Transcript Document 7851673

HOMDYN
(Higher Order Modes DYNamics)
[email protected]
Acknowledgements:
J. B. Rosensweig, L. Serafini,
J.P. Carneiro, J. Clendenin, H. Edwards, V. Fusco, L. Giannessi, M.
Migliorati, A. Mosnier, D.T. Palmer, L. Palumbo, Ph. Piot, M. Quattromini ,T.
Ronsivalle, J. Sekutowicz, F. Tazzioli.
Q ui ck Ti m e ™ an d a T I FF ( U nc om p r es se d) de co m pr e ss or ar e n ee de d t o s ee t h is pi ct u re .
Historical motivation:
Superconducting Photo-injectors
Requirements:
Relativistic and Non-Relativistic Beams
==> Space Charge Effects
Long term multi-bunch beam cavity
interaction (msec-1000 bunches)
==> Transients, Beam Loading, HOM
excitation
Self Consistent Code and Reasonable CPU Time
Space Charge
2
 E
1 E
J


2
c t
t
J  f ( R, L )
Fb  qE  v  B 
p b  Fb
The HOMDYN model
Normal Modes Expansion of Cavity fields
We describe the field evolution under the slowly varying
envelope approximation for each resonant mode
Analytical propagation of field from bunch to bunch,
including an external generator
Longitudinal and Transverse Beam Laminarity
We describe the bunch dynamics of a uniform charged
cylinder under the Multi-Slice approximation
Analytically computation of slice Space Charge Fields
Artistic view of the Envelope Equations
 s s2 ÝsRÝs  Kssol  Ksrf Rs
Ý
ZÝ
Ý
Ý
R
2c 2 k p G( s , Ar )
2 G(s , Ar )

1




3
s
Rs s   s
 s 
2
2
4 nth c  1 4  nBc  1
 
 3  
 3
  s  Rs   s  Rs
sc
e Ez  s ,t  


mo c s3  Ezwake ss,t 
acc
e  Ez zs ,t 


mo c s3  Ezsc s ,t  
Multi-Slice approximation and Envelope Equations:
Ý
zs  cs
e
acc
wake
sc
sc
E
z
,t

E
s
,t

E

,t

E







z
s
z
s
z
s
z s,t 
3
mo c s
Ý

s
Dt
L(t)
Rs(t)
Dt
Ý
Ýs   s ÝsRÝs  K
R
2
s
sol
s
2c 2 k p G( s, Ar )
2 G(s ,Ar ) 
 K Rs 

1





3
s 
Rss   s
 s 
rf
s
2
2
4 nth c  1 4  nBc  1

 3  
 3
  s  Rs   s  Rs
Space Charge Field:
MV
m
 s  z s  zt
Aspect Ratio: Ar,s  Rs  s L
Longitudinal Component (on axis)
Q 
2
2
2
2

E  s  

1

L


A



L


A

1

L


L
s
r ,s
s
r, s
s
s

2 o Rs2 
sc
z
  dEz (r  0,z ) R
E (r,z )   

o
dz
 2
Radial Component (on envelope)
Q 
1  s L
E  s  


2
2

4 o Rs L  1   L  A
s
r ,s
sc
r
sc
r

Q
 
G s, Ar,s 
2 
 Ar, s  4 o Rs L
s L
 s L
2
Q 
1  s L
E  s  


2
2

4 o Rs L  1   L  A
s
r ,s
sc
r
=1
Ar,s  Rs  s L

Q
 
G s, Ar,s 
2 
 Ar, s  4 o Rs L
s L
 s L
2
 = 10
=5
Rs
Rs
L
Beam Generation and Cathode Image Charges:
e+
e-
Esc @MVê mD
Esc @MVê mD
5
10
0.0005
5
0.001
0.0015
0.002
Z @mD
-5
0.0005
0.001
0.0015
0.002
Z @mD
-10
-15
-5
-20
-10
-25
No Image Charges
With Images Charges
Elliptical cross section bunch
I
y
Ey 
 c o Y X  Y 
Y
Er 
X Y
R 
2
*
X
I
x
Ex 
 c o X X  Y 
I
2  c o R
2
r
R*
Ex X, z  Ey Y ,z  Er R * ,z
Beam Line
I  s 
kp 
2Io
Space Charge
eBz zs 
 

2mo  s 
2
sol
s
K
Solenoid
e c
kq 
B 
m
Quadrupoles
2
cKkx , y 
k poles  

  
e Ez s Ez 
K 

2 smo  z
c t 
rf
s
Undulator
RF Focusing
SW+TW
Cylindrical Symmetry
Ý
Ýs   s ÝsRÝs  K
R
2
s
sol
s
2c 2 k p G( s, Ar )
2 G(s ,Ar ) 
 K Rs 
 1   s 


3
Rss   s
 s 
rf
s
2
2
4 nth c  1 4  nBc  1

 3  
 3
  s  Rs   s  Rs
Elliptical Symmetry
2
2
2
th
B
2c
k





 1
G(

,
A
)
4

c
1
4

p
s
r
n
nc
Ý
Ý
X s  k q X s  k pol esXs  * 
  
 3  

3
Rs s   s
   s  Xs   s  X 3s
2
2
2
2c k p G( s, Ar )  4 c  1 4 c  1
Ý
Ý
Ys  k qYs  k polesYs  * 
 
 3  

3
Rs s   s
   s  Ys   s  Ys3
th
n
B
n
Undulator (Compressor?)
2

K


Ý
z  c   2 1  cos2k zz




K
R56  Lc

Lc
2
cKkx 
Ý
Ý
X  
X
  
2

cKky 
Ý
Ý

Y 
Y
  
e Brms
K
m ck z
Brms
2
2 
2
2
2
k x  k y  kz   
 u 
Bˆ

2
2
TW structures
˜ SW zsin t    kd  
˜ SW z  d sin t   
EzTW z,t   
z
o
z
o
SW

SW
z z
˜
z z 
sin kd
Wake Fields
Convolution with a Uniform
charge distribution
Delta Wake Function
W// s 
Zo c
2QcZo 
8.6s 

Ez s 
1 1 2 
lb 8.6 
a 
a a2  8.6s
0
225
V/pc/m
200
-0.05
175
w
-0.1
MV/m
MVam
150
-0.15
125
100
-0.2
75
0
0.0005
0.001
s
0.0015
0.002
m
-0.25
0
0.00001
0.00002
dz
0.00003
m
0.00004
Wake field along a 40 m bunch
z= 0.2389 1
z= 1.5
z= 10
0.05
0.02
0
pr _[ rad ]
0.02
Pr
0.04
Pr
0.04
0
- 0.02
0
- 0.02
- 0.04
- 0.04
- 0.05
0
0.00 1 0.00 2 0.00 3 0.00 4 0.00 5 0.00 6
0
R [m]
3.5
0.00 08 0.00 16 0.00 24 0.00 32 0.00 4
0
R [m]
0.00 08 0.00 16 0.00 24 0.00 32 0.00 4
R_[m]
3
rms norm. emittance [um]
2.5
rms beam size [mm]
2
1.5
1
0.5
Gun
Linac
0
0
2
4
6
8
10
z= 1.5
Z= 10
0.00 4
0.00 35
0.00 35
0.00 3
0.00 3
0.00 3
0.00 25
0.00 25
0.00 25
0.00 2
0.00 15
0.00 4
Z_[m]
0.00 35
Rs [m]
Rs [m]
Rs [m]
z= 0.2389 1
0.00 4
0.00 2
0.00 15
0.00 2
0.00 15
0.00 1
0.00 1
0.00 1
0.00 05
0.00 05
0.00 05
0
- 0.003 - 0.002 - 0.001
0
0.00 1 0.00 2 0.00 3
Zs -Zb [m]
0
- 0.003 - 0.002 - 0.001
0
0.00 1 0.00 2 0.00 3
Zs -Zb [m]
0
- 0.003 - 0.002 - 0.001 0 0.00 1 0.00 2 0.00 3
Zs -Zb [m]
Comparison with PARMELA/UCLA
==> good agreement
Emittance evolution for different laser rise times
3.5
(mm-mrad)
3
em it (ideal)
em it (0.5 psec rise)
em it (1 psec rise)
2.5
2

n
1.5
1
0.5
0
0
100
200
300
400
z (cm)
500
600
700
800
Comparison HOMDYN with ASTRA (Ph. Piot)
Experimental validation at the A0 photoinjector
(J. P. Carneiro et al.)
1.6 cells gun, 1.3 GHz, 40 MV/m peak field, 1.3 KG solenoid
9 cells Tesla structure, 1.3 GHz, 15 MV/m accelerating field
Gun
9-cells TESLA structure
Quads
PepperPot
Solenoid Scan @ 8nC
Emittance (mm-mrad)
computed by
HOMDYN
and
PARMELA/Orsay
Homdyn
Parmela
INPUTDECK
FIELD.SEK
FIELD.POI
HOMDYN
HBUNCH.OUT
HTWISS.OUT
HSCREEN.OUT
HSPACE.OUT
HFEL.OUT
HSLICES.OUT
HSUM.OUT
INPUTDECK - 1
(the beam line)
t0
TEND
H1
-1.d-1
200.d-9
1.d-12
ZETA0
ZSTOP
EMEV
0.00045d0
33.d0d0
1.d-6
MAXB
reprate
IPART
CHARGE
1
1000
1
1.d-9
ISAVE
IREAD
ZSAVE
0
0
8.1d0
iflat
0
XEMIT
XBUNCH
XPRIME
ITWISS
0.3d-6
1.d-3
0.d0
0
YEMIT
YBUNCH
YPRIME
ICAT
0.3d-6
1.d-3
0.d0
0
IPOI
ISOL
ISHIELD
IQUAD
ICAV
3
0
0
13
1
ISCAN
STEP
11
-0.1d0
NLOOP
3000
SPREAD
0.d0
DLBUNCH
-11.653d-12
BZCAT
0
IFOUR
0
IGA
55
ITWA
2
iprint
1
IPR2
10
carflut
0.d0
LCOOP
300.d-6
ISWA
0
IWIG
1
iplas ifoil
0
0
Solenoids
Quadrupoles
RF gun
TW
structures
Undulator with Quadrupoles
ZSCREEN
33.d0
INPUTDECK - 2
(the bunch)
t0
TEND
H1
-1.d-1
200.d-9
1.d-12
ZETA0
ZSTOP
EMEV
0.00045d0
33.d0d0
1.d-6
MAXB
reprate
IPART
1
1000
1
ISAVE
IREAD
ZSAVE
0
0
8.1d0
iflat
0
XEMIT
XBUNCH
XPRIME
0.3d-6
1.d-3
0.d0
YEMIT
YBUNCH
YPRIME
0.3d-6
1.d-3
0.d0
IPOI
ISOL
ISHIELD
IQUAD
3
0
0
13
ISCAN
STEP
11
-0.1d0
CHARGE
1.d-9
ITWISS
0
ICAT
0
ICAV
1
NLOOP
3000
SPREAD
0.d0
DLBUNCH IGA
-11.653d-12 55
BZCAT
0
IFOUR
0
ITWA
2
ISWA
HREAD.COR
iprint
1
IPR2
10
carflut
0.d0
LCOOP
300.d-6
IWIG
0
iplas
1
ifoil
0
ZSCREEN
0
33.d0
INPUTDECK - 3
(integration step)
t0
TEND
H1
-1.d-1
200.d-9
1.d-12
ZETA0
ZSTOP
EMEV
0.00045d0
33.d0d0
1.d-6
MAXB
reprate
IPART
1
1000
1
ISAVE
IREAD
ZSAVE
0
0
8.1d0
iflat
0
XEMIT
XBUNCH
XPRIME
0.3d-6
1.d-3
0.d0
YEMIT
YBUNCH
YPRIME
0.3d-6
1.d-3
0.d0
IPOI
ISOL
ISHIELD
IQUAD
3
0
0
13
ISCAN
STEP
11
-0.1d0
CHARGE
1.d-9
ITWISS
0
ICAT
0
ICAV
1
NLOOP
3000
SPREAD
0.d0
DLBUNCH
-11.653d-12
BZCAT
0
IFOUR
0
IGA
55
ITWA
2
ISWA
iprint
1
IPR2
10
carflut
0.d0
LCOOP
300.d-6
IWIG
0
iplas
1
ifoil
0
ZSCREEN
0
33.d0
INPUTDECK - 4
(the output)
saving output data in HBUNCH.OUT and HTWISS.OUT
every
saving output data in HSPACE.OUT
every
dt1=TEND/NLOOP
dt2=dt1*IPR2
t0
TEND
H1
-1.d-1
200.d-9
1.d-12
ZETA0
ZSTOP
EMEV
0.00045d0
33.d0d0
1.d-6
MAXB
reprate
IPART
1
1000
1
ISAVE
IREAD
ZSAVE
0
0
8.1d0
iflat
0
XEMIT
XBUNCH
XPRIME
0.3d-6
1.d-3
0.d0
YEMIT
YBUNCH
YPRIME
0.3d-6
1.d-3
0.d0
IPOI
ISOL
ISHIELD
IQUAD
3
0
0
13
ISCAN
STEP
11
-0.1d0
CHARGE
1.d-9
NLOOP
3000
SPREAD
0.d0
DLBUNCH
-11.653d-12
IGA
55
iprint
1
IPR2
10
carflut
0.d0
LCOOP
300.d-6
HSAVE.COR
ITWISS
0
ICAT
0
ICAV
1
BZCAT
0
IFOUR
0
ITWA
2
Zw
ISWA
IWIG
0
iplas
1
ifoil
0
ZSCREEN
0
33.d0
saving outputs every DZ=ZSCREEN in
files HSCREEN.OUT and HFEL.OUT
INPUTDECK - 5
(parameters scan)
t0
TEND
H1
-1.d-1
200.d-9
1.d-12
ZETA0
ZSTOP
EMEV
0.00045d0
33.d0d0
1.d-6
MAXB
reprate
IPART
10
1000
1
ISAVE
IREAD
ZSAVE
0
0
8.1d0
iflat
0
XEMIT
XBUNCH
XPRIME
0.3d-6
1.d-3
0.d0
YEMIT
YBUNCH
YPRIME
0.3d-6
1.d-3
0.d0
IPOI
ISOL
ISHIELD
IQUAD
3
0
0
13
ISCAN
STEP
11
-0.05d0
CHARGE
1.d-9
ITWISS
0
ICAT
0
ICAV
1
NLOOP
3000
SPREAD
0.d0
DLBUNCH
-11.653d-12
BZCAT
0
IFOUR
0
IGA
55
ITWA
2
ISWA
iprint
1
IPR2
10
carflut
0.d0
LCOOP
300.d-6
IWIG
0
iplas
1
ifoil
0
Range of the parameter scan MAXB*STEP
ZSCREEN
0
33.d0
INPUTDECK - 6
(elements)
SOLMAP
'sanel'
'sanel'
'gtfbz'
ZQUAD
8.636d0
8.918d0
12.60d0
12.882d0
14.875d0
Z0CAV
0.d0
ZK
0.00045d0
nmod
1
MODO
'new45'
MODO
'twnew'
Z0TWA
5.d0
Z0WIG
18.1d0
ZSOLEN
1.3223500d0
4.900d0
0.000d0
WN
2856.d6
Z0FR
1.5d0
ZPER
3.d-2
BMAX
0.06d0
0.0d0
0.27d0
QGRAD
4.7828d0
-4.7828d0
-0.2281d0
0.2281d0
4.8562d0
FI0
27.5d0
taug
-10.d-6
ik
0
QEX
23616.74
DNCEL
86
FI0TW
-13.d0
NW
71
QLENGTH
0.132d0
0.132d0
0.132d0
0.132d0
0.132d0
EPEAK
120.d6
rfoff
0.801d0
itrans
0
USTOR
0.39478e-05
ZINC
0.05248467
BRMS
0.504d0
VSFH
0.999892d0
WN
2856.d6
EPTWA
33.33d6
KX
0.d0
IRISWF
-11.6d-3
PSI
120.
FI0
-8.
EP
33.33d6
NMODULES DRIFT
6
0.36d0
bl
1
IRISWF
11.6d-3
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HomDyn HomeWork for the SPARC project
Solenoids
Quadrupoles
RF gun
TW
structures
Undulator with Quadrupoles