  The numerical simulation of the development of a streamer discharge in a gap
with an external longitudinal magnetic field was used to demonstrate the
self-focusing of such discharges. Self-focusing is caused by a sharp
deceleration of the radial ionization wave due to a change in the electron
energy distribution function, a decrease in the average electron energy, the
rate of gas ionization and the electron mobility in crossed electric and
magnetic fields as compared to the case of the discharge development without a
magnetic field. The self-focusing effect of a streamer discharge in an external
longitudinal magnetic field is observed for both positive and negative pulse
polarities. The paper proposes an estimate of the critical value of the
magnetic field, which makes it possible to control the development of pulsed
high-voltage discharges at various gas pressures.
