Laminar Velocity Bunching
A. Bacci
V – LI2FE Collaboration meeting, 15-16 March 2011, Frascati
Giotto – Genetic Interface for OpTimising Tracking with Optics
New Genetic code able to find , more or less complex ,beam-line configurations, useful to
answer at many different problems, by using fully 3D simulations.
The search for the best beam-line settings is driven by a fitness function which can by
freely defined from the user.
The fitness function can be wrote using all data computed by the tracking code (Astra), or
computed by a post processor, which is dedicated to multi bunches simulations:
PosZ, time, En,Den,SigZ,Xemit,sigX,divergX,Yemit,SigY,divergY,emitY
Multi bunches post_pro:SCurrent(NSpike), SemitX(Nspike),SemitY,Sdist(Nspike)
All variable definite in the Astra input file (or in the Astra generator) can be chosen as a
Giotto variable to be optimized (genes) (ex. Phi(1)…Phi(50),maxe(1),maxb(1),
sig_x,sig_clock --- No limit in the number)
A typical simulation works with 3-15 variables and takes from 1h up to 2 days (by using a
quite old 8 core workstation) - The speed scale linearly with the cpu number.
Giotto can be switched from Genetic Optimizations to Statistical Analysis. Each Astra
variable can be analyzed and the sampling interval used for the optimization analysis
becomes the jitters interval, which can be sampled in uniform o Gaussion way – A
statistical analysis is quite fast; 300 test cases take just some hours.
Used for Vbunching strongly space charge dominated – TNSA Proton Acceleration – Laser
Comb - Single spike FEL, ecc…
--- Next upgrade (switchable Astra-Tstep-Homdybn) ---
Full velocity bunching -Sband
Q=1nC – sig_x=0.5 mm – dt=10ps Flat-Top
1) Best
Emit&Curr
C=11.3
2) Push-up
Energy by
VI,VII,VIII,IX
cavities
Current & emit distribution
C=10.6
emit=1.2
emit=2.0
[mm-mrad] [mm-mrad]
<I>= 1KA
σz=78 μm
1Slice=σz,s=3.8 μm
The emittance and envelope are in
opposition of phase (emit.correction)
E=170 MeV
E=340 MeV
Is it necessary to add coils on
the III S-band Cavity?
Envelope equation for a round Kapchinskii-Vladimirski beam. Ellipsoidal
uniform charge distribution with r  2x and rms longitudinal semi-axis  z :





K



I



I
z
zz
2
4
0
x
External forces: VB longitudinal focusing
gradient
sin
4

0

(z
)
0
K

with

0max
acc
.
z
0
3

(

)
RF
eE
 acc
0
,
2
m
c
0
2
z
2
63
z
Internal forces: space-charge –
emittance pressure
Longitudinal laminarity (spacecharge/emit):
23
22
I


Qc


z
z


z
2
2
I


I


0
x
z
0
x
z

z




(z
) 1

0
 2

c
1


VB Compression in longitudinal beam laminarity regime :







23
2
I
Qc
(
)
1
z
z



1
z
2
2
I
I
0
x
z
0
x
z



 





1
K


0



zz
z
2
z
2
62
z
2
zz
Equilibrium between space charge and longitudinal compression is preserved until the
LINAC end; No over compression – Longitudinal Laminar Beam
Under particular conditions (*) it is possible to find an Analytical solution
CM
CM  with
0 cos
0
CM2







CM 2
CM

, 


(*)    0

 CM  0

 CM  0
I
I0 




z
0
0

0


z




K




1
z
z z
63
2

z
2




1

4
2 2


 z

2


K
z
z

4
1
4
2
 


1

1

z
 2 2 

z 

2
 
K
z
1
4
2
 


1

1

z
 2 2 

z 

2
 
K
z
VB 5 TW – 4 on crest


VB over-compression – 3 TW

 





1


0


K
zz
z
2
z
2
62
z
2
zz
E=340 MeV
All VB 9 TW
E=170 MeV
on crest – 3 TW
Electron density, current and ρz
Conclusion:
New simulations with C band cavities are under study. These will be performed by Giotto
controlling the ρz parameters along the simulation.
The analytical study needs further considerations.
CM  ki





(
K



2



)



1

3
6
z z
z
 z2 small
5
z
z
2
z
1
d

4
tan




(
z
)
0

dz
2


RF
Short bunches: the compressing factor can be pushed at very high values:
C
 0
ex

 0 sin  ex
 1  0 

 04  
  0  0 
2

sin  ex
 0
Very strong de-bunching:
Lb , p     r02
r
Lb , sol  r02  B02  /  
It is not true for very short bunch!
Considering A=(R/L) >> 1
Lb ,ch arg e  4Q /  2  Rb2 
 t  0.9 fs (0.28 m)


Comp 100 !


Sub-fs e- 1 pC bunches @ SPARC First attempt
 0.1%