Nonlinear circuit analysis of harmonic currents in a floating Langmuir probe with a capacitive load

Abstract

Plasma diagnostics using the floating harmonic technique were first used to obtain the electron temperature in a tokamak plasma. In this technique, the electron temperature depends on the ratio of the harmonic currents in a resistive sheath. Because these harmonic currents are determined by a modulated sheath voltage, calculation of the exact modulated voltage across the sheath is important; in general, the voltage is calculated using a phase of the first harmonic current. However, when a series load capacitance is present, the second harmonic currents are abnormally reduced compared to those expected by the conventional floating harmonic model, resulting in an unreliable measurement of the electron temperature. To describe this phenomenon, we used a modified floating harmonic model by applying the harmonic balance technique, a method that analyzes nonlinear circuits. Theoretical prediction of the harmonic current obtained from the modified model was compared with the experimental results, and they are in good agreement. In addition, the degrees of sheath nonlinearity, defined as the ratio of the second harmonic current (or voltage) to the fundamental current (or voltage), are discussed.