1. Contour plots of electron density 2D PIC in units of  [n |e|] cr wake wave breaking accelerating field laser pulse Blue:electron density green: laser field Red: longitudinal electric field bubble trapped electrons DLA bubble at later time accelerated electrons pulse erosion Self Focusing,Channeling Underdense homogeneous plasma Fixed ions Maxwell’s equations+Equation of motion Assuming These equations can be solved analytically in 2D (F. Cattani et al, PRE, 2001). Complete evacuationPartial electron evacuation half of channel width Numerical Results Red points correspond to analytical solution Greens and blue points correspond to numerical results Comparison with theoretical results: channel evacuated of electrons contour plot of electron density Plot of electron density vs. y evacuated channel Strong electrostatic wake E x Contour plot of electron density 2D PIC (SP) in units of  [n |e|] cr Contour plots of Laser intensity 2D PIC (SP) a in unit of(eE/m  c) In 2D PIC, data taken from a cut along x in the middle of the box. Laser pulse enters from left and propagates along x. Laser pulse as it enters the plasma Laser pulse after propagating 240 micrometers electron density Wave-breaking and electron acceleration Accelerated electrons electrons in front n accelerating field pulse erosion cavity 25 Mev dN/dE [Arb. Units] Energy in ev Phase space at time= 1031 fs After wave-breaking electrons are accelerated and injected into the pulse and the accelerating field. 4.8% of total number of electrons are accelerated. energy of accelerated electrons time=1395 fs Theoretical studies and particle-in-cell (PIC) simulations of nonlinear processes related to short pulse laser propagation in underdense plasmas. For the laser power above critical power for relativistic self-focusing in two spatial dimensions PIC simulation results converge to stationary laser filaments. Conditions for the formation of multifilament structures are discussed and demonstrated in simulations for relatively long pulses. For short laser pulses nonlinear propagation at relativistic intensities involves pulse erosion, frequency shift and characteristic steepening at the front of the pulse. Different mechanisms of particle acceleration are described including particle trapping at the front of the pulse, acceleration by the plasma wake fields and by the electromagnetic wave. These processes are simulated and discussed in the context of recent experiments with gas jet targets on the ALLS facility. Abstract Relativistic self-focusing, electron acceleration and ultra-short laser pulse propagation in underdense plasmas Neda Naseri, Paul-Edouard Masson-Laborde, Valery Bychenkov, Wojciech Rozmus, University of Alberta, Lebedev Physics Institute 1 1 2112 Filamentation of intense laser beam in plasma By using transversely flat modulated laser pulse, filamentation instability is being studied. Contour plot of Laser intensity 2D PIC a in unit of(eE/m  c) Wave breaking, acceleration (SP) Contour plot of electron density 2D PIC (SP). The picture on the left shows the wave breaking and the picture on the right shows injected electrons. injected electrons wave breaking Relativistic self-focusing Maximum intensity is 3 times bigger than maximum initial Intensity (SP). parameters as SP Contour plot of Laser intensity 2D PIC (SP) Snapshots of laser intensity cross section Pulse erosion, 1D in hydro pulse erosion Pulse Field Density Longitudinal Field Strong steepening of longitudinal field Relativistic fluid model Model equations in 1D: Maxwell + Full Hydro + Poisson Maxwell Equation Hydro: continuity + motion equations Poisson equation dN/dE [Arb. Units] Electron energy in ev 180 Mev Electron energy spectrum Phase space Threshold power for bubble regime Gordienko, phys plasmas, 2005 Numerical models Particle-in-cell code MANDOR (1D, 2D): Romanov et al. PRL, 2004 Relativistic cold plasma approximation and Maxwell equations in 1D-limited by the absence of kinetic effects Standard parameters (SP) - consistent with experimental conditions: pulse duration,  =30fs, spot size=13  m, intensity, I=4*10 18 W/cm 2, density, n=5* 10 19 cm -3, p-polarized. The experiment carried out at the Advanced Laser Light Source (Z. L. Chen, Y. Y. Tsui, R. Fedosejves) Homogeneous plasma slab with 40 microns linear ramp in the front. 400-800 microns in length - propagation distance is limited by laser pulse scattering and absorption. ALLS bubble I=4 10 18,  =30fs, n=5 10 19 cm-3 I=10 20,  =20fs, n=10 19 cm-3  [fs ] P[TW] From laser plasma accelerators, quasi monoenergetic 70 – 170 MeV, Mangles et al. Nature 2004, Geddes et al. ibid 2004, Faure et al. ibid 2004. longitudinal filed DLA electrons 100 Mev DLA electrons electrons in front part of bubble electrons in back of bubble electrons in front part of bubble electrons in back of bubble Input modulated laser pulse filaments Laser intensity (eE/m  c) filaments Simulation parameters: