A detailed study has been carried out on the propagation of a solitary wave along the magnetic field in a cold collision-free plasma. With the quasi-neutral approximation and the conservation of momentum flux and energy flux in the wave-frame, the exact analytical solutions of the stationary solitary pulse in terms of particle densities, parallel and transverse velocities, and transverse magnetic fields are presented without performing numerical integration. Graphical representations of the solutions and in particular the 3D structures of the transverse magnetic and velocity field lines are presented.

Modelling the transport of 'dust' particles in a magnetically confined plasma device is an area of active research, and requires a detailed understanding of the forces experienced by dust immersed in a plasma. One of the most significant of these is the 'ion drag force'. Dust transport codes employ a model of this force that was not specifically designed for fusion plasmas, and so does not consider the relevance of strong magnetic fields. However, it is shown here that the effect of magnetic fields on the ion drag force is significant for such plasmas. In this work, the Monte Carlo code DiMPl is employed to perform the first detailed characterisation of the dependence of the ion drag force on magnetic fields. A semi-empirical model of this dependence is fitted onto the simulation data, so that these magnetic effects may be straightforwardly captured by dust transport codes. The limiting behaviour of the ion drag force in the case of very strong fields is derived analytically, and shown to be consistent with the simulation results. The validity of the results is further motivated through a novel theoretical treatment of the ion drag force at intermediate magnetic field strengths.

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On the basis of Vlasov-Kinetic model and using Maxwell-Juttner distribution function, dispersion relation of electrostatic wave in a collisionless homogeneous relativistic electron plasma is derived. The analysis of the oscillation spectra is carried out in a weak magnetic field limit ω − kv th ≥ Ω. Approximate analytic expression for the weakly damped mode is obtained in the subluminal limiting range. It is shown that the relativistic weakly damped mode can be estimated analytically in the range where the wave phase velocity v φ becomes greater than relativistic thermal velocity of the electron but less than speed of light. Results in the non-relativistic and the ultrarelativistic cases are also discussed.