Trajectory Estimation of Nonneutral Plasmas via Inversion of Capacitive Probe Signals

Reconstructing the center of mass trajectory of confined charge distributions is essential for time-resolved diagnostics in nonneutral plasma traps, where dynamics influence transport, confinement, and stability. Conventional imaging methods, such as MCP and phosphor screen based systems, are destructive and require multiple reproducible discharges, limiting their applicability. Capacitive probe arrays offer a noninvasive alternative, but the mapping between charge motion and signal is nonlinear. Even simple, symmetric motion produces strongly nonlinear signals due to the spatial structure of the Green's function and the finite extent of the source, making direct interpretation of signals unreliable. To overcome this, probe response is modeled by solving Poisson's equation in a grounded two-dimensional domain for finite-sized Gaussian charges. A spatial probe response map is constructed over a fine grid, and a cost function based inversion is applied to reconstruct the full center of mass trajectory and total charge from time-resolved probe signals. The method is accurate, geometry agnostic, and suitable for implementation in arbitrary in-plane motion of the charge blob. These results establish probe signal inversion using precomputed electrostatic response maps as a necessary tool for reliable charge trajectory reconstruction in non-neutral plasmas.