1. Elena Benedetto, CERN 16/12/08
Beam stability in the SPL-based accumulator: issues and planned studies
Elena Benedetto, CERN
16/12/08
EUROn WP2 joint with IDS Target kickoff meeting,
15-17/12/08 at CERN

2. Beam stability in the SPL-based accumulator: issues and studies
Why?
What?
How?
Many thanks to M. Aiba, R. Garoby, M. Martini, M. Meddahi, E. Metral, for introducing me to the subject. The work they have done (with many other people) is the starting point of my studies.
Elena Benedetto

3. Why and What(1/3)? Motivations
Proposed CERN SPL based Proton Driver
→ R.Garoby (see M.Martini’s talk)
Accumulator ring
Isochronous (h=0), no RF, 400ms, beam frozen longitud. to preserve Dp/p
6 bunches, 120ns bunch length
Compressor ring
rapid phase rotation in ~36ms, strong RF, large slippage factor h
~2ns bunch extraction to the Target
→ M.Aiba, CERN-AB BI
Instabilities may arise in the accumulator, with t<400ms
No synchrotron motion to stabilize
Collective effects studies done in the past, for a different scenario, via analytical estimations
→ R.Cappi, J.Gareyte, E.Metral, D.Mohl, CERN/PS (AE)
They will be repeated for the designed new machine via analytical estimations AND simulations.
Elena Benedetto

4. What(2/3)? Impedances in a machine:
EM interactions of the beam with the environment → wake-fields
Impedance = Fourier transform of the wake-field
Can induce beam instabilities:
single bunch and coupled bunch
In the transverse and longitudinal plane 2b
A bunch passing offset through a discontinuity (e.g. RF cavity) leaves behind itself a wake-field which interacts with the subsequent bunches
Courtesy G.Rumolo
If the head of a bunch is displaced with respect of the pipe axis, via interaction with the conducting wall, it generate a wake filed that affects the tail,… in our case (h=0) no mixing between head-tail to help stabilizing!
Elena Benedetto

5. What(3/3)? Impedances in a machine:
EM interactions of the beam with the environment → wake-fields
Resistive wall (beam pipe, kickers, collimators,…)
Single-bunch
Coupled-bunch
“Broad-band” impedance
“Resonators” (RF cavities, kickers,…)
The effects (instabilities) induced by wake-fields are intensity dependent
Elena Benedetto

6. How(1/3)? Impedances in a machine:
EM interactions of the beam with the environment → wake-fields
Resistive wall (beam pipe, kickers, collimators,…)
“Broad-band” impedance
“Resonators” (RF cavities, kickers,…)
In the longitudinal plane:
if h0 the rise time goes to →
CAREFUL! high order terms h~a=a0+a1(Dp/p) +… may become important!
→ estimated via analytical formula
→ study of instability threshold and/or rise-time gives the allowed impedance in the machine
→ such components must be carefully designed to keep the impedance as small as possible
Elena Benedetto

7. How(2/3)? The HEADTAIL code
The analytical estimations will be supported by a simulation campaign.
The HEADTAIL code: Macroparticle simulations, the bunch is sliced and interacts slice-by-slice with the wake-fields.
Developed at CERN, in 2002 (G.Rumolo (G.R.), F.Zimmermann, CERN-SL-Note AP)
Studies of beam interactions w. electron-cloud and w. broad-band wake-fields, in 2004-’06 (G.R., E.Benedetto, F.Zimmermann)
Upgraded to study a large variety of wake fields (broad-band, resistive-wall, kickers,...) and single-bunch instabilities, in 2007-’08
(G.R., D.Quatraro, E.Metral, B.Salvant)
In the near future will be included multi-bunches capabilities (G.R., E.Metral)
Localized impedance source
Courtesy G.Rumolo
Elena Benedetto

8. How(3/3)? Plans
HEADTAIL already contains (almost) all the tools needed for the beam stability study in the accumulator
Evaluate the expected machine impedance
→ (to be put in the code)
…and the allowed one!
Eventually propose cures:
Introduce non-linear elements (sextupoles, octupoles) to stabilize
Relax the constraint h=0 → CAREFUL! Need RF cavities → they will increase impedance
Carefully design machine elements …
3 or 1 bunches option(?)
Elena Benedetto

9. Thanks for your attention!

10. Slides from R.Garoby and M.Aiba
Back-up material
Slides from R.Garoby and M.Aiba

11. n FACTORY: SPL-based proton driver (1/4)
from M. Aiba
An HP-SPL based 5 GeV – 4 MW proton driver has been designed (HP-SPL + 2 fixed energy rings (accumulator & compressor)
Feasibility Study of Accumulator and Compressor for the 6-bunches SPL based Proton Driver
R.G. @ ETH Zurich
18/11/2008
R.G. 11
R.G. 11
2 December, 2008

12. n FACTORY: SPL-based proton driver (2/4)
Accumulator
[120 ns pulses -
95 ns gaps]
Accumulation
Duration = 400 ms
Compression
t = 0 ms
t = 12 ms
t = 24 ms
t = 36 ms
etc. until t = 84 ms
SPL beam
[42 bunches -
33 gaps]
Compressor
[120 ns bunch -
V(h=3) = 4 MV]
Target
[2 ns bunches – 5 times]
R.G. 12
R.G. 12
2 December, 2008

13. n FACTORY: SPL-based proton driver (4/4)
from M. Aiba
R.G. 13
R.G. 13
2 December, 2008

14. Accumulation scenarios
M.Aiba
# bunches
# acc. turns/time
(ms)
# ppb (end of acc.)
Acc. circum. (m)
Acc. bunch length (ns) 6
400 / ~400
1.67E+13
318.5
120 3
740 / ~460
3.33E+13
185.8 1
1920 / ~1200
1.00E+14
Use the same accumulator for 1 and 3 bunches options
No big tolerance to change the accumulator circumference, especially in 1 bunch and 3 bunches
Transverse S.C. would not be an issue because of long bunch length in accumulator and the kinetic energy of 5 GeV
Longitudinal S.C. could be managed by making the bunch in good shape (linear slope at both ends, parabolic with compensation RF for 1 bunch)
Details are in CERN-AB and CERN-AB-Note
Elena Benedetto

15. Alternative choice Accumulator with barrier bucket conserve dP/P
M.Aiba
Accumulator with barrier bucket
conserve dP/P
have h~0.06 or more(?)
but have larger impedance with barrier RF cavity
would be technically challenging to realize rather short barrier length (~20 ns)
cost barrier RF cavity
Elena Benedetto