A. Bruce Langdon

Electron, Photon, and Ion Beams from the Relativistic Interaction of Petawatt Laser Pulses with Solid Targets

In recent Petawatt laser experiments at Lawrence Livermore National Laboratory, several hundred joules of 1 μm laser light in 0.5–5.0-ps pulses with intensities up to 3×1020 W cm−2 were incident on solid targets and produced a strongly relativistic interaction. The energy content, spectra, and angular patterns of the photon, electron, and ion radiations have all been diagnosed in a number of ways, including several novel (to laser physics) nuclear activation techniques. About 40%–50% of the laser energy is converted to broadly beamed hot electrons. Their beam centroid direction varies from shot to shot, but the resulting bremsstrahlung beam has a consistent width. Extraordinarily luminous ion beams (primarily protons) almost precisely normal to the rear of various targets are seen—up to 3×1013 protons with kTion∼several MeV representing ∼6% of the laser energy. Ion energies up to at least 55 MeV are observed. The ions appear to originate from the rear target surfaces. The edge of the ion beam is very shar...

Direct implicit large time-step particle simulation of plasmas

Abstract A recently developed implicit method for solving the set of coupled particle and field equations arising in particle-in-cell plasma simulation is described in detail. This implicit integration scheme is motivated by the desire to study efficiently low-frequency, long-wavelength plasma phenomena using a large time step. In particular, this method allows the use of a time step which is larger than the electron plasma period, when electron plasma oscillations are not of interest, and provides selective damping of the distorted remnant of the electron plasma oscillation. The implicit scheme presented here uses particle data directly without introducing fluid moment equations as an intermediary between the field and particle equations. In an electrostatic model, the essence of our scheme is a linearization of the charge density at the advanced time about an explicit approximate density and the computation of the incremental correction to the charge density that is linear in the advanced field. We are led to an elliptic field equation whose coefficients depend directly on particle data accumulated on the spatial grid in the form of an effective linear susceptibility. Prediction and iterative refinement of the solution of the implicit equations, and spatial difference representations of the equations are given. Residual restrictions on time step are described. It is demonstrated that convergence is superior when spatial diferencing and filtering are done in a consistent manner.

Implicit time integration for plasma simulation

Abstract To increase the size of the time step, and thereby extend the applicability of kinetic plasma simulation, analysis of the stability and accuracy of implicit time integration schemes for plasma particle-in-cell simulation and the synthesis of new algorithms have been undertaken. Three classes of implicit algorithms are considered in general form. Stability and accuracy calculations provide guidelines for the design and application of implicit simulation algorithms, as illustrated in the construction of new difference schemes with desirable properties. Of particular interest- are the relaxation of stability constraints on the time step, strong damping of unwanted high-frequency modes, accuracy of the simulation of low-frequency phenomena, numerical secular acceleration, and numerical stability of fast and slow space-charge waves. The potency of higher order accurate differencing schemes in reducing undesirable numerical effects is demonstrated.

Resonantly excited nonlinear ion waves

One- and two-dimensional simulations and supporting analysis of nonlinear ion acoustic waves as might be associated with the saturation of stimulated Brillouin backscattering (SBBS) are presented. To simulate ion wave phenomena efficiently, while retaining a fully kinetic representation of the ions, a Boltzmann fluid model is used for the electrons, and a particle-in-cell representation is used for the ions. Poisson’s equation is solved in order to retain space-charge effects. We derive a new dispersion relation describing the parametric instability of ion waves, evidence for which is observed in our simulations. One- and two-dimensional simulations of plasma with either initially cold or warm ions (and multi-species ions) exhibit a complex interplay of phenomena that influence the time evolution and relaxation of the amplitude of the excited ion wave: ion trapping, wave steepening, acceleration, heating and tail formation in the ion velocity distribution, parametric decay into longer wavelength ion waves...

Analysis of the time integration in plasma simulation

Abstract This paper treats the collective behavior of hot plasma as modified by the numerical time integration methods used to integrate the particle equations of motion in computer simulation of plasmas. No approximation, other than ignoring roundoff errors, is made in analyzing the finite-difference algorithms. Our results reduce simply and exactly to the corresponding results of plasma theory in the limit Δt → 0. The possibility of nonphysical instability is considered. The results of this and of previous papers are combined to describe both the spatial and temporal difference algorithms. The theory is generalized to a class of integration schemes, some algorithms are analyzed, and a new example is synthesized. The difficulty of developing algorithms stable at very large time steps is examined. The present analysis may be combined with an earlier rigorous analysis of the spatial grid used for field equations, to develop a kinetic theory of simulation plasmas paralleling that for real plasmas. This theory may be of use in the design and interpretation of computer simulation experiments.

Particle-in-cell simulations of ultra intense laser pulses propagating through overdense plasma for fast-ignitor and radiography applications

Zohar (two-dimensions, particle-in-cell) [C. K. Birdsall and A. B. Langdon, Plasma Physics via Computer Simulation (McGraw–Hill, New York, 1985)] simulations of ultra intense laser beams boring into overdense plasmas whose parameters are guided by the fast-ignitor concept and radiography applications are presented. Complex low frequency magnetic field structures, narrow channel formation, and beam deflection are all evident. Particle tracking diagnostics elucidate the nature of the currents that produce and interact with these static magnetic fields which are larger than 109 G for simulations at 1021 W/cm2 in a 50nc plasma. Tracking electron orbits provides a more complete understanding of the hot electron generation as the short pulse, high intensity laser penetrates overdense plasma. Particles which constitute the current in the narrow channel are partially confined by the low frequency magnetic field. In contrast, the return current particles on the outside of the channel are defocused by the high magn...

Evolution of the Weibel instability in relativistically hot electron–positron plasmas

Analytical and numerical studies of the evolution of the Weibel instability in relativistically hot electron–positron plasmas are presented. Appropriate perturbations on the electromagnetic fields and the particle orbits, corresponding to a single unstable mode, are determined analytically and used as initial conditions in the numerical simulations to excite a single unstable mode. A simple estimate of the saturation amplitude is also obtained analytically. Numerical simulations are carried out when a single unstable mode is favorably excited. Comparisons of the simulation results with the analytical ones show very good agreement. Also observed in the simulations are mode competition, mode suppression, and the difference in the long‐term evolution between the magnetized and unmagnetized plasmas. For relativistic unmagnetized plasmas, energy‐like global constraints, which are conservation laws in addition to the conservation of energy and momentum, are derived. Numerical simulations of the multimode evolut...

Absorption of laser light in overdense plasmas by sheath inverse bremsstrahlung

The original sheath inverse bremsstrahlung model [P. J. Catto and R. M. More, Phys. Fluids 20, 704 (1977)] is modified by including the v×B term in the equation of motion, as the evanescent magnetic field in an overdense plasma is greater than the corresponding electric field. It is shown that the present results are significantly different from those derived without the v×B term. The v×B term is also important in interpreting the absorption mechanism. If the v×B term were neglected, the absorption of the light would be incorrectly interpreted as an increase in the transverse components of the canonical momentum, in the case of a normally incident laser light. It is also shown that both the sheath inverse bremsstrahlung and the anomalous skin effect are limiting cases of the same collisionless absorption mechanism. Results from particle‐in‐cell (PIC) plasma simulations are compared with the absorption coefficient calculated from the linear theory. Finally, the effects of finite density gradients are inves...

Weibel instability in relativistically hot magnetized electron–positron plasmas

A linear stability analysis is carried out for the Weibel instability in relativistic magnetized electron–positron‐pair plasmas, with the propagation direction parallel to the background magnetic field. The instability in the ultrarelativistic regime, with the typical Lorentz factor γ much greater than unity, is emphasized for its relevance to astrophysical sources of synchrotron radiation. Detailed stability properties are examined, in the ultrarelativistic regime, for two model distribution functions, the water‐bag distribution function, and a smooth distribution function. The dispersion relations are obtained in closed analytic forms for both distribution functions. The necessary and sufficient conditions for instability are determined when the temperature along the background magnetic field is cold (T∥=0). The dispersion relations are solved numerically with T∥≠0 over a wide range of system parameters to determine the detailed dependence of the instability on the strength of the background magnetic fi...

Mechanisms for collisionless absorption of light waves obliquely incident on overdense plasmas with steep density gradients

For p‐polarized laser light obliquely incident on overdense plasmas with steep density gradients, a new collisionless absorption mechanism (sheath‐transit absorption) is studied analytically and numerically. Complementary to Brunel’s ‘‘not‐so‐resonant’’ resonant absorption, and to the conventional resonant absorption, the sheath‐transit absorption is most effective for steep density gradients and when the light pressure is less than the plasma pressure. It is also shown that the assumption of instantaneous particle reflection, usually a reasonable assumption for the normal incidence case, is invalid for the p‐polarized oblique incident case. A test‐particle model which provides a simple physical picture of the sheath‐transit absorption is presented. Absorption coefficients obtained from the test‐particle model agree reasonably well with those from particle‐in‐cell (PIC) simulations. The transition from the resonant absorption to the sheath‐transit absorption as the density gradient steepens is demonstrate...