First theoretical model of the enhancement of space-charge limited thermionic current caused by trapped ions

Historical understanding dating back to Langmuir states that the electron current from a strongly emitting cathode in a plasma cannot exceed the Marginal Space Charge Limited (MSCL) value due to the creation of a potential well in the sheath that repels any excess thermoelectrons back to the surface. However, simulations have shown that ion trapping expands this well in space and weakens its voltage, thereby reducing its effectiveness at limiting the current. We present the first complete theoretical model calculating the current enhancement by trapped ions in cylindrical and spherical cathode geometries. The steady state current enhancement factor depends on a dynamical balance between the creation of trapped ions (by charge-exchange collisions) and their leakage over the potential well. Our model quantifies these rates and derives the transmitted current as a function of emitted flux in terms of system parameters. Currents exceeding the MSCL value by orders of magnitude are possible. We predict that in practice, the actual factor setting the maximum steady current from a cathode with increasing emission is not the onset of a potential well but a maximum to the quantity of trapped ions that can accumulate in this well before an instability from breakdown of neutrality occurs.