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

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

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

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

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

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+

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

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

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, (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.

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

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

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

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

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) mm ILC CLIC

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

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)

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

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

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

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

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, (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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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 /14/2015S. Nagaitsev | Beam quality preservation and power considerations24 Growth length: 5 mm for 1 pC (~10 7 particles) for ext. focusing

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

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 arXiv:

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