Using Nonlinear Zeeman Spectroscopy to obtain In-Situ Magnetic Field Measurement in a Hall Thruster

*† ‡ We present the experimental results based on a novel non-intrusive method for obtaining the magnetic field magnitude profile in a 6-kW Hall thruster operating at the nominal condition. We used the Xe I 6s’[1/2] 0 1 → 6p’[3/2]2 transition at 834.912 nm (vacuum) to perform laser-induced fluorescence spectroscopy inside the channel near the exit plane. Due to the Zeeman effect, the obtained spectra contain magnetically-split hyperfine structures. A nonlinear error-minimizing solver, utilizing nonlinear Zeeman theory, extracts the magnitude of the magnetic field. A comparison is made between the magnetic field strength in air, which is measured via a Hall probe, and the in-situ magnetic field strength to study the effects of the self-field induced by the Hall current. The magnetic field is found to be weaker than its air value around the middle of the thruster channel in the interrogated axial positions but matches air values very well near the wall. The differences are found to vary by as much as 30 Gauss. The uncertainty analysis that follows helps identify the strengths and weaknesses of this technique for in-situ magnetic field measurements in Hall thrusters.