A method to calculate the electron sheath profile of the nonaxisymmetrical magnetic insulation

The nonaxisymmetrical magnetic insulation would occur due to the disalignment of inner electrodes in long magnetically insulated transmission lines, or the nonuniform distributions of injected currents in induction cavities of magnetically insulated induction voltage adders (MIVA). The electron sheath profile is a very important parameter to characterize the nonaxisymmetrical magnetic insulation. In the past, the three-dimensional particle in cell simulation was usually used to determine the electron sheath profile, which is extremely time-consuming and inefficient. In this paper, a fast and efficient calculation method is proposed. The classical one-dimensional Creedon theory of the magnetic insulation equilibrium is generalized to a two-dimensional plane of (r, θ) via introducing a parameter defined as the azimuthal mode number. Two-dimensional Creedon is developed to model the asymmetric magnetic insulation of the MIVA. Provided the azimuthal distributions of magnetic flux density on the cathode, which is in proportion to the cathode current, the two-dimensional Creedon model is numerically solved. A numerical solution method to calculate the electron sheath profile is proposed, and then the calculation error is also given. As the azimuthal distribution of magnetic flux density on the cathode meets a cosine function, the profile of the electron sheath is approximate to the Gauss function. As the nonuniform portion of cathode current increases, the electron sheath becomes more eccentric, and the calculation error is also much larger.