Trapping, thermal effects, and wave breaking in the nonlinear plasma wake-field accelerator

Single Shot Characterization of High Transformer Ratio Wakefields in Nonlinear Plasma Acceleration

Plasma wakefields can enable very high accelerating gradients for frontier high energy particle accelerators, in excess of 10  GeV/m. To overcome limits on single stage acceleration, specially shaped drive beams can be used in both linear and nonlinear plasma wakefield accelerators (PWFA), to increase the transformer ratio, implying that the drive beam deceleration is minimized relative to acceleration obtained in the wake. In this Letter, we report the results of a nonlinear PWFA, high transformer ratio experiment using high-charge, longitudinally asymmetric drive beams in a plasma cell. An emittance exchange process is used to generate variable drive current profiles, in conjunction with a long (multiple plasma wavelength) witness beam. The witness beam is energy modulated by the wakefield, yielding a response that contains detailed spectral information in a single-shot measurement. Using these methods, we generate a variety of beam profiles and characterize the wakefields, directly observing transformer ratios up to R=7.8. Furthermore, a spectrally based reconstruction technique, validated by 3D particle-in-cell simulations, is introduced to obtain the drive beam current profile from the decelerating wake data.

Vlasov simulations of thermal plasma waves with relativistic phase velocity in a Lorentz boosted frame

For certain classes of relativistic plasma problems, performing numerical calculations in a Lorentz boosted frame can be even more advantageous for gridded momentum-space-time (e.g., Vlasov) problems than has been demonstrated for position space-time problems and result in a potential reduction in the number of calculations needed by a factor ∼γ_{b}^{6}. In this study, the Lorentz boosted frame technique was applied to the problem of warm wave-breaking limits of plasma waves with relativistic phase velocity. The numerical results are consistent with analytic conclusions. By appropriate normalization and for sufficiently warm plasma, the dynamics for the Vlasov equation in different Lorentz frames were found to be independent of γ_{p}.

Relativistic warm plasma theory of nonlinear laser-driven electron plasma waves

A relativistic, warm fluid model of a nonequilibrium, collisionless plasma is developed and applied to examine nonlinear Langmuir waves excited by relativistically intense, short-pulse lasers. Closure of the covariant fluid theory is obtained via an asymptotic expansion assuming a nonrelativistic plasma temperature. The momentum spread is calculated in the presence of an intense laser field and shown to be intrinsically anisotropic. Coupling between the transverse and longitudinal momentum variances is enabled by the laser field. A generalized dispersion relation is derived for Langmuir waves in a thermal plasma in the presence of an intense laser field. Including thermal fluctuations in three-velocity-space dimensions, the properties of the nonlinear electron plasma wave, such as the plasma temperature evolution and nonlinear wavelength, are examined and the maximum amplitude of the nonlinear oscillation is derived. The presence of a relativistically intense laser pulse is shown to strongly influence the maximum plasma wave amplitude for nonrelativistic phase velocities owing to the coupling between the longitudinal and transverse momentum variances.

Phase mixing of relativistically intense waves in a cold homogeneous plasma

We report on spatiotemporal evolution of relativistically intense longitudinal electron plasma waves in a cold homogeneous plasma, using the physically appealing Dawson sheet model. Calculations presented here in the weakly relativistic limit clearly show that under very general initial conditions, a relativistic wave will always phase mix and eventually break at arbitrarily low amplitudes, in a time scale omegapetaumix approximately {3/64(omegape2delta3/c2k2)|Deltak/k|(|1+Deltak/k|)](1+1|1+Deltak/k|)}(-1). We have verified this scaling with respect to amplitude of perturbation delta and width of the spectrum (Deltakk) using numerical simulations. This result may be of relevance to ultrashort, ultraintense laser pulse-plasma interaction experiments where relativistically intense waves are excited.

Ionization-induced electron trapping in ultrarelativistic plasma wakes

The onset of trapping of electrons born inside a highly relativistic, 3D beam-driven plasma wake is investigated. Trapping occurs in the transition regions of a Li plasma confined by He gas. Li plasma electrons support the wake, and higher ionization potential He atoms are ionized as the beam is focused by Li ions and can be trapped. As the wake amplitude is increased, the onset of trapping is observed. Some electrons gain up to 7.6 GeV in a 30.5 cm plasma. The experimentally inferred trapping threshold is at a wake amplitude of 36 GV/m, in good agreement with an analytical model and PIC simulations.

Warm wave breaking of nonlinear plasma waves with arbitrary phase velocities

A warm, relativistic fluid theory of a nonequilibrium, collisionless plasma is developed to analyze nonlinear plasma waves excited by intense drive beams. The maximum amplitude and wavelength are calculated for nonrelativistic plasma temperatures and arbitrary plasma wave phase velocities. The maximum amplitude is shown to increase in the presence of a laser field. These results set a limit to the achievable gradient in plasma-based accelerators.

Particle simulation of an ultrarelativistic two-stream instability

A two-stream instability in an unmagnetized plasma is examined by a particle-in-cell simulation. Each beam initially consists of cold electrons and protons that stream at a relative Lorentz factor 100. This is representative for plasma close to the external shocks of gamma-ray bursts. An electrostatic wave develops which saturates by trapping electrons. This wave collapses and the resulting electrostatic turbulence gives an electron momentum distribution that resembles a power law with a spectral break. Some electrons reach Lorentz factors over 1000.

Plasma electron trapping and acceleration in a plasma wake field using a density transition

A new scheme for plasma electron injection into an acceleration phase of a plasma wake field is presented. In this scheme, a single, short electron pulse travels through an underdense plasma with a sharp, localized, downward density transition. Near this transition, a number of background plasma electrons are trapped in the plasma wake field, due to the rapid wavelength increase of the induced wake wave in this region. The viability of this scheme is verified using two-dimensional particle-in-cell simulations. To investigate the trapping and acceleration mechanisms further, a 1D Hamiltonian analysis, as well as 1D simulations, has been performed, with the results presented and compared.