The formation of current filaments in n-type GaAs due to the low temperature impurity breakdown has been investigated in crossed electric and magnetic fields with a laser scanning microscope. In a highly compensated, low mobility, epitaxial layer the lateral displacement and stretching of a filament due to the Lorentz force has been observed at currents slightly larger than those required to form a filament between point contacts. The transverse elongation of the filament increases linearly with rising magnetic field strength until the filament is disrupted. In this case periodic current oscillations are generated by a repetitive filament ignition and extinction. The elongation decreases with rising current and finally vanishes even at high magnetic fields. This stiffening of a current filament is attributed to an increased electron temperature and mobility in the filament, which cause the charges of the Hall field to be accumulated at the filament borders rather than at the edges of the sample.