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.

In simulations of a 10PW laser striking a solid we demonstrate the possibility of producing a pure electron-positron plasma by the same processes as those thought to operate in high-energy astrophysical environments. A maximum positron density of 10 26 m −3 can be achieved, seven orders of magnitude greater than achieved in previous experiments. Additionally, 35% of the laser energy is converted to a burst of gamma-rays of intensity 10 22 Wcm −2 , potentially the most intense gammaray source available in the laboratory. This absorption results in a strong feedback between both pair and γ-ray production and classical plasma physics in the new 'QED-plasma' regime.Electron-positron (e − e + ) plasmas are a prominent feature of the winds from pulsars and black holes [1,2]. They result from the presence of electromagnetic fields strong enough to cause non-linear quantum electrodynamics (QED) reactions [3] in these environments leading to a cascade of e − e + pair production [4]. These fields can be much lower than the Schwinger field for vacuum breakdown [5] if they interact with highly relativistic electrons (γ >> 1) [3]. Non-linear QED has been probed experimentally with lasers in two complementary ways:(1) with a particle accelerator accelerating electrons to the necessary γ and a laser supplying the fields [6-8]; or (2) with a laser accelerating the electrons and goldnuclei supplying the fields [9][10][11]. An alternative configuration, using next-generation high-intensity lasers to provide both the acceleration and the fields [12], has the potential to generate dense e − e + plasmas. Analytical calculations and simulations exploring this configuration have shown that an overdense e − e + plasma can be generated from a single electron by counter-propagating 100PW lasers [12][13][14][15]. Here we will show that such a plasma can be generated with an order of magnitude less laser power by firing the laser at a solid target, putting such experiments in reach of next-generation 10PW lasers [16].The dominant non-linear QED effects in 10PW laserplasma interactions are: synchrotron gamma-ray photon (γ h ) emission from electrons in the laser's electromagnetic fields; and pair-production by the multiphoton Breit-Wheeler process, γ h + nγ l → e − + e + , where γ l is a laser photon [3,17,18]. Each reaction is a strongly multiphoton process, the former process being non-linear Compton scattering, e − + mγ l → e − + γ h [19,20], in the limit m → ∞. Therefore, these reactions only become important at the ultra-high intensities reached in 10PW laser-plasma interactions. The importance of synchrotron emission is determined by the parameter η. This depends on the ratio of the electric and magnetic fields in the plasma to the Schwinger field [5] (E s = 1.3 × 10 18 Vm −1 ). For ultra-relativistic particles 17,18]. γ is the Lorentz factor of the emitting electron or positron, β is the corresponding velocity normalised to c and E ⊥ is the electric field perpendicular to its motion. As η approaches unity each emitted photon takes a ...

In high-intensity (> 10 21 Wcm −2 ) laser-matter interactions gamma-ray photon emission by the electrons can strongly effect the electron's dynamics and copious numbers of electron-positron pairs can be produced by the emitted photons. We show how these processes can be included in simulations by coupling a Monte-Carlo algorithm describing the emission to a particle-in-cell code. The Monte-Carlo algorithm includes quantum corrections to the photon emission, which we show must be included if the pair production rate is to be correctly determined. The accuracy, convergence and energy conservation properties of the Monte-Carlo algorithm are analysed in simple test problems.