Particle acceleration in plasma By Prof. C. S. Liu Department of Physics, University of Maryland in collaboration with V. K. Tripathi, S. H. Chen, Y. Kuramitsu,

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Particle acceleration in plasma By Prof. C. S. Liu Department of Physics, University of Maryland in collaboration with V. K. Tripathi, S. H. Chen, Y. Kuramitsu, L. C. Tai, S. Y. Chen, J. Wang, N. Kumar, and B. Eliasson

Cosmic ray acceleration

Magnetosphere of the Earth

The Earth’s magnetic field and magnetosphere

Cavity flow with reentrant jet

“Mono-energetic” electrons on the Earth

Acceleration gradient of plasma wave can be large Maximum acceleration gradient limited by the wave breaking or giving,, for Non-relativistic wave- breaking amplitude Relativistic wave-breaking amplitude is the Lorentz factor for plasma wave SLAC on a slab !!! Electron can be accelerated by plasma wave:

How to generate plasma wave ?? 1.Mode conversion 2.Beat wave excitation with two laser pulses 3.Raman scattering 4.Relativistic wake plasma wave excitation by electron beam or short pulse laser

1) Mode conversion + + An EM wave obliquely propagates into a plasma with density gradient. An oscillatory current can cause space charge oscillations. EM wave → ES wave

2) Beat wave excitation –Two long laser pulses –Plasma wave excitation possible if, –Maximum saturated amplitude of the plasma wave due to relativistic mass effect (Rosenbluth and Liu, PRL, 1972) Backscattering, Forward scattering,

Nonlinear frequency-amplitude relation

Laser light: Scattered light: 3) Raman Scattering by Plasma Wave Plasma: Current: Feed back Instability Growth rate:

Raman heated electrons

Raman scattering causes electron acceleration

Maximum electric field of the plasma wave 4) Relativistic wake plasma wave excitation by electron beam or short pulse laser

Acceleration of a SLAC electron beam Hogan et.al. Phys. Rev. Lett. 95, (2005) Demonstration of acceleration in beam driven wakefield (SLAC)

Mono-energetic electron beam by short pulse laser Mangles et.al, Nature, 431, 535 (2004), Faure et.al., Nature, 431, 541 (2004), Geddes et.al., Nature, 431, 538 (2004) Observation of mono-energetic beam of electrons with energy MeV by three groups.

Chen, et.al.(Particle accelerator group, Academia Sinica, NCU) First direct measurement of acceleration gradient; eE=2.5 GeV/m ~ 10 3 of linac.

Micro magnetosphere Relativistic self focusing whereLaser power, Relativistic dielectric constant Relativistic effect increases Ponderomotive effect decreases Resultant effect ion channel formation Laser wakefield acceleration and ion channel formation in laser

Electron trajectories

Number density of electrons on axis

Wake field on axis

Injection and acceleration of mono-energetic electrons by a self-modulated laser pulse Experiments at Academia Sinica (PRL, 2006) OOPIC (object-oriented particle-in-cell) code –two spatial and three velocity components –pre-ionized electron-proton plasma –linearly polarized Gaussian laser pulse –s-polarization (normal to the density perturbation) –moving window –immobile ions Parameters –Peak laser intensity: I 0 = 8x10 18 W/cm 2 (a 0 = 2.) –Laser wavelength: = 0.81  m –Pulse duration:  = 45 fs –Gas density: n = 4x10 19 /cm 3 (  p /  L = 0.15) –Initial waist size: w 0 = 4  m –Chirp bandwidth: 27 nm

Initial Plasma Density

Time = 0.735ps

Time = ps

Time = 1 ps

Time = 1.1 ps 50 MeV mono energetic electron beam

The wake field bunches the electrons in real space. Time = 1.1 ps

The modulated laser field traps electrons and push electrons moving with the laser pulse. Time = 1.1 ps

The modulated laser field traps electrons and push electrons moving with the laser pulse. (The plasma is turned off at time = 1.33 ps) Time = 1.43 ps 50 MeV mono energetic electron beam E z of laser pulse

Distribution function

p x - x phase space

Weibel instability kxkx EyEy BzBz u+u+ u-u- Growth rate:

Thank you

Outline Plasma universe Plasma wave excitation and trapping of resonant electrons Laser driven acceleration and production of the mono-energetic electrons beam Ion acceleration Concluding remark

Plasma universe Three minutes after Big Bang Plasma dominated universe Radio jets, X-ray sources,  -ray bursts, pulsar, accretion disk etc…. We observe our universe mostly by EM waves. Its dispersion relation,

Ion bubble formation by different a