Operation of a plasma source with a hot disk cathode and a cylindrical hollow anode in axial magnetic field is sensitive to the cathode-to-anode diameter ratio. When the cathode edge maps along magnetic field lines to the inner anode surface, the discharge voltage is relatively low, and the plasma stream with moderate density occupies the entire cross-section of the anode bore. By contrast, when the cathode projection is fully inside the anode bore with the radial cathode-to-anode gap ~ 1 cm, the discharge voltage jumps to much higher values exceeding 250 V. The plasma density profile becomes Gaussian-like with the width matching the cathode radius according to magnetic flux surfaces. The plasma density in the high-voltage cross-field discharge reaches 10 13 cm -3 , and the discharge parameters almost do not change with magnetic field up to 1.5 kG in the anode area. This plasma source is suitable for the use in linear devices for plasma-material interaction studies.