1. potential CERN facilities to study proton-driven plasma acceleration
Frank Zimmermann
Munich MPI, 9 December 2008

2. CTF-3

3. existing accelerator chain (LHC beam)
PS booster PS
SPS
LHC
final momentum [GeV/c]
2.1 26
450
7000
protons/bunch [1011] 17
1.3
1.15
rms longitudinal emittance [eVs]
0.11
0.03
0.06
0.2 (0.08*)
rms bunch length [ns]
143 1
<0.5
0.25 (0.16*)
relative rms energy spread [10-3]
0.32
0.3
0.11 (0.07*)
rms transverse emittance [mm]
2.5
3.0
3.5
3.75
bunch spacing [ns]
N/A 25
# bunches / cycle
4 (4 rings) 72
288
2808
cycle time
1.2 s
3.6 s
~22 s
5-10 h?
* w/o longitudinal blow up in the LHC
1 ns = 30 cm, 3x10-4 ns = 100 mm

4. present and future LHC injectors
Proton flux / Beam power
Linac2
Linac4
50 MeV
160 MeV
PSB
(LP)SPL
1.4 GeV
4 GeV
(LP)SPL: (Low Power) Superconducting Proton Linac (4-5 GeV)
PS2: High Energy PS
(~ 5 to 50 GeV – 0.3 Hz)
SPS+: Superconducting SPS
(50 to1000 GeV)
SLHC: “Superluminosity” LHC
(up to 1035 cm-2s-1)
DLHC: “Double energy” LHC
(1 to ~14 TeV) PS
26 GeV
PS2
50 GeV
Output energy
SPS
450 GeV
SPS+
1 TeV
LHC /
SLHC
DLHC
7 TeV
~ 14 TeV
Roland Garoby, LHCC 1July ‘08

5. layout of new LHC injectors
SPS
PS2, ~2017
SPL,~2017 PS
Linac4
~2012
R. Garoby, CARE-HHH BEAM07, October’07; L. Evans, LHCC, 20 Feb ‘08

6. injector upgrade schedule synchronized with LHC IR upgrades
R. Garoby,
LHCC 1 July 2008
LHC IR phase 1
2013: PSB
with linac4
LHC IR
phase 2
2017: SPL+PS2

7. upgraded accelerator chain (LHC beam)
SPL
PS2
SPS
LHC
final momentum [GeV/c] 5 50
450
7000
protons/bunch [1011]
2.5x10-4 4
rms longitudinal emittance [eVs]
7.3x10-7
0.05
0.06
0.2 (0.08*)
rms bunch length [ns]
1.9x10-4 1
<0.5
0.25 (0.16*)
relative rms energy spread [10-3]
0.18
0.3
0.11 (0.07*)
rms transverse emittance [mm]
0.35
3.0
3.5
3.75
bunch spacing [ns]
2.8 25
# bunches / cycle
200,000
144
288
2808
cycle time
20 ms
2.4 s
~13 s
5-10 h?
* w/o longitudinal blow up in the LHC
1 ns = 30 cm, 3x10-4 ns = 100 mm

8. phase space at SPL exit
M. Eshraqi
A. Lombardi

9. intermediate conclusions
the only proton beam which is naturally “short” is the one from the SPL, ~60 micron rms length, with 2.5x107 protons / bunch and available at the earliest in 2017
the beam from the SPS must be compressed by a factor 10,000 to obtain rms bunch lengths of mm
equilibrium bunch length scales with the inverse 4th root of RF voltage and with the 4th root of the momentum compaction factor
four other possibilities come to mind:
rapid change in momentum compaction factor followed by bunch rotation in mismatched bucket
or transverse deflecting cavity?!
damping by intrabeam scattering below transition?!
coherent electron cooling?!

10. mismatch d
bunch
pulse fast
quadrupoles
to change
momentum compaction, and quickly raise RF voltage
shape of linear rf bucket z
extract after ¼ synchrotron oscillation when bunch length is minimum
bunch length scales with the square root of pulsed momentum compaction factor

11. → expect compression by factor 2 x 10-2 /Sqrt(10) ~ 0.006 ~ 1/160
initial momentum compaction ac,initial ~ we may hope for ac,new ~ initial RF voltage ~ few MV we may hope for final RF voltage ~ 10x higher
→ expect compression by factor 2 x 10-2 /Sqrt(10) ~ ~ 1/160

12. transverse deflecting cavity+
bending system
can the plasma
wave excited by
crabbed beam be used for e- acceleration?
drift
bending
system?
transverse deflecting cavity
can something like this work?
short
bunch!
idea is to convert transverse size
into longitudinal size
(above schematic ignores x-dependent energy change from
crab cavity)
or transverse crab cavity followed by “slit”?

13. coherent e- cooling CeC proof-of- V. Litvinenko, Y. Derbenev
damping times in hours:
CeC proof-of-
Principle experiment at RHIC in 2012
V. Litvinenko, Y. Derbenev
promise of
1-hr damping
time at 7 TeV!
interesting, but still too small for our purpose

14. final conclusion to get “high-energy” proton bunch lengths below 1 mm,
we can use the beam from the SPL, or
we need strong cooling or bunch compression or an x(y)-z 4/6-D emittance exchange transformation or a combination thereof

15. appendix: thoughts on scattering limits and chances
scattering limits and maximum energy reach of plasma accelerators
the return of fixed target experiments?

16. scattering limits and energy reach
at the plasma-acceleration WG of CLIC08 Andrei Seryi and Tor Raubenheimer reported that 500 GeV acceleration in a plasma was possible, but that 1.5 TeV was excluded by Coulomb scattering – this seemed odd at first glance since Coulomb scattering gets weaker at higher energy
scattering limits were previously looked at by Montague & Schnell (1985) and Katsouleas & Dawson (1987)

17. A. Seryi
CLIC08 workshop, Plasma wakefield acceleration working group, CERN, Oct. 2008
B.W. Montague, W. Schnell
Multiple scattering and synchrotron radiation in the plasma beat wave accelerator. 2nd Int. Workshop on Laser Acceleration of Particles, Los Angeles, CA, Jan 7-18 Jan 1985, AIP Conf.Proc.130: ,1985.
T. Katsouleas, J.M. Dawson
Plasma acceleration of particle beams AIP Conf.Proc.184: ,1989.

18. scaling of the multiple scattering limit
multiple scattering from my memory
indeed the normalized emittance grows as the
square root of the final
energy, but no hard limit in energy reach
to avoid this limit the b function must increase less than with the
the square root of energy (e.g. tapered plasma density)

19. bremsstrahlung
most important vacuum limit at high energy e+ or e- machines
this effect would suggest that the total distance
travelled through the plasma cannot be more than
one or a few radiation lengths
for example X0~10 m for 4x1022 e/cm3
using the rough estimate of 30 GV/m for 1x1017e/cm3 this gives an ultimate energy of ~200 TeV

20. nuclear interaction of protons with plasma?
similar magnitude as radiation length
variation with beam energy?

21. return of fixed target experiments
since extremely high gradients are feasible with plasmas but the collision of two such beams may be difficult to achieve, could fixed target experiments become attractive again? Pantaleo Raimondi in particular they could be interesting for proton driven plasma accelerators with a single proton beam, a single stage, and very high proton and electron energy; possibly high luminosity experiment might be different from present colliders