Self-consistent theory for crossed-field diode current fluctuations

Abstract

Applying a perturbation expansion to the self-consistent Poisson equation for a planar, space-charge-limited crossed-field diode, we have derived four universal diode functions (independent of any particular diode specification), in addition to the usual Fry-Langmuir function for unperturbed, unmagnetized planar diodes. A crossed-field diode is completely specified by three external parameters: its normalized width X = xa/λDb, anode voltage V = φa/φTb, and magnetic field Ω = ωc/ωpb. Here a and b, respectively, denote anode and cathode quantities, λDb is the electronic Debye length, ωpb is the plasma frequency, φTb is the electron temperature in volts, and ωc is the electron gyrofrequency. Evaluating the universal functions at abscissas appropriate for a particular set of X, V, and Ω then allows the calculation of the anode noise power (mean square current fluctuation at the anode) as a function of X, V, and Ω. The range of external parameters for which the theory is applicable is specified by a simple constraint relation for X, V, and Ω, which ensures that the diode is space-charge limited both with and without the applied magnetic field. The results of our analysis show that the noise level of a space-charge-limited diode increases monotonically from the reduced level at zero magnetic field. These results are for a range of magnetic fields well below the threshold where the diode enters the regime of magnetic-field-limited flow in which the noise power reaches the temperature-limited level. Thus the range of the space-charge-limited regime studied is always associated with a reduced noise level which is, nevertheless, greater than the unmagnetized space-charge-limited level.