A one-dimensional model for the low-pressure glow discharge in a transverse magnetic field is presented. Longitudinal confinement of electrons in the model is provided by a transverse magnetic field. The ion mean free path and ion gyro radius are assumed greater than the distance between the anode and the cathode, thus the influences of the magnetic field and collisions on movement of ions can be neglected. Based on these assumptions it is shown that existence of the self-maintained glow discharge without the cathode fall is possible. The numerical results for the case of a glow discharge in 1 mTorr argon gas are presented and discussed in order to investigate the dependencies of plasma parameters on the values of magnetic field. The condition under which the cathode fall in a glow discharge with a transverse magnetic field would disappear is also discussed for the case when the anode-cathode distance is much greater than the ion mean free path.
