A new emissive-probe method for electron temperature measurement in radio-frequency plasmas

Abstract

A new method to measure electron temperature by an emissive probe has been proposed. The method is based on measurement of the functional relationship between the floating potential and the heating voltage of emissive probe. From the measured data of the floating potential change as a function of the heating voltage, the electron temperature could be determined by comparing with the theoretical curve obtained under the assumption of Maxwellian distribution. The overall characteristic of the floating potential change could be explained as a function of the heating voltage. The electron temperatures obtained by the present method were consistent with those measured by the rf-compensated Langmuir probe within the error. These experimental verifications were made in the electron density range of 2.6x10(11)-2.8x10(12) cm(-3). It was stressed that the present method is advantageous in that the probe is operated in a floating condition, hence applicable to plasmas produced in an insulated container.

Recommended Practice for Use of Emissive Probes in Electric Propulsion Testing

“…17 [41]. Outlet power at 50 or 60 Hz is often used, but higher frequencies can be used as well [67]. Care must be taken that the I-V trace is recorded quickly with respect to the cooling time of the probe (typically on the order of 10 ms) when using ac heating in conjunction with the inflection point method.…”

Emissive probes

“…A percentage error in estimating α c − α h is directly passed to error in measuring T e , so the uncertainties can be quite large. Emissive probes can be used to characterize the electron temperature as shown by Kusaba and Shindo, though not in the same manner as collecting probes [42,87]. Consider a floating emissive probe that is heated by a 40 kHz square-wave potential between 0 V and V H so that the emitted current is constant throughout the cycle, but the heating voltage is not constant.…”

“…Since the emission current is temperature limited, it stays constant regardless of the collected current, so the effect of the heating voltage is a change in the floating potential ( V F ). Assuming that the voltage drop across the filament is linear, the emission current is constant, and the electrons are Maxwellian, a relationship is derived relating the electron temperature, V H , and V F [42]: (14) when…”

“…This condition is satisfied when the heating voltage is below some critical value on the order of 10 V. If this condition is not satisfied, V F and T e are related in a more complicated way [42]:…”

“…Practically, this correction for high heating voltages is not necessary as the electron temperature can be determined just from the low heating voltages [88]. Figure 32 shows experimental data from an inductively coupled RF plasma graphed with theoretical curves for various electron temperatures [42]. By fitting the data points to equation (14), the electron temperature was determined to be 2.0 eV.…”