Previous theories on the subject have not been able to determine clearly the appropriate combinations of anode voltage,
Va, magnetic flux density,
B, and anode radius, ra which will give the maximum discharge current,
Imax, and the maximum pumping speeds,
Smax. In the present paper, a new theory has been developed in which certain relevant paramaters are taken into account. These are the kinetic energies of electrons, radial distributions of the potential, onization probabilities, collision frequencies, sticking probabilities, sputtering yields of the cathode material and geometrical factors. Discharge currents and pumping speeds are expressed as a function of (
Va/
Br
a) which corresponds to the electron velocities. The values of (
Va/
Br
a) giving
Imax and
Smax are derived, and the appropriate combinations of
Va,
B and ra can be etermined from this ratio. Experimental work has also been performed, and the results show fairly good agreement with the theoretical values.
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