Proton‐driven Plasma Wakefield Accelera5on John Adams Ins5tute, Oxford February 9, 2012 1. Introduc+on – why do we need new technologies ? 2. Plasma Wakefield Accelera+on a) In general b) Beam driven c) CERN demonstra+on experiment for proton‐driven PWA Allen Caldwell Max‐Planck‐Ins+tut für Physik 1
Par5cle Physics Few MeV alpha par+cles Rutherford 7‐18 GeV electrons SLAC-MIT,… HERA: high resolution proton structure measurements HERA 27.5 GeV electrons 920 GeV protons The nuclear structure story … 2
The most important tool in this story was the par+cle accelerator. 3
Par+cle physicists are convinced there are more discoveries to come: Standard Model not consistent without the Higgs par+cle – expect to discover at LHC Many things not explained in the standard model: • why three families • ma]er/an+ma]er imbalance • neutrinos and neutrino mass • hierarchy problem/unifica+on • dark ma]er • dark energy • … 4
Supersymmetry Extends symmetries (fermion-boson symmetry) possible candidate for dark matter unification of forces at extremely high energies >1/2 the particles have not been seen [and still no sign at LHC] 5
Superstrings ? Smallest objects are not point-like but finite- dimensional. 10 space dimensions, 3 are discovered. Most of the others small, invisible. Some large extra dimensions? 6
The Livingston plot shows a satura+on … Prac+cal limit for accelerators at the energy fron+er: Project cost increases as the energy must increase! New technology needed… 7
Why a Linear Electron Collider or Muon Collider? Leptons preferred: proton P P Collide point par+cles rather than complex objects But, charged par+cles radiate energy when accelerated. Power α (E/m) 4 Need linear electron accelerator or m large (muon 200 heavier than electron) 8
Linear Colliders are expensive with today’s gradients e + e - collisions at 500-1000 GeV
New Livingston Plot – Plasma Wakefield Accelera+on 10
Acceleration of Electrons in a Plasma Wave "#$%&'$(%)(*%+,-+-*$'%./%"0%"(1&2(%(3'%40%50%6()*-37 "#$%&'(!)'*!++'" 8-90%:; 7%+0<=>7%?@A>AB %&'()*+,-./ ! ! ! " # # # " $ ! " # Original proposal – use a laser ! ! " ## ! ! n $ " # eE mc ~ 1 TeV/m || p n � 1 · 10 15 cm − 3 λ p = 2 π p = 4 π n p e 2 k p = ω p = 1 mm ω 2 c k p n p m 11
Laser Wakefield Accelera+on 12
But – Accelera+on is DEPLETION‐LIMITED i.e., the lasers today do not have enough energy to accelerate a bunch of par+cles to very high energies e.g., 10 10 electrons · 10 12 eV · 1 . 6 · 10 − 19 J / eV = kJ This is orders of magnitude larger than what can be done today. If use several lasers – need to have rela+ve +ming in the 10’s of fs range Many stages, effec+ve gradient reduced because of long sec+ons between accelera+ng elements … 13
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I) Generate homogeneous plasma channel: Gas Ioniza+on of gas via: • Laser Plasma • Beam • RF II) Send dense rela+vis+c electron beam towards plasma (E field radial in rest frame of plasma): Beam density n b E = ion = electron Gas density n 0 15
III) Excite plasma wakefields: Electrons are expelled r z Ion channel Space charge force of beam ejects plasma electrons promptly along radial trajectories Posi+vely charged channel is lej 16
Electron mo+on solved with ... Space charge of drive driving force: beam displaces Space charge plasma electrons. oscilla5ons (Harmonic Plasma ions exert oscillator) restoring force: restoring force - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + - - + + + + + + - - + + + - + + + + + + - + + + + + - + + + + - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + - electron - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - beam - - - - - - - - - - - - - - - - - - - - - - - - - Longitudinal fields can accelerate and decelerate ! Plasma also provides super‐strong focusing force ! (many thousand T/m in frame of accelerated par5cles) 17
Experimental Layout (E-157) � UCLA � Located in the FFTB � Ionizing Ionizing � Streak Camera � Streak Camera e - or e + � Laser Pulse Laser Pulse � � Cdt Cdt � Li Plasma Li Plasma � (1ps resolution) � (1ps resolution) (193 nm) (193 nm) � n e � 2·10 2·10 14 14 cm cm -3 -3 � L � 1.4 m 1.4 m � X-Ray � X-Ray Diagnostic � Diagnostic N=2·10 N=2·10 10 10 � Bending Bending � � z =0.6 mm =0.6 mm � Cerenkov � Cerenkov Magnet Magnet � Optical Transition Optical Transition � E=30 GeV E=30 GeV � Dump � Dump Radiator Radiator � Radiators � Radiators 12 m 12 m � FFTB 18
I. Blumenfeld et al., Nature 445 , 741 (2007) !"#$%&'()*#&' 19
Why not con+nue with electrons ??? There is a limit to the energy gain of a trailing bunch in the plasma: R = ∆ T witness ≤ 2 T is the kinetic energy ∆ T drive See e.g. SLAC‐PUB‐3374, R.D. (for longitudinally symmetric bunches). Ruth et al. This means many stages required to produce a 1TeV electron beam from known electron beams (SLAC has 45 GeV) Proton beams of 1TeV exist today ‐ so, why not drive plasma with a proton beam ? 20
Why Proton‐Driven Wakefield Accelera5on Both laser‐driven and electron‐bunch driven accelera+on will require many stages to reach the TeV scale. We know how to produce high energy protons (many TeV) in bunches with popula+on > 10 11 /bunch today, so if we can use protons to drive an electron bunch we could poten+ally have a simpler arrangement ‐ single stage accelera+on. Linear regime (n b <n 0 ): Need very short proton bunches for strong gradients. Today’s proton beams have 21
Issues with a Proton Driven PWA: Small beam dimensions required • 2 N 0.6 eE linear = 240(MeV/m) 4 ⋅ 10 10 σ z (mm) σ z = 100 µ m ,N =1 10 11 yields 21 GeV/m Can such small beams be achieved with protons ? Typical proton bunches in high energy accelerators have rms length >20 cm 22
Issues with a Proton Driven PWA: Phase slippage because protons heavy (move more slowly than • electrons) 2 c 4 δ = π L 1 1 ≈ π L M P − E driver , i E driver , f λ p γ 1 i γ 1 f γ 2 i γ 2 f λ p E driver , i E driver , f L ≤ 1 λ p ≈ 300 m for E driver , i = 1 TeV , E driver , f = 0.5 TeV , λ = 1 mm 2 c 4 2 M P Few hundred meters possible but depends on plasma wavelength 23
Issues with a Proton Driven PWA con+nued: Longitudinal growth of driving bunch due to energy spread • 2 c 4 ) L ≈ 2 Δ E M P − 2 − γ 2 ( − 2 d = Δ v ⋅ t ≈ Δ β ⋅ L = γ 1 L E 2 E Δ E For d = 100 µ m , L = 100 m , E = 1. TeV , E = 0.5 Large momentum spread is allowed ! 24
Issues ‐ con+nued Proton interac+ons • λ = 1 1 n = 1 ⋅ 10 15 cm − 3 λ = 1000 km n σ < ⇒ n (10 − 23 cm 2 ) Only small frac+on of protons will interact in plasma cell Biggest issue iden+fied so far is proton bunch length. Need large energies to avoid phase slippage because protons are heavy. Large momentum spread is allowed. 25
Simula+on study Assume proton bunch compression solved ! Quadrupoles used to guide head of driving bunch 26 Nature Physics 5, 363 ‐ 367 (2009) A. Caldwell, K. Lotov, A. Pukhov, F. Simon
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