Ultra-High-Intensity Laser-Plasma Interactions: Comparing Experimental Results with Three- Dimensional,Fully-Relativistic, Numerical Simultations Donald Umstadter Scott Sepke

“Moore’s Law” for Peak Laser Intensity

Intense optical laser light can generate radiation across the entire spectrum Characteristics Femtosecond Tunable Collimated Synchronized Bench-top Bright Micron source Type THz Infrared X-rays Electrons Positrons Protons Neutrons Applications Non-destructive testing Radiography Lithography Micro-machining Ultrafast reactions Metrology

Relativistic self-channeling leads to collimation of the laser beam, which leads to collimation of the electrons. Beam divergence found to be reduced with increasing laser intensity P laser =30 TW E = 180 MeV  = e -  laser = 30 fs  ~ 0.25 o LANEX  laser = 400 fs  = 1°

Laser wakefield plasma waves can accelerate electons to energy 100 MeV in a single millimeter F ~IF ~I ll E max at t~  p

“Monoenergetic” electrons with energy exceeding 150 MeV J. Faure et al., Nature 431, 541 (2004) C.G. R. Geddes et al., Nature 431, 538 (2004) S.P.D Mangles et al., Nature 431, 535 (2004) PIC code prediction experimental result

Particle-in-Cell Laser-Plasma Simulations An exact field and particle motion solver. Maxwell’s Equations Equation of Motion E,B Fields ( , J) LSP is a hybrid fluid/particle-in-cell code: ¤ Models include plasmas, lasers, ionization, particle beams, QMD equations of state, TE and TM modes… ¤ Allows migration between fluid and kinetic solvers. ¤ Uses explicit and stable implicit particle and field solvers.

LSP Particle-in-Cell Simulations GHz Opteron (64-bit) processors 128 nodes each containing 4 GB of RAM PrairieFire Beowulf Cluster Fully relativistic 1,2,3D Cartesian and cylindrical geometry Self-consistent laser-plasma interactions Plasma wave 30fs laser pulse Self-injected electrons Plasma “bubble” Average Velocity Longitudinal Electric Field

Peak Power Rate (PW-Hz) 1 30-fs pulse duration 3-J energy per pulse 100-TW peak power 10-Hz repetition rate UNL soon to have a laser with peak power- rate of 1 PW-Hz, highest of any in the US

Diffraction limited laser focusing requires exact-field solutions Electron deflection experiment/simulations show that accurate laser fields are essential. We have derived exact solutions for arbitrary, focused Gaussian and super-Gaussian laser profiles. These models are complex and must be solved numerically.

Concluding Remarks High-intensity laser-plasma interactions (including laser accelerators) is one of few physical systems in plasma physics (which is a many-many-body problem) that can be numerically modeled with reasonable accuracy. The computing power required for 3-D modeling was reached only in the last decade. The availability of greater computing power will enable simulations with larger domains and longer durations, which can more accurately model larger interaction regions and higher plasma densities. The simultaneous rapid increases in laser and computer power are good example of technological convergence.

Basic mechanisms by which light interacts with matter at high field strengths Ultrahigh laser fields (TeV/cm) cause electrons to quiver at relativistic velocities p e  MeV 8 Relativistic mass shift and v x B force nonlinear index of refraction phase-modulation, ultrashort pulse compression … Gigabar light pressure displaces electrons but not the heavier ions, creating huge electrostatic forces –Plasma waves accelerate electron beams –Electrostatic sheaths accelerate ion beams Tightly focused laser fields can deflect electron beams Undulating electrons radiate x-ray beams

Self-focusing can balance diffraction resulting in guiding Threshold: Self-channeling arises from ponderomotively driven plasma expulsion Uniform density F Density channel r I

Single-Pulse Drives Electron Betatron Oscillations E. Esarey et al., Phys. Rev. E 65, (2002).

Ponderomotive Deflection of an Electron Beam by a Counterpropagating Laser Beam 1 2 1st laser pulse – accelerates e-beam 2nd laser pulse – deflects e-beam imaging screen Create the electron bunches with the shortest duration and lowest emittance ever produced Ultrafast electron diffraction Ultrafast X-ray sources S. Banerjee et al., Phys. Rev. Lett. 95, (2005). initial e-beam final e-beam 2 nd laser pulse

A Well-Collimated Beam of keV- Energy X-Rays are Emitted photons/shot in a collimated beam A. Rousse et al., Phys. Rev. Lett. 93, (2004).