Transcript Slide 1

Beam Dynamics and
FEL Simulations for FLASH
Igor Zagorodnov and Martin Dohlus
08.02.2010
Beam Dynamics Meeting, DESY
FLASH I
parameters
FLASH I layout is considered. But the results are equally applicable for FLASH II (SASE).
short radiation wavelength  ~
1
high electron energy
2
In accelerator modules ACC1, ACC2,..., ACC6 the energy of
the electrons is increased from 5 MeV (gun) to 1000 MeV (undulator).
~ 6.5 nm
ACC39
In compressors the peak current I is increased from 1.5-50 A (gun) to 2500 A (undulator).
short gain length
Lg ~
 5/ 6
I
1  O( ) 
2
E
(for the optimal beta function)
high peak current
FLASH I
parameters
small emittance
short gain length
Lg ~
 5/ 6
I
1  O( ) 
2
E
(for the optimal beta function)
small energy spread
high peak current
Electron beam properties for good lasing
High peak current ~ 2500 A.
Small slice emittance  (0.4-1 mm).
Small slice energy spread E (< 300 keV).
High harmonic module in 2010
FLASH I
parameters
energy 1 GeV
radiation wavelength ~ 6.5 nm
ACC39
Only SASE mode of operation is investigated.
Charge tuning (20-1000 pC) allows to tune
- the radiation pulse energy (30-1400 mJ),
- the pulse width FWHM (2-70 fs).
FLASH I
parameters
Technical constrains
1.4 
ACC39
r1
 1.93
m
5.3 
r2
 16.8
m
r56 0... -0.56 mm
V1  150 MV
V39  26 MV
V2  360 MV
How to provide (1) a well conditioned electron beam and
(2) what are the properties of the radiation?
(1) Self consistent beam dynamics simulations.
(2) FEL simulations.
FLASH I
3d simulation method (self-consistent)
ACC39
W1
TM
W3
2W1
TM
3W1
TM
ASTRA ( tracking with space charge, DESY)
CSRtrack (tracking through dipoles, DESY)
ALICE (3D FEL code, DESY )
W1 -TESLA cryomodule wake (TESLA Report 2003-19, DESY, 2003)
W3 - ACC39 wake (TESLA Report 2004-01, DESY, 2004)
TM - transverse matching to the design optics (V2+, V.Balandin &N.Golubeva)
FLASH I
simulation methods (looking for working points)
1d analytical solution without collective effects
(8 macroparameters -> 6 RF settings)
initial guess
1d tracking with space charge and wakes
~ seconds
(1 cpu)
accelerator
E1 s1   E0 s0   V cosks0   
s1  s0
compressor
E1 s1   E0 s0 

s1 s0   s0  r56  t566 2  u5666 3
~ 5 iterations

quasi 3d tracking with all collective effects
accelerator
~ 30 min
(1 cpu)
E1 s1   E0 s0   V cosks0   
s1  s0
~ 5 iterations
matrix transport for x & y
CSRtrack
3d tracking with all collective effects
~ 10 h
(46 cpu-s)
Astra
CSRtrack
final result
FLASH I before and after upgrade
rollover compression vs. linearized compression
Q=0.5 nC
ACC39
Q=1 nC
~ 1.5 kA
slice emittance > 2mm
~2.5 kA
slice emittance ~ 0.3 - 1mm
Optics correction
 y [m]
 x [m]
35
50
30
new
40
25
30
20
V2+
15
20
10
10
0
5
0
20
40
60
80
100
120
z [m]
20
40
60
80
100
a small transverse bunch size before the last dipole
M.Dohlus, T. Limberg, Impact of optics on CSR-related emittance growth
in bunch compressor chicanes, PAC 05, 2005
120
z [m]
Working points (8 macroparameters)
C11
s
 1 (0)
s
C 1 
E1
E2
r1
r2
s2
(0)
s
p1   sC 1
p2   2s C 1
?
s - particle position before BC2
s1 - particle position between BC2 and BC3
s2 - particle position after BC3
s=s1=s2=0 for the reference particle
What is the optimal choice?
Working points (8 macroparameters)
What is the optimal choice?
V1  150 MV
E1  ?
5% reserve
   2 
8
E1  E0  0.95eV1 1      5MeV  0.95 150MeV  130MeV
9
  3  


E1  130MeV
V2  360 MV
10% reserve
E2  E1  eV2  0.9  450 MeV
E2  450MeV
E2  ?
r1  ?
r2  ?
C ?
C1  ?
 s C 1  ?
 2s C 1  ?
Working points (8 macroparameters)
1.4 
r1
 1.93
m
- low compression in BC1 and high compression in BC2
- maximal energy chirp transported through BC1for the same C1
(it looses the voltage requirements on RF system ACC2/ACC3)
r1  1.93m
I 0  52A
I f  2500A
C
If
I0
 48
E1  130MeV
E 2  450MeV
r1  ?
r2  ?
C ?
C1  ?
 s C 1  ?
 2s C 1  ?
Working points (8 macroparameters)
r2
m
E1  130MeV
10
V39  26MV
E 2  450MeV
9
p1   s C 1  0
8
p2   2s C 1  0
7
r1  1.93m
V21  360MV
V39  26MV
2
C1  2
C1  2.84
3
4
C  48
C1  ?
 s C 1  ?
V21  360MV
6
r2  ?
5
C1
 2s C 1  ?
Working points (8 macroparameters)
r2
m
10
V39  26MV
9
p1   s C
1
0
8
p2   2s C 1  0
7
V21  360MV
r2  ?
V21  360MV
2
3
4
5
working point
C1
5% reserve
r2 
C  48
C1  2.84
 s C 1  ?

E2  E1 
o
2  acos 
  22
 max(V2 )  0.95 
r562 
E 2  450MeV
r1  1.93m
V39  26MV
6
E1  130MeV
 2s C 1  ?
(C2  1)r561
1
C2 ((C1  1) E10 E20
 g)
LB
sin r562 /(3LB  4LD )
gk
V2
r562sin2
E20
r2  6m
Working points (8 macroparameters)
C 1(s)
p1  0; p2  0
C 1(s)
p1  0; p2  0
0.3
0.08
0.06
0.04
0.2
Too strong compression!
Local maximum of
compression!
0.1
0.02
0.02
0.01
0.01
0.02
0.02
0.02
0.01
s[m]
0.1
0.04
0.06
E1  130MeV
E 2  450MeV
p2  0
0.01
r1  1.93m
r2  6m
C  48
C1  2.84
 s C 1  ?
 2s C 1  ?
0.02
s[m]
Working points (8 macroparameters)
p1   sC 1  0
Tolerances (10 % change of compression)
0.16
0.01
0.14
 13
V1
0.12
deg
V1
0.1
0.008
0.006
V13
0.004
V13
0.002
0
0
5000
10000
15000
0.08
 1
0.06
deg
0.04
0
20000
2000
-2
V13C
C V13
2
V1C
C 2V1
 V13  3 Ak sin(13 )  B cos(13 ) 
 V1  Ak sin(1 )  B cos(1 ) 
r

r
r r
A    561  562  k 561 562 V2 sin(2 ) 
E2
E1 E2
 E1

6000
8000
10000
p2[m-2 ]
p2[m ]
working point
4000
working point
C
C 13
C
2
C 21
 V13  B sin(13 )  3 Ak cos(13 ) 
 V1  B sin(1 )  Ak cos(1 ) 
 t
t 
k 2 r561 r562
B
V2 cos(2 )  2  1' 561   2' 562  
C1 E1 E2
E2 
 E1
 t r
t
r 
 2k  1' 561 562   2' 562 561  V2 sin(2 )
E2 E1 
 E1 E2
Working points (8 macroparameters)
E1  130MeV
1.4
V3
26MV
1.3
E 2  450MeV
r1  1.93m
1.2
V1
150MV
1.1
r2  6m
C  48
C1  2.84
1
0.9
 s C 1  ?
0.8
0.7
-5000
0
working point
5000
10000
-2
p2[m ]
 2s C 1  2000m -2
Working points (8 macroparameters)
I [kA]
3000
p1  0
2500
p1  0
E1  130MeV
E 2  450MeV
2000
r1  1.93m
1500
p1  0
1000
C1  2.84
r2  6m
500
p2  2000m 2
0
-100
-50
0
50
100
s [μm]
1 
C=48
p1
m
-1
 1 - a free parameter to move the peak
Working points (8 macroparameters)
Charge
Q,
nC
Energy
in BC2
E1,
[MeV]
Deflecting
radius in BC3
r2,
[m]
Compression
in BC2
C1
Total
compression
C
First
derivative
p1,
[m-1]
Second
derivative
p2,
[m-2]
1
6
2.84
48
1
2e3
0.5
6.93
4.63
90
1
3.5e3
7.8
6.57
150
0.7
4e3
0.1
9.3
10.3
240
0
4e3
0.02
15.17
31.8 (12)
1000
-0.5
5e3
130
0.25
Energy
in BC3
E2,
[MeV]
Deflecting
radius in BC2
r1,
[m]
450
1.93
C1 : scaling for different charges
x''  k x x 
re
I
ec 3  x ( x   y )
x
we have used another scaling
max[ I1 (Q)]
 r 2 (Q)
~
max[ I1(Q)] max[ I0 (Q)] C1(Q)
~
~ const
2Q
 (Q)
max[ I 0 (Q)] C1 (Q)
4Q
~ const
Working points (6 equations => 6 RF parameters)
8 macroparameters
define 6 equations
s1

1
E
(0)

E
,
E
(0)

E
(0)

C
20
1
10
1 ,
 2
s


2
3

s

s

s2

1
2 (0)  p ,
 2 (0)  C ,
(0)  p2 .
1
2
3


s
s
s

Analytical solution without self-fields*
A0 (x0 )  f0
x0  A01 (f0 )
nonlinear operator
(defined analytically)
*M.Dohlus and I.Zagorodnov,
A semi analytical modelling of two-stage
bunch compression with collective effects, (in preparation)
 V1 



 1
 V13 
x0  


 13 
 V2 


 2 
 E10 


E
 20 
 C1 
f0  

C


 p1 


 p2 
Analytical solution without self-fields
x0  A01 (f0 )
Solution with self-fields
A(x)  f0

x  A01 A0 (x)  f0  A(x)
nonlinear operator
(tracking with self-fields)

numerical tracking
fn1  A(xn1)

xn  A01 A0 (xn1 )  f0  A(xn1 )

fn1  f0  fn1
gn  gn1  fn1
xn  A01(gn )
residual in
macroscopic
parameters
analytical correction
of RF parameters
FLASH I
simulation methods (looking for working points)
1d analytical solution without collective effects
(8 macroparameters -> 6 RF settings)
x0  A01 (f0 )
initial guess
A1(x1)  f0
~ 5 iterations
1d tracking with space charge and wakes
~ seconds
(1 cpu)
accelerator
E1 s1   E0 s0   V cosks0   
s1  s0
compressor
E1 s1   E0 s0 

s1 s0   s0  r56  t566 2  u5666 3
quasi 3d tracking with all collective effects
accelerator
~ 30 min
(1 cpu)
s1  s0
matrix transport for x & y
x0  x1
A 2 ( x 2 )  f0
~ 5 iterations
CSRtrack
3d tracking with all collective effects
~ 10 h
(46 cpu-s)
E1 s1   E0 s0   V cosks0   

Astra
CSRtrack
A(x2 )  f
f  f0
final result
Working points (6 equations => 6 RF parameters)
s1

1
E
(0)

E
,
E
(0)

E
(0)

C
20
1
10
1 ,
 2
s


2
3

s

s

s2

1
2 (0)  p ,
 2 (0)  C ,
(0)  p2 .
1
2
3


s
s
s

8 macroparameters
define 6 equations
Analytical solution without self-fields
+ iterative procedure with them
RF settings in accelerating modules
Charge,
nC
V1,
[MV]
1,
[deg]
V39,
[MV]
39,
[deg]
V2,
[MV]
2,
[deg]
1
144
-4.66
22.6
145
350
23.4
0.5
143.7
4.042
19.65
158.4
351
23.65
0.25
143.36
2.493
20.81
153.9
352.6
23.96
0.1
144.8
-6.31
25.6
137.5
356.5
25.62
0.02
144.9
-3.894
25.58
141.65
339.8
19.385
ACC39
Q=1 nC
E [MeV]
Phase space
Current, emittance, energy spread
2.5
1006
I [kA]  x [μm]
1004
1002
2
1000
998
340 fs
1.5
996
-50
0
 y [μm]
50
1
0.5
0
-100
s [μm]
 E [MeV]
-50
0
50
100
s [μm]
 xproj  3 [μm]
 yproj  1.4 [μm]
Q=0.5 nC
E [MeV]
Phase space
Current, emittance, energy spread
2.5
1004
1002
2
I [kA]
1000
130 fs
998
-50
1.5
0
 x [μm]
50
1
 y [μm]
0.5
0
-60
 E [MeV]
-40
-20
0
20
40
60
s [μm]
s [μm]
 xproj  2.5 [μm]
 yproj  0.84 [μm]
Q=0.25 nC
E [MeV]
Phase space
Current, emittance, energy spread
2.5
1003
1002
I [kA]
1001
2
1000
999
50fs
998
-20
-10
0
10
20
30
1.5
1
 x [μm]
 y [μm]
0.5
Space charge
impact
0
-30
s [μm]
 E [MeV]
-20
-10
0
10
20
30
s [μm]
 xproj  1.14 [μm]
 yproj  0.74 [μm]
Q=0.1 nC
E [MeV]
Phase space
Current, emittance, energy spread
1004
2.5
1002
1000
998
2
I [kA]
996
-10
-5
0
5
10
1.5
25fs
1
0.5
0
-15
 y [μm]
 x [μm]
 E [MeV]
-10
-5
0
5
10
15
s [μm]
s [μm]
 xproj  2 [μm]
 yproj  0.6 [μm]
Q=0.02 nC
E [MeV]
Phase space
Current, emittance, energy spread
1004
1.5
1002
1000
I [kA]
998
996
-10
-5
0
5
10
1
6 fs
0.5
 E [MeV]
0
-5 -4 -3 -2 -1
 x [μm]  y [μm]
0
1
2
3
4
5
s [μm]
s [μm]
 xproj  0.48 [μm]
 yproj  0.25 [μm]
Q=0.02 nC
1.6A31.8
51A 31.4=1600A
ACC39

proj
x, y
 xproj  0.2 [μm]
 yproj  0.17 [μm]
 0.17 [μm]
 xproj  0.27 [μm]
 yproj  0.17 [μm]
E [MeV]
E [MeV]
E [MeV]
CSR impact
0.3
0.15
0.25
 E [keV]
0.2
0.15
I [A]
10
 x [μm]
0.1
0.05
0
-5000
0
5000
s [μm]
 x [μm]
1.5
I [kA]
0.1
I [kA]
0.05
 y [μm]
0.5
 E [MeV]
0
-100
-50
0
50
1
100
s [μm]
0
-10
-5
0
5
10
s [μm]
Q=0.02 nC
r56 =0 [m], t566=0.06 [m]
ACC39
 xproj  0.29 [μm]
 yproj  0.23 [μm]
 xproj  0.5 [μm]
 yproj  0.24 [μm]
E [MeV]
 xproj  0.5 [μm]
 yproj  0.25 [μm]
E [MeV]
E [MeV]
Space charge
impact
I [kA]
1.5
1
0.5
0.5
-10
-5
0
5
I [kA]
1.5
1
0
10
s [μm]
s [μm]
s [μm]
s [μm]
0
I [kA]
1.5
1
0.5
-10
-5
0
5
10
s [μm]
0
-5
0
5s
[μm]
Tolerances (analytically) without self fields (10 % change of compression)
Q, nC
ACC1
ACC39
1
0.5
0.25
0.1
0.02
|V|/V
0.001
0.004
0.0012
0.0003
0.00004
||, degree
0.065
0.025
0.013
0.007
0.0014
0.008
0.01
0.0026
0.0008
0.00013
0.13
0.061
0.033
0.02
0.004
0.0042
0.0033
0.0026
0.0024
0.0016
0.15
0.15
0.15
0.17
0.17
|V|/V
~O(C-1)
||, degree
ACC2/3
|V|/V
||, degree
~O(C2-1)
Tolerances (from tracking) with self fields agree with this table
FLASH
parameters
How to provide (1) a well conditioned electron beam and
(2) what are the properties of the radiation?
(1) Self consistent beam dynamics simulations.
We are able to provide the well conditioned
electron beam for different charges.
But RF tolerances for small charges are tough.
(2) FEL simulations (next slides).
Slice parameters for SASE simulations
Slice parameters are extracted from S2E simulations for SASE simulations


x  y
x
y
x
y
x'
I [kA]
Q  1 nC
1
x  y
I
current
slice emittance
 x [ m m]1.5
2.5
Q  1 nC
Q  0.5 nC
Q  0.25 nC
2
Q  0.25 nC
1.5
Q  0.02 nC
1
0.5
Q  0.02 nC
0
y'
0.5
s s
-2
-1
0
1
2
0
s
-50
0
50
Charge Q, nC
1
0.25
0.02
Longitudinal electron beam size s, mm
42
13
3.6
Transverse electron beam size r, mm
80
68
36
s [μm]
Radiation energy statistics (200-500 runs)
E  μJ 
Q  nC 
z
Mean energy
Radiation pulse width (RMS)
fs
90
3
10
80
1 nC
70
2
10
60
0. 02 nC
0
50
1 nC
40
10
0.25 nC
30
0. 25 nC
20
10
-2
10
0
5
10
15
0.02 nC
0
0
20
5
10
15
20
z [m]
Charge, nC
Mean radiation energy, mJ
Pulse radiation width (FWHM), fs
25
z [ m]
1
0.5 0.25 0.1 0.02
1000-1400 700 500 200
70
30
17
7
30
2
Radiation energy statistics
Q=1 nC
1
2.5
p( E )
Q=0.02 nC
p( E )
Gamma distr.
0.8
14%
M48
2
1.5
z=10m
50%
M4
0.6
0.4
1
0.2
0.5
0
0
12
0.5
1
1.5
2
2.5
3
E
E
0
0
p( E )
3
z=20m
8
1.5
4
1
2
0.5
0.5
1
1.5
2
2.5
1.5
3
E
E
2
2.5
3
p( E )
12%
2
6
0
0
1
2.5
3%
10
0.5
E
E
0
0
0.5
1
1.5
2
2.5
3
E
E
Temporal structure
Q= 1 nC
Q=0.02 nC
0.8
0.6
0.7
Pi
GW
0.5
0.4
z=10m
0.5
0.4
0.3
0.2
0.1
GW
-100
0
100
200
300
0
-20
t [fs]
10
-10
0
10
10
Pi
GW
8
GW P
i
GW
0.2
P
-200
P
0.3
I [a.u]
0.1
0
-300
I [a.u]
0.6
z=20m
I [a.u]
6
P
I [a.u]
4
GW
4
P
2
2
GW
0
-300
t [fs]
Pi
GW
8
6
20
-200
-100
0
100
200
300
t [fs]
0
-20
-10
0
10
20
t [fs]
Summary
with harmonic module
Bunch charge, nC
1
0.5
0.25
without*
0.1
0.02
0.5-1
Wavelength, nm
6.5
6
Beam energy, MeV
1000
1000
2.5
Peak current, kA
2.1
1-1.5
1.3-2.2
Slice emmitance,mm-mrad
1-1.3
0.7-0.9
0.5-0.7
0.4-0.5
0.3-0.4
1.5-3.5
Slice energy spread, MeV
0.1-0.2
0.1-0.2
0.25
0.2-0.4
0.25
0.3
Saturation length, m
13
12
11
10
11
22-32
Energy in the rad. pulse, mJ
10001400
700
500
200
30
50-150
Radiation pulse duration FWHM, fs
70
30
17
7
2
15-50
5-7
Averaged peak power, GW
Spectrum width, %
0.4-0.6
Coherence time, fs
4-5
2-4
0.8-1
-
0.4-0.6
-
*) E.L.Saldin at al, Expected properties of the radiation from VUV-FEL at DESY, TESLA FEL 2004-06, 2004.
-
FLASH
Simulation results
(1) Self consistent beam dynamics simulations
We are able to provide the well conditioned
electron beam for different charges.
But RF tolerances for small charges are tough.
(2) FEL simulations
The charge tuning (20-1000 pC) in SASE mode
allows to tune
- the radiation pulse energy (30-1400 mJ)
- the pulse width (FWHM 3-70 fs).