Ensemble Kalman Update for Inference of Spatial Uniformity of Emission across an Electrospray Array

The spatial uniformity of emission across an electrospray thruster array can impact several performance characteristics of the thruster such as the thrust vector and overall thruster lifetime. For example, spatial variation of emission across an array could lead to variations of the center of thrust of the thruster which can induce undesired disturbance torques on the spacecraft. However, the small size of many electrospray thruster arrays means that most of the performance characteristics are determined on a global scale since emitter-to-emitter performance variations cannot be directly measured. The ability to determine emitter-to-emitter variations could greatly increase our understanding of how such thrusters operate as well as inform the design of future thrusters. Previous methods to determine the spatial uniformity of emission have led to the ability to visualize the spatial distribution in a qualitative manner, but cannot provide quantitative emission characteristics at the individual emitter scale. This work explores the use of the ensemble Kalman update, a form of approximate Bayesian inference, in order to infer individual emitter emission properties based on measurements of the emitted current density taken downstream of the array. The use of an inference method alleviates the issue of attempting to directly measure the emission properties of individual emitters and could simplify the required measurement setups in order to determine spatial uniformity of emission. The efficacy of this method is demonstrated on simulated data for a 300-emitter circular array with point measurements of the current density, but is easily extendable to other array geometries and measurement systems. Uncertainty in the angular distribution of the emitted ion beam is also discussed and incorporated.