Electric field in gas gap between two electrodes¶

Consider a two-electrode gas-filled gap with flat electrodes. Let one of the electrodes emit charged particles into a gaseous medium. If the potential collecting these charged particles is set to another electrode, then a current will flow through the gap.

Conditions:

Emittivity of the emitter is unlimited, i.e. emission of charged particles is much greater than current between electrodes.
There is gaseous medium between electrodes.

Links:

Wikipedia — Space charge. See “Mott—Gurney law”.

electric_field_strength¶: electric_field_strength at a point between the electrodes.

Symbol:: E
Latex:: \(E\)
Dimension:: voltage/length

coordinate¶: position of said point on the axis which runs from the cathode to the anode.

Symbol:: x
Latex:: \(x\)
Dimension:: length

distance¶: euclidean_distance between the electrodes.

Symbol:: d
Latex:: \(d\)
Dimension:: length

voltage¶: voltage between the electrodes.

Symbol:: V
Latex:: \(V\)
Dimension:: voltage

law¶

E = 3 * sqrt(x / d) * V / d / 2

Latex:: \[E = \frac{3 \sqrt{\frac{x}{d}} \frac{V}{d}}{2}\]