Two-dimensional multi-timescale fully electromagnetic relativistic particle simulation is used to investigate relativistic electron heating in laser-produced plasmas. When laser pulses with peak intensities 1019 W cm−2 and different durations (e.g. 118 fs and 442 fs) are incident on overdense plasma slabs with step-like density profiles, the dynamics of plasmas and Fourier frequency spectra from our particle simulations demonstrate distinctly different properties in hot-electron temperatures, absorption, relativistic electron heating, and so on. The particular motions of the critical surfaces are discussed. From the two examples simulated in this paper, it is concluded that the interactions between plasmas and laser pulses with the same intensities and different durations are dominated by different mechanisms, which can lead to dissimilar dynamics of plasmas, relativistic heating, and so on.

The one-dimensional MHD system first introduced by J.H. Thomas [Phys. Fluids 11, 1245 (1968)] as a model of the dynamo effect is thoroughly studied in the limit of large magnetic Prandtl number. The focus is on two types of localized solutions involving shocks (antishocks) and hollow (bump) waves. Numerical simulations suggest phenomenological rules concerning their generation, stability and basin of attraction. Their topology, amplitude and thickness are compared favourably with those of the meromorphic travelling waves, which are obtained exactly, and respectively those of asymptotic descriptions involving rational or degenerate elliptic functions. The meromorphy bars the existence of certain configurations, while others are explained by assuming imaginary residues. These explanations are tested using the numerical amplitude and phase of the Fourier transforms as probes of the analyticity properties. Theoretically, the proof of the partial integrability backs up the role ascribed to meromorphy. Practically, predictions are derived for MHD plasmas.

Radiofrequency heating in toroidal geometry is described. Starting from a general theory, expressions for the dielectric response and the radiofrequency diffusion operator are obtained. The computationally most efficient simplified expressions bear a close resemblance to the results of uniform plasma theory, but differ from them in their interpretation. In cases where the simplified expressions do not describe the physics faithfully, more general but computationally slower ones are available. Rigorously accounting for the geometry and the wave field yields fine structure that is commonly overlooked. Aside from causing the well-known k∥-upshift or downshift impacting on the Doppler shift, the non-zero poloidal magnetic field modifies the orbital topology and forces one to account for the poloidal inhomogeneity of the static magnetic field. The expressions obtained restore intuition on how an electric field interacts with a charged particle, but, in so doing, cast doubt on the degree of realism of predictions of simplified models that do not account for the constructive or destructive interference phenomena introduced by the orbital topology non-uniformity. The expressions represent a numerical challenge, but show the necessity for the detailed description: the ‘coarse-graining’ underlying simplified models yields a result that has the right order of magnitude for interference related to crosstalk between resonances or multiple encounters with a given resonance, but may be an order of magnitude wrong for predictions on the combined effect of a poloidal mode spectrum. A Fokker–Planck code BATCH (Bounce-Averaged Tool for Cyclotron Heating), relying on the expressions obtained, is presented and some results are discussed.