Thermal Electron Flow in a Planar Crossed-Field Diode

Abstract

A self-consistent model of steady-state electron flow in a planar crossed-field diode with a thermionic cathode is presented. Our formulation is a generalization of the classic work of Fry and Langmuir, to include a constant magnetic field B of arbitrary strength parallel to the electrode surfaces. Some effects of the magnetic field on the electron flow are illustrated in an example. Index Terms-Crossed-field diode, Hull cutoff, space charge limited, temperature limited, thermionic emission. I. INTRODUCTION T HERMIONIC cathodes are widely used as electron sources. In a diode, as the cathode temperature is raised, the anode current transitions from the temperature-limited value, which is described by the Richardson-Dushman law [1], [2] to the space charge-limited value, which is described by the Child-Langmuir law [3], [4]. The 1-D theory of this transition is given in the classic articles by Langmuir [4] and Fry [5], who found that, above a certain transition temperature, the anode current is controlled by the appearance of a potential minimum in front of the cathode. This potential minimum is also known as a virtual cathode [6]-[8]. We recently extended the 1-D theory of Fry and Langmuir to 2-D in order to study various effects of nonuniform emission [9]. This work was motivated by our attempt to understand the physical basis for the shape of the Miram curve [10], which is a plot of the anode current as a function of the cathode temperature at a fixed voltage. The Miram curve usually exhibits a smooth "knee" which marks the transition from the temperature-limited regime to the space charge-limited regime. Operation in the knee region is often chosen for stability and long cathode life. Much less developed is the thermionic theory of a crossed-field diode, in which an external magnetic field B is imposed parallel to the cathode surface. The anode current Manuscript

Explicit Brillouin Flow Solutions in Magnetrons, Magnetically Insulated Line Oscillators, and Radial Magnetically Insulated Transmission Lines

“…The above background motivated us to provide a foundational study of Brillouin flow that is applicable to both MILOs and RMs. Brillouin flow is also well investigated [40]- [69] and is generally regarded as the prevalent equilibrium state in crossed-field devices [32], [44], [52], [55], [57], [67], [68]. Our recent particle-in-cell simulations on these devices reliably show a profile consistent with Brillouin flow, albeit with some noise due to the finite particle nature of the simulation [66], [67].…”

“…This article is a significant extension of the plenary paper [75] given at the 2020 IEEE International Conference on Plasma Science. Various topics presented in [75] were published in [76]- [79], [67], [68].…”

“…Brillouin flow is also well investigated [40]- [69] and is generally regarded as the prevalent equilibrium state in crossed-field devices [32], [44], [52], [55], [57], [67], [68]. Our recent particle-in-cell simulations on these devices reliably show a profile consistent with Brillouin flow, albeit with some noise due to the finite particle nature of the simulation [66], [67]. The Brillouin flow profile has been used to derive the Hull-cutoff (HC) condition and the BH condition for magnetrons [8], [44], [46], [48], [57], [69].…”

Analysis of Injected Electron Beam Propagation in a Planar Crossed-Field Gap

“…In this injected beam model, electrons cycloid at a location above the sole and do not reduce the electric field at the sole surface. In addition, a new study [32] argues that there is practically no threshold current density for this state to occur. Accordingly, the phenomenon observed here is a transition to unstable beam propagation rather than to a near-Brillouin state.…”