the physics and applications of high brightness electron beams - erice, october 9-14, 2005...
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The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005
Simulations of coherent Simulations of coherent synchrotron radiation effects synchrotron radiation effects
on beam dynamicson beam dynamics
G. Dattoli, M. Migliorati, A. SchiaviG. Dattoli, M. Migliorati, A. Schiavi
The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005
0)s,z(WE
Ne
zs 0
2
Vlasov equation for longitudinal distributionVlasov equation for longitudinal distribution
z
3/13/23/10
||
dxdx
s,xd
xz
1
R3
2
4
1
'd'dz)s,','z()'zz(Ws,zW
CSR
The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005
)0,,z()s,z(E
Ne
zsexp)s,,z(
0
2
s
0'ds)'s,z(W)s,z(
TEO codeTEO code(Transport by Exponential Operators)(Transport by Exponential Operators)
the formal solution of the Vlasov equation can be the formal solution of the Vlasov equation can be written aswritten as
For small ‘s’ (steps), by using For small ‘s’ (steps), by using the the symmetricsymmetric split we obtain split we obtain
0),s,s
2
1z(A),s,s
2
1z(sA
2
1sz)s,,z(
The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005
smooth evolution smooth evolution of distribution of distribution
function (example function (example with CSR without with CSR without
noise)noise)
The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005
CSR effectsCSR effectswith initial noisewith initial noise
The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005
Example of microbunching due to Example of microbunching due to CSRCSR
The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005
Comparison with tracking codeComparison with tracking code
-20
0
20
40
60
80
100
120
-0.06 -0.04 -0.02 0 0.02 0.04
[1/m]
z [m]
The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005
Comparison with tracking codeComparison with tracking code
0
50
100
150
200
250
-0.03 -0.02 -0.01 0 0.01 0.02 0.03
[1/m]
z [m]
The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005
Phase space distribution
The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005
0)s,z(WE
Ne
zs 0
2
Vlasov equationVlasov equation
z
3/13/23/10
CSR dxdx
s,xd
xz
1
R3
2
4
1s,zW
It is convenient to use dimensionless variables:It is convenient to use dimensionless variables:
0z
z'z
andand
0
'
The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005
0'
''s,'zF
'z
''
N
NC
's
'
1'd'dz'
2
3/10z
3/22000
e
RE4'CN
sRE4
Ne
3
2's
3/40z
3/2000
2
3/1
'z
3/1 dydy
's,y'd
y'z
1's,'zF
The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005
CSR instability thresholdCSR instability threshold
bunch)(Gaussian 4
6C
e
RE4CNN
3/1
2/5
2
3/10z
3/22000
th
The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005
The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005
CSR effect on dynamicsCSR effect on dynamics(Gaussian bunch)(Gaussian bunch)
If N / NIf N / Nthth and and s’ are the same, the s’ are the same, the
beam dynamics is the same beam dynamics is the same (fixed the type of distribution)(fixed the type of distribution)
sRE4
Ne
3
2's
3/40z
3/2000
2
3/1
2
3/10z
3/22000
th e
RE4CN
3/1
2/5
4
6C
The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005
N = 5e10σε0 = 7e-4σz0 = 7e-3 mη = 1.4e-3E0 = 1.5 GeVL = 1000 m
N = 6.35e10σε0 = 1e-3σz0 = 1e-3 mη = 5e-3E0 = 0.5 GeVL = 28 m
λ’ λ’
z’ z’
The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005
The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005
Preliminary simulations for SparxinoPreliminary simulations for SparxinoIn 80 cm the wake field does not perturb the uncorrelated gaussian
distribution (N/Nth ~ 3.2e-3).
The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005
Phase space grid 300x300
The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005
Phase space grid 300x300
The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005
Phase space grid 500x500
The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005
Phase space grid 2000x500
The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005
Fit of the distributionFit of the distribution(work in progress)(work in progress)
The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005
Initial distribution (2000x500)Initial distribution (2000x500)
The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005
Evolution of Evolution of longitudinal longitudinal distribution distribution
without noise without noise
The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005
Evolution of Evolution of longitudinal longitudinal distribution distribution with noise with noise
The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005
phase space distributionphase space distribution
The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005
Work to doWork to do
Improve the fit of initial distributionImprove the fit of initial distribution
Do a more realistic modelization of the Do a more realistic modelization of the compressor (e.g. add drifts, longitudinal compressor (e.g. add drifts, longitudinal space charge effect)space charge effect)
……