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For this study, we use a combined experimental and computational approach to investigate the near-surface dynamics and structure of plasma confined by a permanent magnet cusp. Improved understanding in this region allows electric propulsion designers to take advantage of cusp confinement for micro-scale discharges (≤ 1 cm), enabling high performance microthrusters that are attractive for both microsatellite and formation flying missions. An electron gun experiment designed specifically for this effort provides detailed data on the plasma for a single permanent magnet cusp for electron-only conditions and multispecies (electron, neutral, and ion) weakly ionized conditions. For these experimental conditions, a multispecies particle-in-cell model is developed that uses an adaptive mesh and analytical solutions for permanent magnets to provide high resolution for particle motion and interactions in the cusp region. Results from the experiment and model agree well and are consistent with existing theory for the "leak radius" at the cusp. Nomenclature a = coefficients for 2D quadratic equation A = amplitude of oscillation dS = differential area along a surface, m 2 E = electric field, V/m E = particle energy, eV E 0 = atomic unit of energy (= 27.21eV) m = particle mass, kg q = charge, C r = radial position, m r l = leak radius, mm R = error of the 2D quadratic equation, V t = time, s U = random number between 0 to 1 v = particle velocity, m/s w l = leak width, mm z = axial position, m Subscripts i = initial k = cell number n = number of neighboring cells f = final Symbols β = magnetic pressure Δt = time step, s ρ h , ρ e , ρ i = hybrid, electron, and ion gyroradii ρ p , ρ s = primary and secondary electron gyroradii φ = electric potential, V χ = deflection angle, rad

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Ring-cusp discharges use multiple permanent magnet rings to facilitate confinement of the high energy electrons and other plasma species. The magnetic field configuration consists of converging fields toward the magnetic cusps with a large ratio of the maximum to the minimum magnetic field strength. In such configurations, a plasma fluid simulation with a regular mesh can lead to undesirable numerical diffusion errors caused by the anisotropicity of plasma and the misalignment of the grid with the field. In this paper, details of a custom technique for magnetic field aligned (MFA) mesh generation are provided. The MFA meshes may consist of irregular nodes that are attached to more than four mesh elements. The numerical method developed here can be applied to such meshes to solve the plasma diffusion equation. The combination of the MFA mesh generation and the numerical method is applied to two test cases: perfectly anisotropic plasma in a single cusp configuration and moderately anisotropic plasma in a ring-cusp discharge-like configuration. It is shown that a simulation with the MFA mesh can provide a more accurate solution compared with the regular mesh with a similar number of mesh elements. However, realizing the inherent benefits of the MFA mesh often requires improvements on the mesh quality near the boundary, in particular, the smoothness of the near-boundary elements.