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In this paper we study the influence of the magnetised thermal conductivityon the propagation of a nanosecond $10^{14} \mathrm{Wcm}^{-2}$ laser in anunderdense plasma by performing simulations of a paraxial model laser in aplasma with the full Braginskii magnetised transport coefficients. Analytictheory and simulations show the shortening of the self-focal length of a laserbeam in a plasma as a result of the reduction of the plasma thermalconductivity in a magnetic field. Furthermore the filamentation of a laser viathe thermal mechanism is found to have an increased spatial growth rate in amagnetised plasma. We discuss the effect of these results on recent magnetisedinertial fusion experiments where filamentation can be detrimental to laserpropagation and uniform laser heating. We conclude the application of externalmagnetic fields to laser-plasma experiments requires the inclusion of theextended electron transport terms in simulations of laser propagation.

Magnetised Thermal Self-focusing and Filamentation of Long-Pulse Lasers in Plasmas Relevant to Magnetised ICF Experiments