1. Beam quality preservation and power considerations Sergei Nagaitsev Fermilab/UChicago 14 October 2015

2. PWFA Potentials Large accelerating fields of about 10 GV/m in the plasma cell and about 1 GV/m effective average field along the linac, Strong transverse focusing (MT/m) for accelerated electrons supported by accelerating wave itself Smaller overall facility footprint dominated by the beam delivery systems with short linacs (1.5 km/linac at 3 TeV), Wide range of colliding beam energy from Higgs factory to multi-TeV. 10/14/2015S. Nagaitsev | Beam quality preservation and power considerations2

3. Introduction (actually, these are our opinions) To compete with ILC or CLIC designs, a plasma-based concept needs to achieve a luminosity of ~2x10 34 at ~1 TeV c.m. The upper energy for an electron-positron collider, ~3 TeV, is limited by beamstrahlung (not by accelerating technology). We should keep in mind that particle physicists are asking for an electron-positron collider, NOT electron-electron. Thus, it is important for a plasma-based concept to work equally well for both electrons and positrons. 10/14/2015S. Nagaitsev | Beam quality preservation and power considerations3

4. The question is: can we achieve the luminosity of >10 34 cm -2 s -1 ? –With reasonable assumptions about cost, power, etc. Opinions in accelerator community vary –There are both fundamental and technical challenges 10/14/2015S. Nagaitsev | Beam quality preservation and power considerations4

5. Beam-based vs. laser-based There is some misconception (at least among non-experts) that beam-based plasma acceleration concepts are different from laser-based Actually, the physics of particle acceleration in plasma is largely independent of the driver. Opinion: Laser-based concepts offer more advantages –More flexibility with transverse and long. laser pulse shaping. –Huge opportunity for cost reduction because of commodity laser market; –Con: large number of accelerating plasma sections 10/14/2015S. Nagaitsev | Beam quality preservation and power considerations5

6. Quasi-linear regime vs “Bubble” (a.k.a blow-out) regime These two regimes apply to the trailing beam, not the drive beam. 10/14/2015S. Nagaitsev | Beam quality preservation and power considerations6 suitable for both e- and e+ Quasi-linearBubble Suitable for e-, not suitable for e+

7. Main challenge for collider applications How to make plasma acceleration efficient (in terms of power transfer to the trailing beam), –while maintaining beam parameters suitable for a collider application (small emittance and energy spread) 10/14/2015S. Nagaitsev | Beam quality preservation and power considerations7

8. Acceleration in ILC cavities The ILC cavity: ~1 m long, 30 MeV energy gain; f 0 = 1.3 GHz, wave length ≈ 23 cm The ILC beam: 3.2 nC (2x10 10 ), 0.3 mm long (rms); bunches are spaced ~300 ns (90 m) apart Each bunch lowers the cavity gradient by ~15 kV/m (beam loading 0.05%); this voltage is restored by an external rf power source (Klystron) between bunches; (~0.5% CLIC) Such operation of a conventional cavity is only possible because the Q-factor is >> 1; the RF energy is mostly transferred to the beam NOT to cavity walls. 10/14/2015S. Nagaitsev | Beam quality preservation and power considerations8

9. Acceleration in plasma The Q-factor is very low (for high fields) – must accelerate the bunch within one plasma wavelength of the driver! Cannot add energy between bunches, thus a single bunch must absorb as much energy as possible from the wake field. 10/14/2015S. Nagaitsev | Beam quality preservation and power considerations9 M. Tzoufras et al., PRL 101, 145002 (2008) To achieve L ~10 34, bunches should have ~10 10 particles (similar to ILC and CLIC). In principle, we can envision a scheme with fewer particles/bunch and a higher rep rate, but the beam loading still needs to be high for efficiency reasons.

10. Efficiency of energy transfer in a quasi-linear regime Shaping of bunch profile can significantly reduce accelerating voltage variations along the bunch –Growth of accelerating voltage is compensated by growth of decelerating force along the bunch 10/14/2015S. Nagaitsev | Beam quality preservation and power considerations10 Longitudinal bunch density and loaded accelerating voltage for 50% beam loading The total bunch length is (60 deg. for 50% beam loading) Zero energy spread Creating such shapes with required beam brightness is a challenge

11. Two main challenges (in our opinion) There are more than two, but there is not enough time in this talk to cover all of them 1.The transverse beam break-up instability 2.Acceleration of positrons 10/14/2015S. Nagaitsev | Beam quality preservation and power considerations11

12. Transverse wake in plasma There is no transverse wake in a uniform plasma –However focusing of trailing particles does exist (detuning wake) Beam acceleration perturbs plasma density and creates an accelerating channel and, consequently, transverse wake For small beam size (σ b  <<c/ω p ) the wake field is nearly uniform in transverse plane –The wake-function grows almost linearly with distance –In a logarithmic approximation it is where σ  is the rms size of plasma channel In the blow-out regime we can approximately write 10/14/2015S. Nagaitsev | Beam quality preservation and power considerations12

13. How strong is the transverse wake? In a blow-out regime with 50% beam loading the wake defocusing force at the bunch end excited by the entire bunch displacement Δx is comparable to the plasma focusing force at the same position Δx 10/14/2015S. Nagaitsev | Beam quality preservation and power considerations13

14. Transverse beam break-up Transverse wakes act as deflecting force on bunch tail –beam position jitter is exponentially amplified 10/14/2015S. Nagaitsev | Beam quality preservation and power considerations14 Short-range transverse wake a ≈ 35 mm (ILC) a ≈ 3.5 mm (CLIC) a ~ k p -1 (PWFA) 0.02-0.04 mm ILC CLIC

15. Transverse beam stability Transverse wake excites the head-tail instability of convective type –An oscillation of bunch head leads to increased bunch oscillations of its tail To prevent emittance growth and achieve beam stability the BNS (Balakin-Novokhatsky-Smirnov) criterion has to be satisfied: –I.e. the betatron frequency along the bunch needs to be changed so that amplitude of all particles would stay the same –the only way to obtain a focusing change in the blow-out regime is a momentum change along the bunch. –Assuming all particles moving with the same amplitude we obtain required variation of momentum along the bunch 10/14/2015S. Nagaitsev | Beam quality preservation and power considerations15

16. CLIC strategy: BNS damping + µm alignment of cavities 10/14/2015S. Nagaitsev | Beam quality preservation and power considerations16 This strategy is very challenging for PWFA because for ~10 10 particles it requires >50% energy spread along the bunch to make it stable (in a bubble regime). Dependence of particle momentum along bunch required for BNS stability in blow-out regime: beam loading 50%, longitudinal density is adjusted to the one required for beam loading compensation (see slide 11)

17. Strategy was also used at the SLC… 10/14/2015S. Nagaitsev | Beam quality preservation and power considerations17

18. Beam breakup in various collider proposals ILC –Not important; bunch rf phase is selected to compensate for long wake and to minimize the momentum spread CLIC –Important; bunch rf phase is selected to introduce an energy chirp along the bunch for BNS damping (~0.5% rms). May need to be de-chirped after acceleration to meet final-focus energy acceptance requirements PWFA –Critical; BNS damping requires energy chirp comparable to beam loading. De-chirping and beam transport is very challenging. 10/14/2015S. Nagaitsev | Beam quality preservation and power considerations18

19. Beam loading and BNS damping Beam loading and the transverse beam stability are closely coupled: –higher beam loading requires higher energy spreads along the bunch to keep the bunch transversely stable (by BNS damping). –Consequence of Panofsky-Wenzel theorem In a bubble regime (where focusing forces are the strongest) the transverse bunch stability requires energy spread comparable to beam loading: 50% beam loading requires ~50% energy spread (in a linear BNS theory) Conclusion: New ideas are needed on how to make the beam stable for high beam loading (and high power efficiency). 10/14/2015S. Nagaitsev | Beam quality preservation and power considerations19

20. Positrons 10/14/2015S. Nagaitsev | Beam quality preservation and power considerations20

21. Acceleration of positrons Acceleration of positrons is possible (in principle) in a quasi- linear regime ( ) –Challenging for colliders: Coulomb scattering leads to high emittances ( V. L. and S. N., PRST-AB 16, 108001 (2013) ) In a regime of dense positron bunches,, the plasma electrons get pulled into the positron bunch and create highly- nonlinear focusing 10/14/2015S. Nagaitsev | Beam quality preservation and power considerations21 A trajectory of a plasma electron inside of the positron bunch (4x10 9 )

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24. Challenges with a hollow-plasma channel Unclear how to make a channel without plasma and gas Transverse beam break-up is more severe because there is no plasma focusing (like in a bubble regime). –The effect has been known since 1999 10/14/2015S. Nagaitsev | Beam quality preservation and power considerations24 Growth length: 5 mm for 1 pC (~10 7 particles) for ext. focusing

25. Opinion There is still no suitable (for collider) concept for positron acceleration. 10/14/2015S. Nagaitsev | Beam quality preservation and power considerations25

26. Technical challenges with beam driver technologies To make a cost-effective 2 x 24-MW CW beam driver requires substantial R&D in SCRF technology 10/14/2015S. Nagaitsev | Beam quality preservation and power considerations26 SLAC-PUB-15426 arXiv:1308.1145

27. Summary Plasma Wake-Field Acceleration schemes have huge potentials in many areas, however, collider applications remain challenging. Fermilab would like to help (but is presently not funded): –Can offer expertise in conventional colliders; –Interested in confirming (by modeling and experiments) our findings about BNS damping vs beam loading –Interested in positron acceleration. For beam-driven PWFA schemes, the cost is determined by conventional accelerator technologies. New ideas are needed on how to reduce it. 10/14/2015S. Nagaitsev | Beam quality preservation and power considerations27