Plasma Diagnostics and Nonlinear Wave Studies with a Gridded Electrostatic Energy Analyzer
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Abstract:
A simplified theory relating the collector current to the grid bias and other plasma parameters has been developed for a multiple-gridded electrostatic energy analyzer. Experiments have shown that the theory is only approximately valid, but the temperature obtained agrees closely with that from a Langmuir probe. It is found that temperature measurements depend on the grid bias potentials and the ratios of grid hole radius to electron Debye length. As a result, the conditions for the best performance of the energy analyzer as an accurate diagnostic device have been determined. A theory has also been worked out for the second-order change in the electron distribution function due to a cyclotron damped wave. This, together with experimental results, will provide valuable information on the thermal anisotropy of a plasma.Keywords:
Langmuir Probe
Electron temperature
The measurement of electron temperature in plasma by Langmuir probes, using ramped bias voltage, is seriously affected by the capacitive current of capacitance of the cable between the probe tip and data acquisition system. In earlier works a dummy cable was used to balance the capacitive currents. Under these conditions, the measured capacitive current was kept less than a few mA. Such probes are suitable for measurements in plasma where measured ion saturation current is of the order of hundreds of mA. This paper reports that controlled balancing of capacitive current can be minimized to less than 20 μA, allowing plasma measurements to be done with ion saturation current of the order of hundreds of μA. The electron temperature measurement made by using probe compensation technique becomes independent of sweep frequency. A correction of ≤45% is observed in measured electron temperature values when compared with uncompensated probe. This also enhances accuracy in the measurement of fluctuation in electron temperature as δTpk-pk changes by ∼30%. The developed technique with swept rate ≤100 kHz is found accurate enough to measure both the electron temperature and its fluctuating counterpart. This shows its usefulness in measuring accurately the temperature fluctuations because of electron temperature gradient in large volume plasma device plasma with frequency ordering ≤50 kHz.
Langmuir Probe
Electron temperature
Saturation current
Biasing
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In this work, electron temperature was measured with both the asymmetric double Langmuir probe (ADLP) and the single Langmuir probe to investigate the reliability of the ADLP on the electron temperature measurement in multi-temperature Maxwellian plasmas. A series of I–V traces of the ADLP were obtained at various plasma conditions with different area ratios and analyzed with different methods including conventional ADLP analysis and two-temperature Maxwellian fitting with results measured by a single planar Langmuir probe analyzed with three-temperature Maxwellian fitting as reference. The measured Te of the ADLP is found to reflect that of the temperature of the degraded primary electrons when the area ratio of the probe tips is close to ∼16 and approaches the real effective electron temperature as the area ratio increases to a value of ∼30% higher than that measured by a single Langmuir probe, which occurs even when the area ratio is higher than the flux ratio of electrons and ions entering their respective sheaths. This effect is consistent with the distortion effect of Langmuir probe I–V traces caused by the presence of hotter electron species, which was computationally reconstructed and agreed well with the experimental observations. This result implies that an area ratio, possibly ∼20 times much larger than what was conventionally assumed, is needed for an ADLP to be reliably treated as a single Langmuir probe in practical settings, where electron energy distribution functions of plasmas are generally expected to be multi-temperature Maxwellian. This effect is also analogous to the current balance between a single Langmuir probe and the device wall, implying that this effect would also affect the application of the single Langmuir probe in plasmas, where the ion loss to the device wall can be reduced, such as plasmas in miniaturized devices, strong magnetic fields, or a highly ion-neutral collisional environment.
Langmuir Probe
Electron temperature
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Langmuir Probe
Electron temperature
Saturation current
Glow discharge
Ion current
Plasma parameter
Torr
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A nonlinear least-squares curve-fitting routine has been used to analyze single-tip Langmuir probe measurements from the Tandem Mirror Experiment Upgrade during high-density (≊1×1012 cm−3) operation. This procedure provided estimates of uncertainties (variances) in the electron temperature and plasma density due to noise in the probe current. The electron temperature and plasma potential inferred from the fit were found to increase with the upper cutoff voltage used above a certain voltage. This effect appears to be due to a departure of the electron current from an exponentially increasing function for probe positions inside the limiter radius only. The fitted values for electron temperature and plasma density are consistent with previous measurements obtained with a double-tipped probe and the fitted values of space potential indicate a linear relationship with electron temperature.
Langmuir Probe
Electron temperature
Limiter
Tandem
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Electron temperature fluctuations have been investigated in the plasma of “Thorello,” a small toroidal device (minor radius a=8 cm and major radius R=40 cm) which produces a magnetized plasma in steady-state condition without rotational transform (n≅1011 cm−3; Te≅2 eV; B=1000 G).1 In our experiment two techniques are applied to estimate T̃e: triple Langmuir probe technique and fast-sweep Langmuir probe method, in both cases, varying the density of the neutral source (in our plasma, H2). The so-called triple probe is the conventional method used to investigate T̃e, while fast-sweep Langmuir probe is a new diagnostic technique recently developed on Thorello.2 Our measurements have been performed in the frequency range between 0 and 500 kHz. The turbulent plasma exhibits a spectrum quite broad in frequency: power spectra of floating potential and density show the characteristic frequencies are in the range 0–100 kHz, while power spectra of electron temperature can extend up to 150–200 kHz. In the plasma core relative levels of electron temperature fluctuations are about 20%, but in the edge region these relative levels raise up to 50%. In situations where electron temperature fluctuations are not negligible, the measurement of T̃e is essential for obtaining a correct interpretation of density and potential fluctuations. In our case the level of electron temperature fluctuations is not negligible in the edge region and it was possible to separate ĨSi and ñ according to the hypothesis ĨSi/ISi=ñ/n+12T̃e/Te and to the theory of thermal drift wave turbulence. Then we can particularly compare the mean values of Te, the level of temperature fluctuations measured in the same plasma, the power spectrum, and the correlation between temperature, density, and potential fluctuations applying the digital correlation technique.3
Langmuir Probe
Electron temperature
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Triple Langmuir probe (TLP) diagnostic system with its necessary driving circuit is developed and successfully applies for time-resolved measurement of plasma parameters in the negative glow region of pulsating-dc discharge. This technique allows the instantaneous measurement of electron temperature [T−], electron number density [n−] as well as plasma fluctuations without any voltage or frequency sweep. In TLP configuration two probes are differentially biased and serve as a floating symmetric double probe whereas the third probe is simply floating into plasma to measure floating potential as a function of time and thus incorporates the effect of plasma fluctuations. As an example of the application to time-dependent plasmas, basic plasma parameters such as floating potential, electron temperature, and electron number density in low pressure air discharge are determined as a function of time for different fill pressure. The results demonstrate temporal evolution of plasma parameters and thus plasma generation progression for different fill pressures.
Langmuir Probe
Electron temperature
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The cylindrical Langmuir probe under orbital-limited conditions was used to determine the charge density in a low-density collisional plasma. The Langmuir's theory was applied to both electron and ion saturation currents in their respective accelerating regions. Present study indicates that the length of the probe significantly affects the probe characteristics. A probe of suitable length under orbital-limited conditions may be useful under the experimental conditions where the radius of the probe is much smaller than the Debye lengt.
Langmuir Probe
Debye
Debye sheath
Saturation (graph theory)
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Langmuir probes, because of their convenience and their ability to give time-resolved measurements, are often used for temperature measurements in plasmas. Since probe results are subject to suspicion, we compare probe and spectrometric electron temperature measurements in a particular low-temperature plasma in which this is possible. We find probe temperatures to be significantly higher over an electron temperature range (measured spectrometrically) of at least 410° to 820°K.
Langmuir Probe
Electron temperature
Atmospheric temperature range
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Technological advancement in the microelectronics industry requires an understanding of the physical and chemical processes occurring in plasmas of fluorocarbon gases used as etchants to optimize various operating parameters. This paper reports data on electron number density and temperature, electron energy distribution function (EEDF), and plasma potential measured using Langmuir probe in inductively coupled plasmas of mixtures of various compositions. The probe data were recorded at several radial positions providing radial profiles of these plasma parameters at 10-50 mTorr and 200 and 300 W of radio frequency (rf) power. The measurements indicate that the electron and ion number densities increase with power; the plasma potential and electron temperature decrease with an increase in pressure, and they depend weakly on rf power. The radial profiles show that the electron and ion number densities and the plasma potential peak at the center of the plasma and drop toward the wall. Within the experimental error, the electron temperature is nearly constant in the electrode region and decreases toward the wall. As the content increases in the mixture, the electron temperature increases but the electron density decreases. At low concentration, the electron and ion densities increase with pressure, but the densities are nearly independent of pressures at high concentrations. The EEDFs have a characteristic drop near the low energy end at all pressures and powers and their shapes represent a non-Maxwellian plasma. © 2002 The Electrochemical Society. All rights reserved.
Langmuir Probe
Electron temperature
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