Particle-in-cell (PIC) methods have a long history in the study of laser-plasma interactions. Early electromagnetic codes used the Yee staggered grid for field variables combined with a leapfrog EM-field update and the Boris algorithm for particle pushing. The general properties of such schemes are well documented. Modern PIC codes tend to add to these high-order shape functions for particles, Poisson preserving field updates, collisions, ionisation, a hybrid scheme for solid density and high-field QED effects. In addition to these physics packages, the increase in computing power now allows simulations with real mass ratios, full 3D dynamics and multi-speckle interaction. This paper presents a review of the core algorithms used in current laser-plasma specific PIC codes. Also reported are estimates of self-heating rates, convergence of collisional routines and test of ionisation models which are not readily available elsewhere. Having reviewed the status of PIC algorithms we present a summary of recent applications of such codes in laser-plasma physics, concentrating on SRS, short-pulse laser-solid interactions, fast-electron transport, and QED effects.

/pdf/contemporary-particle-in-cell-approach-to-laser-plasma-1hb69lir4e.pdf

Contemporary particle-in-cell approach to laser-plasma modelling

https://digital.library.unt.edu/ark:/67531/metadc1072678/m2/1/high_res_d/5410301.pdf

Gyrokinetic particle simulation model

A novel method by C. Zhou and R. Betti [Bull. Am. Phys. Soc. 50, 140 (2005)] to assemble and ignite thermonuclear fuel is presented. Massive cryogenic shells are first imploded by direct laser light with a low implosion velocity and on a low adiabat leading to fuel assemblies with large areal densities. The assembled fuel is ignited from a central hot spot heated by the collision of a spherically convergent ignitor shock and the return shock. The resulting fuel assembly features a hot-spot pressure greater than the surrounding dense fuel pressure. Such a nonisobaric assembly requires a lower energy threshold for ignition than the conventional isobaric one. The ignitor shock can be launched by a spike in the laser power or by particle beams. The thermonuclear gain can be significantly larger than in conventional isobaric ignition for equal driver energy.

http://absimage.aps.org/image/DPP06/MWS_DPP06-2006-000513.pdf

Shock Ignition of Thermonuclear Fuel with High Areal Density

Multi-scale simulations of plasma with iPIC3D

The use of high plasma density and low gas density, a recent trend in plasma-assisted materials processing, requires a particle simulation method for plasmas and gas flows. The kinetic theory basis of the particle simulation method is first described. Based on this theoretical viewpoint, state-of-the-art probabilistic treatments of collisions are described for electron-molecule, ion-molecule, molecule-molecule, and Coulomb collisions.

Probability theory of electron-molecule, ion-molecule, molecule-molecule, and Coulomb collisions for particle modeling of materials processing plasmas and cases

Implicit moment particle simulation of plasmas

A Grid-Based Coulomb Collision Model for PIC Codes

A multifluid implicit plasma simulation code has been used to study the transport of hot electrons generated by an intense $(\ensuremath{\ge}3\ifmmode\times\else\texttimes\fi{}{10}^{18}\phantom{\rule{0ex}{0ex}}\mathrm{W}/\mathrm{cm}{}^{2})$ short-pulse 1.06 \ensuremath{\mu}m laser into plasma targets over a broad range of densities $[(0.35--200){n}_{\mathrm{crit}}]$, as arising in the Fast Ignitor approach to inertial confinement fusion. The most intense (16--250 MG) magnetic fields generated in this interaction are traced to the ponderomotive push on background electrons, and tardy electron shielding. These fields can focus the heated electrons toward the axis of the beam, while impeding the direct return flow of background electrons.

Magnetic field generation in high-intensity-laser-matter interactions

Particle-in-cell simulations aimed at improving the coupling efficiency of input laser energy deposited to a compressed core by using a double cone are described. It is found that the number of high-energy electrons escaping from the sides of the cone is greatly reduced by the vacuum gap inside the wing of the double cone. Two main mechanisms to confine high-energy electrons are found. These mechanisms are the sheath electric field at the rear of the inner cone wing and the quasistatic magnetic field inside the vacuum gap. The generation mechanism for the quasistatic magnetic fields is discussed in detail. It is found that the quasistatic fields continue to confine the high-energy electrons for longer than a few picoseconds. The double cones provide confinement and focusing of about 15% of the input energy for deposition in the compressed core.

Enhancing the number of high-energy electrons deposited to a compressed pellet via double cones in fast ignition.

The fast ignitor is a modern approach to laser fusion that uses a short-pulse laser to initiate thermonuclear burn. In its simplest form the laser launches relativistic electrons that carry its energy to a precompressed fusion target. Cones have been used to give the light access to the dense target core through the low-density ablative cloud surrounding it. Here the ANTHEM implicit hybrid simulation model shows that the peak ion temperatures measured in recent cone target experiments arose chiefly from return current joule heating, mildly supplemented by relativistic electron drag. Magnetic fields augment this heating only slightly, but capture hot electrons near the cone surface and force the hot electron stream into filaments.

R. J. Mason

Papers

Implicit moment particle simulation of plasmas

A Grid-Based Coulomb Collision Model for PIC Codes

Magnetic field generation in high-intensity-laser-matter interactions

Enhancing the number of high-energy electrons deposited to a compressed pellet via double cones in fast ignition.

Heating mechanisms in short-pulse laser-driven cone targets.