External Injection in Plasma Accelerators R. Pompili, S. Li, F. Massimo, L. Volta, J. Yang
Why Plasma Accelerators? Conventional RF cavities: 50-100 MV/m due to electrical breakdown Plasma: E>100 GV/m fields sustainable non-relativistic wave-breaking field E wb= me c 3 ω p 96 n0 (cm ) e 100 GV/m (n0~1018 cm-3)...but... 2πc λ p = ω 30μ m p whereas the typical microwave wavelength is ~cm It's challenging to place a bunch of electrons in such a microscopic wave! 2/11
Self Injection vs. External Injection Self Injection: c Problems: The electrons are repulsed by the driver, and slip at the back of the bubble Some of them are accelerated The trapping stops automatically when the charge contained in the cavity compensates the ionic charge Requires high intensity laser Requires high plasma density (slow plasma wave phase velocity) v g 1/ n 0 High energy spread (100%) Difficult charge control Nonlinear process: crucially depends on driver evolution (different from shot to shot) Difficult to control the emittance and tunability of self-injected electrons need to move to external (controlled) injection of electrons! 3/11
Laser driven scheme Driven by the ponderomotive force, causing the electrons to move along the direction of laser's propagation with 2 c F p = me a2 2 Emax a2 Ewb 1+ a 2 a= (linear) eλe 2 π me c 2 2πc λ p= ω p Advantage: high electric field (>10 GV/m, relativistic optical guiding if a>>1), compactness. Rayleigh range (diffraction): w ( z)=w 0 1+( z / L R )2 with L R=π(2 σ r )2 / λ L Dephasing length (velocity mismatch): λ 3p /2 λ 2L ( a) if a>>1 Pump depletition: Low accelerating length, low rep. rate, staging needed! 3 2 λ p /2 λ L 2/a 2 ( a) if a>>1 4/11
v g 1/ n 0 High density Low density Colliding laser pulses 30 fs lasers counter-propagating 1st laser: 3.4x10^18 W/cm2 (a=1.3) 2nd laser: 4x10^17 W/cm2 (a=0.4) 20 um spot size Electron beams up to 200 MeV. Advantages: stable and reproducible electron beam over laser shots; tunable energy and charge by choosing the position and polarization of laser injection. Disadvantage: no monoenergetic beam, using gas jet only 2mm acceleration length. Colliding pulse Colliding pulse (orthogonal polarization) 5/11
Injection and trapping of tunnel-ionized e - The wakefield is excited in a 9:1 mix of He and N2 that has multiple ionization states. The injection of tunnel-ionized electrons reduce the necessary wake potential and then the a 0 for trapping. Laser pulse enrgies < 500 mj a0 ranged from 1.6 to 2.5 ne = 1.4x1019 cm-3 6/11
Beam driven scheme Nb Accelerating gradients E acc [ MV / m]=244 2 1010 nb=109 (200 pc), σz=20μm (60 fs) 10 GV/m ( 600 σ z [μ m ] 2 ) (plasma density 7x1019 cm-3) Blowout possible when nb>n0 electron depletion inside the wake Transfomer ratio R=Eacc/Edec limited to 2 (simmetric bunches) 7/11
Plasma Photocathode Emission Simulation: in a mixture of He and Li gas, using a driver e-beam to first ionize the Li with a field lower than trapping threshold, and later using a focused laser beam to ionize He and inject electrons in the wake. Advantage: low emittance and controlled localized injection. Disadvantage: precise synchronization between laser and electron beam needed, low charge Driver Electron Beam: 300 pc, 20 fs, 5 µm radius, 200 MeV, Energy spread 10% n(li): 3.3 x 1017 cm-3 λ(li) = 60 µm Final Energy after 9 mm = 300 MeV (3% energy spread), Slice Emittance 3x10-8 mrad, with 2 pc charge 8/11
Controlled injection by density transition PWFA (16 MeV e-) method with controlled injection by using a localized density gradient dephasing mechanism ω 2p c v g (ω) 1 2 2 ω ( ) kp = n1=5x1013 cm-3 Injection is due to localized nonlaminar motion near the sharp density transition, and at wake amplitudes well below conventional wave breaking Up to 500 pc, need to control the sharpness of the density transition... ωp c n2=3.5x1013 cm-3 good separation with bkg e- Laminar Non laminar vs further theoretical and numerical investigations needed for this this PWFA-based self-injection scheme 9/11
R>2 with asymmetric beam Transformer Ratio: Limits the energy gain in PWFA With symmetric driving bunches, in linear regimes: Transformer Ratio limit can be overcome with asymmetric drivers, like a comb beam COMB @ SPARC_LAB 170 MeV 160 pc 4 pulses 50 fs 1 ps lengths 0 1 ps distance Work in progress... 10/11
Conclusions We discussed the basic mechanisms of plasma acceleration, the advantages and limits of laser wakefield (LWFA) and plasma wakefield acceleration (PWFA). As examples, four experiments/simulations illustrate controlled injection of plasma accelerators by means of different techniques. At the moment there isn't a winner, all techniques have useful peculiarities but still soffer of some problems (high energy spread, low charge, low accelerating lengths, possibility to use multi-staging) PWFA seems the most promising (using high quality preformed e- bunch helps), mostly in asymmetric regimes (shaped bunch, multi-bunch). 11/11
References E. Esarey, C. P. Schroeder, and W. P. Leemans, Review of Modern Physics, 81, 1229 (2009) H. Suk, N. Barov, J. B. Rosenzweig, and E. Esarey, Phys. Rev. Lett. 86, 1011 (2001) J. Faure et al., Nature 444, 737, 2006 A. Pak et al., Phys. Rev. Lett. 104, 025003 (2010). B. Hidding et al., Phys. Rev. Lett. 108, 035001 (2012). A. Mostacci et al., "Advanced Beam Manipulation Techniques at SPARC", Proceedings of IPAC2011, San Sebastián, Spain 12/11
Thank You! 13/11