Kinetic Modeling and Theory of Shear-Flow Instabilities in Crossed-Field Diodes

Electron flow in magnetically insulated transmission lines (MITLs) is susceptible to Kelvin-Helmholtz type instabilities. These shear-flow instabilities can allow for plasma expansion across the anode-cathode gap, causing current loss through the MITL. In this work, electron shear-flow instabilities in crossed-field diodes (XFD) are studied using theory and particle-in-cell (PIC) simulation. The linear stability analysis of electron shear flow in XFDs is revisited, in which a second-order differential eigenvalue equation is commonly solved using the “shooting method” to determine instability growth rates. An alternate solution method is presented, which provides several advantages and brings awareness to a relevant acceleration mechanism in XFDs. The 2D PIC model injects electrons from the cathode surface into an initially vacuum XFD, creating a layer of flowing electrons that transition to instability. The effect of injection current density on instability growth rate is shown.