Diffusion of Electrons Back to an Emitting Electrode in a Gas

An expression is derived for the current

i

between two electrodes, one of which emits (with uniform current density

I_{0}

) electrons with an initial volt velocity,

V_{0}

, when the electrodes are placed in a gas at such a pressure that the electrons suffer only elastic collisions. If

V

is the voltage between the electrodes,

λ

the mean free path of an electron, the current is given by

i = (\frac{16 π}{3}) I_{0} λ C φ

where

C

is the electrostatic capacitance between the electrodes and

φ = (\frac{V}{V_{0}}) \ln (1 + \frac{V}{V_{0}}) .

If the emitted electrons have a Maxwellian velocity distribution, this equation is applicable with slightly modified values of

φ

V_{0}

now being replaced by

\frac{T}{11600}

volts.

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