Mode Transitions in a Magnetically Shielded Hall Thruster I: Experimentally-Informed Derivation of a Model

A reduced fidelity model is presented for the discharge current oscillations exhibited by a 9-kW class magnetically shielded Hall thruster. The low frequency (10-20 kHz) and large amplitude (> 100% background) properties of this oscillation are qualitatively consistent with the canonical Hall thruster breathing mode exhibited by unshielded Hall thrusters. Accordingly, a similar approach for describing the breathing mode in unshielded devices is employed. This is based on quasi-0D governing equations for the neutral density and discharge. In a departure from previous studies on breathing mode dynamics, however, the key simplifying assumptions invoked in the derivation of this model are predicated directly on experimental measurements of the time-resolved plasma properties in the thruster channel at an operating condition of 300 V and 10 A. The resulting two-equation model, which is similar in form to a previous theoretical treatment of the breathing mode oscillation [S. Barral and Peradzynski, IEPC-2009-20] in unshielded thrusters, is shown to agree with the experimental measurements of the time-dependence and phasing of oscillations in the spatially-averaged neutral density and discharge current in the channel. A physical interpretation of the model is presented, and its extensibility to other operating conditions is discussed. The resulting expression ultimately forms the basis for a parametric study of mode transitions in magnetically shielded Hall thrusters presented in Part II.