Iterative machine learning control of the hollow cathode plume mode using Gaussian Process Regression

Abstract Mitigating the sudden onset of deleterious and oscillatory dynamics (often called instabilities or modes) is an open problem in many plasma sources, including hollow cathodes (HC). These dynamics are difficult to address because they are nonlinear, chaotic, and often too fast for traditional active-control systems. In this work, we present an alternative control architecture called Iterative Machine Learning Control (IMLC), where the controller operates slower than the high-speed dynamics. The controller “fingerprints” the dynamics using a nonlinear data representation called Time-Lagged Phase Portrait (TLPP) and then uses Gaussian Process Regression (GPR) to iteratively adjust the HC’s input (control) parameters until the reference dynamics are reproduced (or avoided). We perform three tests to highlight the abilities and limitations of this architecture. First, we identify four control parameters and demonstrate each parameter’s ability to control the plume mode: plasma discharge current, cathode mass flow, chamber backfill mass flow, and an axially-aligned electromagnet. Second, we demonstrate that the controller can control multiple parameters simultaneously and either reproduce or avoid oscillatory dynamics. Finally, we demonstrate that the controller can reproduce known dynamics in the presence of uncontrolled, drifting background pressure. This work underscores the interdisciplinary nature of merging plasma dynamics with machine learning-based control to achieve robust, adaptive tuning. By framing the controller in a data-driven IMLC framework, we address the difficulties posed by high-frequency instabilities that standard real-time controllers often cannot manage directly.