SpaceCharge Effects in Field Emission
Abstract
A progressive reduction of the observed field current below values expected from the empirical law for increasing values of the potential is attributed to space charge. The current density expected in the presence of space charge is calculated from the FowlerNordheim field emission theory using values of the cathode electric field obtained from a solution of Poisson's equation for plane electrodes with boundary conditions appropriate to field emission. The result is a generalization of Child's equation, and is asymptotic to it when the applied potential is large compared with the value required for appreciable field emission. Current densities predicted by the theory are compared with experimental values obtained for several values of the work function by use of the clean tungsten and the bariumontungsten emitting surfaces in high vacuum. The FowlerNordheim theory correctly predicts the observed average current density from clean tungsten for densities in the range from 2 amp/cm^{2} to 4×10^{7} amp/cm^{2}, thus extending a previous test of the theory which was limited to current densities less than 6×10^{6} amp/cm^{2}. Significant features of the electron emission pattern observed at high current densities are explained as effects of space charge.
 Publication:

Physical Review
 Pub Date:
 October 1953
 DOI:
 10.1103/PhysRev.92.45
 Bibcode:
 1953PhRv...92...45B