07/2015
Lanfa Wang
• Motivation
• Physics Model of FPT
• Benchmark with ELEGANT
• Results for new injector beam
2
Motivation
LCLSII Physics meeting, 10/07/2015, L. Wang
Complexity of LCLS-II beam dynamics (compared with
LCLS)
• Strong space charge at injector (CW gun, low beam energy)
• Strong CSR effect (more bending magnets in transportation line)
Strong LSC in linac (long by-pass beamline, low beam energy)
• Low beam energy
For design/optimization purpose, we need a fast program,
which should includes wakefield, CSR and space charge.
• ELEGANT provide detail tracking and including all the collective effects
above, but it is not fast enough
• LiTrack is fast, but CSR and LSC is not included
3
Strong Impact of CSR and space charge
LCLSII Physics meeting, 10/07/2015, L. Wang Ji Qiang, et.al. WEP070, FEL15
without CSR
and space charge
with CSR
+space charge
4
Introduction to FPT
LCLSII Physics meeting, 10/07/2015, L. Wang
Original for collective effects, Longitudinal space charge is
added recently, it includes
Geometric wake and resistive wall wake;
1D CSR in free space (and 2D CSR with shielding)
1D/2D LSC (uniform beam, Gaussian beam, or arbitrary
beam)
5
CSR
LCLSII Physics meeting, 10/07/2015, L. Wang
1D free space CSR [Saldin, E.L. et al. Nucl.Instrum.Meth. A398
(1997) 373]
Pro: Fast computation
con: no shielding, no 2D effect
2D CSR with shielding
Pro: shielding effect, resistive wall effect; 2D effect ;
con: slow computation for very short bunch
0 2 4 6 8 10-50
0
50
100
150
200
250
300
350
400
k (1/mm)
Z (
)
Real, Zhou
Imaginary,Zhou
Real, Wang
Imaginary,Wang
6
2D CSR
LCLSII Physics meeting, 10/07/2015, L. Wang
=6μm (50THz) , 𝜎𝑟=0.1mm
CSR Field at end of the LCLSII BC2 magnet
Integrated field after the magnet
Apply to arbitrary pipe cross-section
Fast CER computation;
Ante-chamber
7
Shielding and CSR energy loss
LCLSII Physics meeting, 10/07/2015, L. Wang
long wavelength dominant;
frequency up to 50 THz is need
-50 0 50 1000
0.5
1
1.5
z (fs)
I (k
A)
beam of 100pC at Undulator Begin, sigz= 29.8906(fs)
-100 -50 0 50 1000
100
200
300
400
500Beam Spectrum
Frequency (THz)
Ma
gn
itu
de
|I(
f)|
100pC
-200 -100 0 100 200 300 400 5000
0.5
1
1.5
z (fs)
I (k
A)
beam of 300pC at Undulator Begin, sigz= 113.57(fs)
-20 -10 0 10 200
100
200
300
400Beam Spectrum
Frequency (THz)
Ma
gn
itu
de
|I(
f)|
300pC
LCLS-II Beam spectrum
-2 -1 0 1 2 30
0.1
0.2
0.3
q
bunc
h de
nsity
-2 -1 0 1 2 30
10
20
30
8
Micro-bunch instability driven by CSR (KEK DR)
LCLSII Physics meeting, 10/07/2015, L. Wang
f up to 0.5THz f up to 1.5THz
N=8.5E10
N=5.5e10
No Saw-tooth instability observed with long
wavelength CSR
Short wavelength (High frequency) CSR is
important for micro-bunch instability
μm CSR is needed for LCLS-II
KEK DR:
• beam energy 1.1GeV; Circumference 135.5m
• Bunch length 6.53 mm;
(L. Wang, H. Ikeda, K. Oide K. Ohmi and D. Zhou,
TUPME017, IPAC13)
9
Longitudinal Space charge (LSC)
LCLSII Physics meeting, 10/07/2015, L. Wang
1D free space for round Gaussian and uniform beam
Pro: Fast computation; good for long wavelength
con: 2D effect (energy spread, damping) is not included
2D LSC with arbitrary beam and chamber [L. Wang, Y. Li, PRSTAB, 18, 024201 (2015)]
Pro: 2D effect and shielding effect; good for all wavelength • Field spread converts to slice energy spread;
• Large slice energy spread for short wavelength;
0 1 2 3 4 5 6 7 80
0.2
0.4
0.6
0.8
1
1.2
/(ka)
Z||(a
rb. u
ints
)
Round uniform beam
10
LCLS 6/19/2014 data, 1kA, 4GeV, 180pC, BC2 R56 = 24.7mm (Yuantao, Ding)
LCLSII Physics meeting, 10/07/2015, L. Wang
LH =2.2uJ,Initial E =10.3keV
t (fs)
E
(M
eV)
-100 0 100-40
-20
0
20
40LH =3.7uJ,Initial
E =11.4keV
t (fs)
E
(M
eV)
-100 0 100-40
-20
0
20
40
LH =5uJ,Initial E =12.3keV
t (fs)
E
(M
eV)
-100 0 100-40
-20
0
20
40LH =7.2uJ,Initial
E =13.8keV
t (fs)
E
(M
eV)
-100 0 100-40
-20
0
20
40LH =9.9uJ,Initial
E =15.6keV
t (fs)
E
(M
eV)
-100 0 100-40
-20
0
20
40
LCLS 4GeV, 180pC, 1kA, LH off
t (fs)
E
(M
eV)
-100 0 100-40
-20
0
20
40
11
ELEGANT Space Charge Model
LCLSII Physics meeting, 10/07/2015, L. Wang
Elegant uses round uniform beam
model with 𝑎 = 3𝜎; good
approximation at long wavelength.
1D LSC
3D space charge
To be released
12
Benchmark FPT with ELEGANT
LCLSII Physics meeting, 10/07/2015, L. Wang
• x-px plane: sigma_x = 0.1227mm, sigma_x' = 0.1411e-4, alphax=-0.524,
emittance_normalized = 0.3 mm-mrad
• y-py plane: same as x-px plane
• z-pz plane: sigma_z = 0.979mm, sigma_dE = 1keV, alphaz = 0.368e-3
Initial beam at 100MeV
13
Without collective effects
LCLSII Physics meeting, 10/07/2015, L. Wang
• Initial Ideal Gaussian beam from 100MeV of LCLS linac
• Without wake, CSR and space charge
• compare Beam at BC2 END
Beam energy 1.6GeV Beam energy 1.644GeV
Red: ELEGANT
Blue: FPT
14
With wake (RF structure, beam pipe)
LCLSII Physics meeting, 10/07/2015, L. Wang
Peak current is lower due to the
effect of wake
16
Wake+CSR+LSC
LCLSII Physics meeting, 10/07/2015, L. Wang
The LSC kicker is compared with ELEGNAT and analysis
For design, we can consider the long wavelength effect only (NOT instability);
which includes the de-chirp effect and also a small number of macro-particle can
be used;
For instability, the main issue is how to handle noise.
some ideas to reduce the noise and improve the resolution; under going
-2000 -1000 0 1000 2000
-0.1
-0.05
0
0.05
0.1
t(fs)
E
(M
eV
)
0 5 10 150
0.02
0.04
0.06
0.08
0.1
0.12
0.14
Bu
nc
hin
g
(m)
FPT: 8 Millions particles
ELEGANT: 50 Millions particles
FPT play trick at L1: Ez 𝑁𝑠𝑖𝑚
𝑁𝑟𝑒𝑎𝑙
For 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 𝑓 > 0.25𝑓𝑐~𝑐
4∆𝑠
Micro-bunching at 2~3um; ubi starts from very beginning
17
Micro-bunch instability by ELEGANT and IMPACT (FEL15, TUP066)
LCLSII Physics meeting, 10/07/2015, L. Wang
50MP, 1024bins, ELEGANT 624MP, 2048 bins, IMPACT
~2.3μm
Amp=0.15%
~3μm
Amp=0.15%
At undulator begin
Wake+CSR+Spacecharge
0 0.5 1 1.5 2 2.5 30
0.5
1
1.5
2x 10
5
(m)
ZL
SC (
)
BC1BEG
BC2BEG
DL1BEG
DL2BEG
DL1END
DL2END
18
LSC for emittance 0.45um
LCLSII Physics meeting, 10/07/2015, L. Wang
bc1beg=120m
bc2beg=335m
dL1beg=928m
dL1end=1030m
dL2beg=2770m
dL2end=3100m
0 500 1000 1500 2000 2500 3000 3500 40000
50
100
150
200
250
300
350
s(m)
(
m)
x
y
Bunching factor 6.7 and 10 are used
Long-by-pass contributed largest
LSC at L1 (blue) and L2 (black)
also important
The wavelength at peak is close
20
300pC beam at 100MeV (Feng Zhou)
LCLSII Physics meeting, 10/07/2015, L. Wang
-20 -15 -10 -5 0 5 10 150
0.1
0.2
0.3
0.4
0.5
0.6
0.7
em
itta
nc
e (m
-ra
d)
t (ps)
Bunch emittance=4.3463e-07/4.3506e-07 (m-rad)
X-emittance
Y-emittance
Head
21
Optimization with FPT, LSC off, example for New 300pC
LCLSII Physics meeting, 10/07/2015, L. Wang
Zero chirp
High peak current >1kA
Smooth current profile • L1 phase=20.8 degree
• Linearizer phase= 155 degree
• L2 Phase= 29.6 degree
• BC1= 80mrad (R56~-33mm)
• BC2= 43.8mrad (R56~-40mm)
Confirmed with ELEGANT with CSR,
(LSC off)
Need to check LSC effect, the impact
on the current profile is likely small.
This is just one example, it can be
further improved with more study
ELEGNAT
Head
22
100pC beam
LCLSII Physics meeting, 10/07/2015, L. Wang
-15 -10 -5 0 5 100
0.05
0.1
0.15
0.2
0.25
0.3
0.35
em
itta
nc
e (m
-ra
d)
t (ps)
X-emittance
Y-emittance100MeV (Feng Zhou)
4GeV at Undulator Begin
• Peak current: 12A
• Emittance: 0.25um
• Peak current: >1.1kA
• Small chirp
Linearizer = 163o
R56BC2= -34 mm
Continue study, matching...
23
Summary
LCLSII Physics meeting, 10/07/2015, L. Wang
FPT provide fast computation with good agreements with
ELEGANT; it provides flexibilities for different models (2D
LSC, CSR shield effect, transverse SC also straight
forward, etc.)
Preliminary study shows optimization with FPT works
well (>1kA, flat current profile)
We demonstrated that the collective effects can be
minimized
24
Next
LCLSII Physics meeting, 10/07/2015, L. Wang
Optimization with (wake+CSR)+LSC
- Optimization with long wavelength effect (not instability), therefore a
small number of particles is required
- Micro-bunch instability (LSC) resolution is limited ~ > 2∆𝑠, improve
the resolution
- Noise reduction schemes
integrated S2E optimization (MOGA/People) with GPT
(injector)+FPT (linac), especially for low charge
…..
Ultimate goal: online optimization.
Lots of works to be done and can be done to improve the
beam quality (we already have very good emittance)!