Space-charge-limited current flow in a spherical double sheath

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Abstract
Solutions to the problem of counterflowing, space-charge-limited, negatively and positively charged particle currents between two spherical surfaces are presented. They show that the current magnitudes exhibit the usual 3/2 power dependence on driving potential difference and square root dependence on particle charge-to-mass ratio. The magnitude of either current is strongly dependent on the radius ratio of the two spherical surfaces. The relative magnitudes of the two counterflowing currents are related by the square root of the mass ratio of the two charged particle species and a radius ratio factor that lies in the range ∼0.1–1.0.

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