Parametric Scaling of the Stability of Relativistic Laminar Flow Magnetic Insulation

The short wavelength limit of the magnetron instability of a relativistic sharp boundary electron sheath is examined. For short wavelengths the mode is localized to the sheath edge. This localization leads to a simple relationship (essentially a Lorentz transformation) between the relativistic and nonrelativistic growth rates. This relationship involves only equilibrium quantities evaluated at the sheath edge and explains previously noted trends that have been observed numerically.