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Plasma Resonance Probe Implementation for Determining Plasma
Densities in Plasma Electric Thruster Plumes Abstract We are developing a resonance probe plasma diagnostic that uses a microwave network analyzer for use in electric propulsion research. To show the feasibility of our resonance probe implementation, we have measured plasma densities in the plume of the 5-kW-class P5 Hall-effect thruster and compared them to measurements made with a Langmuir probe. Our preliminary work in this area indicates that the resonance-probe technique shows considerable promise. The resonance-probe technique should prove to be a useful tool to support electric-propulsion research since it able to provide high temporal-resolution electron density measurements. Background Resonance Probe Technique The resonance probe (also known as the plasma frequency probe or RF impedance probe) technique is used to measure the absolute electron density of a plasma. The typical resonance probe implementation involves immersing an electrically short antenna in a plasma and determining the frequency where the antenna reactance is zero [Jensen and Baker, 1992]. Although the technique has been around since the late 1950s, it has seen limited use due to the dominance of the Langmuir probe (LP) plasma diagnostic. There are, however, several difficulties with the LP diagnostic which can be partially, if not completely, alleviated with the resonance probe diagnostic. These difficulties include the LP’s dependence on probe geometry and current collection regime, sampling rate limitations, and difficulty performing real-time plasma density measurements. The resonance probe technique itself is relatively simple in concept. Plasma electrons have a natural resonant frequency known as the electron plasma frequency which depends on the plasma density. The plasma frequency is given by the equation:
where ne is the electron density, e is electron charge, e0 is the permittivity of free space, and me is the electron mass. When the resonance probe is immersed in the plasma and driven by an RF sweep frequency, the reactance of the antenna/probe becomes zero at the plasma frequency. Modeling the probe–plasma system as a parallel resonant circuit, this zero reactance frequency occurs where the free space capacitive antenna reactance is cancelled by the inductive reactance of the oscillating electrons [Swenson, 1989]. One of the strengths this technique lies in the fact that Equation (1) can be easily rearranged, yielding plasma density directly when the electron plasma frequency is known:
Hence, unlike LPs which rely largely on curve-fitting methods for determining plasma density, resonance probes can quickly yield a value for plasma density. Some resonant probe implementations have yielded ne measurements at a rate 10 kHz [Jensen and Baker, 1992]. If a magnetic field exists in the plasma, the antenna reactance becomes zero at a frequency slightly higher than the plasma frequency known as the upper hybrid frequency [Jensen and Baker, 1992]. The upper hybrid frequency is related to the electron plasma and cyclotron frequencies by the relation
where wuh, wpe, wce, are upper hybrid frequency, plasma frequency, and electron cyclotron frequency, respectively. If the magnetic field is known and static (as it would be near a plasma electric thruster), then this increase in resonant frequency does not complicate the analysis significantly. Proposed Research Effort Our prototype resonance probe implementation utilizes a modern network analyzer (NA) attached to the probe itself as shown in Figure 1. The probe can be moved via the chamber’s positioning table (see Figure 2); both the NA and table are controlled via a computer running National Instrument’s LabVIEW. There are many benefits to using a NA for researching the technique at the prototype stage. First, the NA is extremely flexible and allows the applied probe frequency to be swept over a wide range. This is important since plasma densities, and hence plasma frequencies, may not be known a priori. Second, due to the long cable lengths required of any diagnostic technique placed in the chamber, the losses in the cable can severely affect the transmitted and measured signals. This problem can be partially alleviated by first calibrating out the cable losses via the NA’s calibration kit and then translating the reference plane of the measurement to the probe tip itself via the NA’s delay capability. Third, the time-gating feature of the NA can be used to eliminate signal reflections from the chamber’s walls.
Figure 1 Experimental setup for the prototype resonance probe system
Figure 2 Resonance probe system setup in the PEPL plasma chamber
Figure 3 Picture of the prototype resonance probe system as setup in the chamber This is one of, if not the first, uses of the resonance probe technique with plasma electric thrusters. Some of the expected strengths of the technique as applied to EP include: 1) ability to sweep quickly through the EP plume to avoid sputtering of the probe itself; 2) ability to make high-temporal-resolution plasma density measurements to examine EP-plume plasma density fluctuations; and 3) possible ability to be placed internal to the thruster, perhaps as a conformal probe to continuously monitor thruster performance. References
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