Max eenergy with SPS beam ep separation final

Max. e-energy with SPS beam, e-p separation, final focus (basic physics and some preliminary simulations) A. Petrenko, 3 rd AWAKE-PBC meeting, Nov. 9, 2017

The current AWAKE experiment:

Possible AWAKE Run 2 goals and configuration that we study now: Run I goal: study the Self-Modulation Instability as a way to produce a train of proton microbunches driving the plasma wakefields resonantly (external electron beam will be used to probe these wakefields). Run II goal: accelerate significant electron charge with the best possible beam quality and the highest possible accelerating gradient (achievable with the SPS proton beam and SMI). Electron beam 400 Ge. V protons The first plasma section produces a train of proton micro-bunches The second plasma section accelerates electron beam. ≈ 20 m Plasma density np = 7∙ 1014 1/cm 3 (plasma wave length λp = 1. 2 mm). The SPS proton beam is assumed to be compressed longitudinally by a factor of two (σz ≈ 6 cm, Ipeak ≈ 100 A) – feasible according to the “Prospects for improved SPS p+ bunch parameters for AWAKE” by A. Lasheen, J. Repond, E. Shaposhnikova. What is possible to achieve in this configuration in terms of accelerating gradient and witness beam quality? What are the requirements on electron injector and injection scheme?

The best AWAKE Run-2 gradient so far (2 D LCODE): Still to be reproduced in 3 D simulations… Stable Ez ≈ 800 MV/m (unloaded) The gap is needed to inject electrons into the stable wakefield. The gap can be reduced to few cm instead of 1 m shown here (also see K. Lotov’s side-injection approach). A ~100 m long gap with some optics (quadrupoles, dipoles) can be used to collimate the micro-bunched beam before the accelerator (remove the defocused protons). Ideally the micro-bunching stage + collimation should be a part of the upstream 800 m long beamline.

Beam loading will reduce the accelerating field by some 10 -20% (see details in Alexander Gorn’s report): Higher wakefield allows for the higher e-beam charge. Q = 0. 36 n. C Transverse e-beam distribution is assumed to be gaussian with σx, y = 0. 2 mm (= 1 c/ωp). (for emittance preservation it’s better to use narrower beams).

e-p dephasing will limit the energy and increase the energy spread: γp = 400 γe >> γp With 0. 7 GV/m loaded constant gradient we need 70 m long plasma to get 50 Ge. V electrons. After 70 m Dephasing length in 70 m will be LΔv/c = 70 m*(1 km/sec)/(3 e 5 km/sec) = 0. 22 mm – significant! More like 100 m long plasma is needed to reach 50 Ge. V.

e-p dephasing will limit the energy and increase the energy spread: After 10 m of accelerating section: This preliminary 2 D LCODE simulation is done with a single drive bunch!

e-p dephasing will limit the energy and increase the energy spread: After 50 m of accelerating section: This preliminary 2 D LCODE simulation is done with a single drive bunch!

Wakefield should be initially over-loaded and later under-loaded: After 10 m of accelerating section: After 50 m of accelerating section:

Wakefield should be initially over-loaded and later under-loaded: After 50 m of accelerating section:

Wakefield should be initially over-loaded and later under-loaded: After 50 m of accelerating section: Energy spread ≈ 100% * 0. 6 Ge. V / 33 Ge. V = = 1. 8% (rms energy spread is below 1%)

Wakefield should be initially over-loaded and later under-loaded: After 100 m of accelerating section:

Wakefield should be initially over-loaded and later under-loaded: After 100 m of accelerating section:

Possible e-p separation: Proton energy will be ~10 x times higher. Proton energy spread will be ~10 -20% -- ok for a standard beam transport. Electron beam can be separated and then protons transported to the beam dump. ≈ 5 -20 m e- Experiment 400 Ge. V protons p-beam dump ≈ 50 -100 m (depending on the energy needed) Requirements on electron final focus? (without quads the e-p separation line can be shorter) 15

General scaling of beam parameters with plasma density nplasma = 7∙ 1014 cm-3 nplasma = 4 x(7∙ 1014 cm-3) 2 x higher wakefield 2 x smaller transv. size => 4 x higher beam density. The same angular spread => 2 x lower beam emittance required. The same current => 2 x less particles needed to drive 2 x higher wake. (Also 2 x less accelerated particles). 10 x less particles with 10 x lower emittance and the same current can potentially drive 10 x higher wakefield. Maximum plasma density is essentially defined by the transverse beam emittance. Higher peak current is needed to reduce the number of micro-bunches => less strict tolerances on plasma density. 16

Conclusions Using the 400 Ge. V SPS beam in plasma of 7 e 14/cm 3 a 50 m long AWAKE-type accelerator can reach approximately 30 Ge. V with 1 -2% of total energy spread. In order to reach 50 Ge. V a 100 m long plasma section will be required. Possible ways to reduce the accelerator length: Try to use higher plasma density with existing beam (need more optimization studies) Improve SPS beam transverse emittance (2 x lower emittance will give 2 x higher wakefield in 4 x more dense plasma). Use more efficient micro-bunching technique (2 x gain might be possible). Also higher energy will be possible (120 Ge. V? ) 17

What is beam cooling and why it is important for PWFA? Beam cooling in general is the reduction of beam temperature, i. e. the reduction of beam emittances (transverse and longitudinal). This allows to produce denser beams which can drive higher-amplitude plasma oscillations. -- if electron density perturbation during plasma oscillations are comparable to the initial plasma density. To drive the plasma oscillations efficiently the driver beam density should be comparable to the plasma density. So the beam density defines the plasma density which defines the accelerating electric field amplitude. For example in the AWAKE experiment the proton beam density nbeam ≈ 1013 1/cm 3, therefore we need approximately 100 micro-bunches to drive the ~1 GV/m wakefield at nplasma ≈ 1015 1/cm 3. Beam cooling potentially can increase the beam density significantly (by several orders of magnitude). Longitudinal-only beam cooling reduces the bunch length and simplifies the multi-bunch driven PWFA. Longitudinal and transverse cooling combined allow higher plasma density => higher gradients. Boosting the accelerating gradient can help to address some technical problems like the scalability of the plasma source for example. At few 100 GV/m the LHC beam can be depleted in the AWAKEscale facility. More details… 18

presented by K. Lotov at AWAKE collaboration meeting, Lisbon 10. 03. 2016 Comparison of drive beams Field decrease due to emittancedriven divergence of first bunches 28 equal bunches, average current = baseline peak current, 1. 2 mm mrad (maybe external focusing can help) exponential charge growth (charge of 14 full bunches in total), same average current at the end, 1. 2 mm mrad density step, 3. 6 mm mrad AWAKE baseline Bunch train with growing bunch charge is more efficient than train of equal bunches and self-modulating beam 19

presented by K. Lotov at AWAKE collaboration meeting, Lisbon 10. 03. 2016 Bunch trains from realistic beams n o ctr le e st e t gy pre-bunched “future baseline” case: σz=6 cm, N=2· 1011, =1. 2 mm mrad st e igh er n e h self-modulated “low-emittance baseline” case with a density step, 1. 2 mm mrad Ib( ), number of bunches is reduced for visibility 20

e-p dephasing will limit the energy and increase the energy spread: