Repository logo

A non-invasive Hall current distribution measurement system for Hall effect thrusters




Mullins, Carl Raymond, author
Williams, John, advisor
Shipman, Patrick, committee member
Yalin, Azer, committee member

Journal Title

Journal ISSN

Volume Title


A direct, accurate method to measure thrust produced by a Hall Effect thruster on orbit does not currently exist. The ability to calculate produced thrust will enable timely and precise maneuvering of spacecraft—a capability particularly important to satellite formation flying. The means to determine thrust directly is achievable by remotely measuring the magnetic field of the thruster and solving the inverse magnetostatic problem for the Hall current density distribution. For this thesis, the magnetic field was measured by employing an array of eight tunneling magnetoresistive (TMR) sensors capable of milligauss sensitivity when placed in a high background field. The array was positioned outside the channel of a 1.5 kW Colorado State University Hall thruster equipped with a center-mounted electride cathode. In this location, the static magnetic field is approximately 30 Gauss, which is within the linear operating range of the TMR sensors. Furthermore, the induced field at this distance is greater than tens of milligauss, which is within the sensitivity range of the TMR sensors. Due to the nature of the inverse problem, the induced-field measurements do not provide the Hall current density by a simple inversion; however, a Tikhonov regularization of the induced field along with a non-negativity constraint and a zero boundary condition provides current density distributions. Our system measures the sensor outputs at 2 MHz allowing the determination of the Hall current density distribution as a function of time. These data are shown in contour plots in sequential frames. The measured ratios between the average Hall current and the discharge current ranged from 0.1 to 10 over a range of operating conditions from 1.3 kW to 2.2 kW. The temporal inverse solution at 2.0 kW exhibited a breathing mode of 37 kHz, which was in agreement with temporal measurements of the discharge current.


Rights Access


azimuthal current
Hall current
Hall thruster


Associated Publications