Electron Beam Filamentation Research Articles

Filamentation and focusing of electron beams due to interactions with plasma waves.

Results of numerical modeling of the interaction of an electron beam propagating across relativistic plasma waves indicate that electron beam filamentation and focusing may occur under certain conditions. The model is based on solving the relativistic equation of motion in three dimensions for the individual electrons in a tenuous Gaussian beam, as they pass through a relativistic plasma wave. Several electron beam and plasma wave parameters were varied, and the results are summarized. One of the results is that the spacing of the electron beam filaments correlates with the wavelength of the plasma wave. The electron beam filaments appear as vertical slabs after the beam exits the plasma waves. The electron beam also compresses to a focus after it exits the plasma, and the focal distance depends on several parameters including the electron beam energy and phase velocity of the relativistic plasma wave. It is suggested that these focusing and filamentation phenomena may be the basis for diagnostics schemes for laser plasma interactions. The parameters used in the model were electron beam energies in the 5-50 keV range and plasma wave properties typical for the beat-wave produced by CO2 lasers, which correspond to the facilities available in our laboratory. The limitations of these results to lower energy density beam and plasma regimes and to higher energy density regimes will be discussed.

On the investigation of fast electron beam filamentation in laser-irradiated solid targets using multi-MeV proton emission

The transverse filamentation of beams of fast electrons transported in solid targets irradiated by ultraintense (5 × 1020 W cm−2), picosecond laser pulses is investigated experimentally. Filamentation is diagnosed by measuring the uniformity of a beam of multi-MeV protons accelerated by the sheath field formed by the arrival of the fast electrons at the rear of the target, and is investigated for metallic and insulator targets ranging in thickness from 50 to 1200 µm. By developing an analytical model, the effects of lateral expansion of electron beam filaments in the sheath during the proton acceleration process is shown to account for measured increases in proton beam nonuniformity with target thickness for the insulating targets.

Effect of Lattice Structure on Energetic Electron Transport in Solids Irradiated by Ultraintense Laser Pulses

The effect of lattice structure on the transport of energetic (MeV) electrons in solids irradiated by ultraintense laser pulses is investigated using various allotropes of carbon. We observe smooth electron transport in diamond, whereas beam filamentation is observed with less ordered forms of carbon. The highly ordered lattice structure of diamond is shown to result in a transient state of warm dense carbon with metalliclike conductivity, at temperatures of the order of 1-100eV, leading to suppression of electron beam filamentation.

Electric field generation by the electron beam filamentation instability: filament size effects

The filamentation instability (FI) of counter-propagating beams of electrons is modelled with a particle-in-cell simulation in one spatial dimension and with a high statistical plasma representation. The simulation direction is orthogonal to the beam velocity vector. Both electron beams have initially equal densities, temperatures and moduli of their non-relativistic mean velocities. The FI is electromagnetic in this case. A previous study of a small filament demonstrated that the magnetic pressure gradient force (MPGF) results in a nonlinearly driven electrostatic field. The probably small contribution of the thermal pressure gradient to the force balance implied that the electrostatic field performed undamped oscillations around a background electric field. Here, we consider larger filaments, which reach a stronger electrostatic potential when they saturate. The electron heating is enhanced and electrostatic electron phase space holes form. The competition of several smaller filaments, which grow simultaneously with the large filament, also perturbs the balance between the electrostatic and magnetic fields. The oscillations are damped but the final electric field amplitude is still determined by the MPGF.

One-dimensional particle simulation of the filamentation instability: Electrostatic field driven by the magnetic pressure gradient force

Two counterpropagating cool and equally dense electron beams are modeled with particle-in-cell simulations. The electron beam filamentation instability is examined in one spatial dimension, which is an approximation for a quasiplanar filament boundary. It is confirmed that the force on the electrons imposed by the electrostatic field, which develops during the nonlinear stage of the instability, oscillates around a mean value that equals the magnetic pressure gradient force. The forces acting on the electrons due to the electrostatic and the magnetic field have a similar strength. The electrostatic field reduces the confining force close to the stable equilibrium of each filament and increases it farther away, limiting the peak density. The confining time-averaged total potential permits an overlap of current filaments with an opposite flow direction.

High-Current, Relativistic Electron-Beam Transport in Metals and the Role of Magnetic Collimation

High-resolution coherent transition radiation (CTR) imaging diagnoses electrons accelerated in laser-solid interactions with intensities of approximately 10;{19} W/cm;{2}. The CTR images indicate electron-beam filamentation and annular propagation. The beam temperature and half-angle divergence are inferred to be approximately 1.4 MeV and approximately 16 degrees , respectively. Three-dimensional hybrid-particle-in-cell code simulations reproduce the details of the CTR images assuming an initial half-angle divergence of approximately 56 degrees . Self-generated resistive magnetic fields are responsible for the difference between the initial and measured divergence.

Transverse modulation of an electron beam generated in self-modulated laser wakefield accelerator experiments

Low energy electron beams (E approximately 300 keV) generated in a self-modulated laser wakefield accelerator experiment were observed to filament and be deflected away from the laser axis forming radial jets in the electron beam profile. At higher energies (E>900 keV), the filamentation and jets were suppressed and smooth electron beams copropagating with the laser were observed. The observed electron beam filamentation likely results from laser beam filamentation in the plasma due to relativistic self-focusing effects. The radial jets of low energy electrons are likely caused by transverse ejection of the electrons due to the radial structure of the wakefield and space charge deflection of electrons as they exit the laser focus.

Electromagnetic direct implicit plasma simulation

A 2D electromagnetic version of the direct implicit PIC algorithm has been developed and implemented in the new code AVANTI. The code has been tested on electron beam filamentation and magnetic reconnection problems and has fulfilled most of the promise of implicit PIC. It runs stably with an arbitrarily large time step and is quite robust with respect to large particle fluctuations that result when plasmas are represented with small numbers of particles per cell N c. Several numerical obstacles were overcome during the development of the AVANTI. A method of determining the implicit susceptibility ζ is described which allows the code to avoid a nonlinear instability associated with small N c We find a form of “Simplified differencing” that provides a very robust algorithm without need for explicit smoothing. Another hurdle is the solution of the EM field equations. If the collisionless skin depth is not well resolved in high density regions, the terms containing the tensor ζ dominate the E field equation and strongly couple the components. This strong coupling is handled by simultaneous solution of these equations-generalizing to simultaneous splitting in 2D. In regions where the skin depth is well resolved, terms associated with purely electromagnetic waves dominate but do not fit symmetrically into the simultaneous splitting scheme. Introducing the electrostatic potential, the troublesome asymmetric electrostatic part of E cancels but requires a fourth equation for φ to be solved simultaneously along with the three E components. Finally, extension and generalization of the conventional explicit PIC divergence correction step, necessary to maintain Gauss' law, is needed. By using a more complex form for the correction factor, one that incorporates some implicit shielding, the correction step provides an opportunity to control or prevent spuriously large implicit currents from moving across strong magnetic fields and across steep density gradients from vacuum regions.