The distorting effect of the ion current on electron temperature measured by an electric probe

Transcription

1 The distorting effect of the ion current on electron temperature measured by an electric probe A. Kudryavtsev 1, S.A. Gutsev 1, V.I. Demidov 2,1 1 St.Petersburg State University, St. Petersburg, Russia 2 West Virginia University, Morgantown, WV, USA

2 What is the electron temperature in plasma? At the beginning I would like to remind that the concept of temperature makes sense only in the local thermodynamic equilibrium (LTE) conditions, and its use in systems found far from equilibrium such as low-temperature plasma has no physical meaning and irrational. Certainly, it is possible to call temperature 2/3 of the average electron energy and to introduce temperature of electrons, but such a procedure can lead only to a rough approximation which does not have a serious physical foundation. We note, by the way, that the word 'temperature' itself creates an illusion that all-powerful tools of formal thermodynamics can also be applied to strongly nonequilibrium systems, and this is exactly what we should not do.

3 What is the electron temperature in plasma? Therefore, it even does not seem to be absolutely correct to call the weakly ionized gas-discharge plasma 'lowtemperature'. Not to philosophize over, we note that by electron current to the probe should determine the EDF (but not electron temperature) and, if possible, the density of electrons. The only exception is the case when the electron-electron collisions establish a Maxwellian electron distribution much faster than the electron energy relaxation in collisions with heavy particles occurs. This requires either a high degree of ionization or low electron temperature. The last condition is satisfied in the afterglow plasma, where the bulk of the EDF may be considered Maxwell.

4 Influence of ion current Recall that an electric probe, placed into a plasma, measures total electron and ion current components: I = I e + I n + I p, where I e, I p and I n are currents of electrons, positive and negative ions, respectively. Therefore, in determining the parameters of the charged particles, the problem of extracting corresponding current component arises. In measurements of EDF proportional to the second derivative of the electron current to the probe I e, a differentiation procedure is usually applied to the whole probe current that consists of the electron and ion components. Therefore, one may expect an influence of the second derivative on the ion current I i on the measured EDF.

5 Influence of ion current This question was considered in different paper, f.e. review [V.A. Godyak, V.I. Demidov. J. Phys. D: Appl. Phys., v. 44, (2011), ]. It has been shown that an appreciable influence of I i may occur for thin probes, light gases and large negative probe voltages.

6 The electron temperature The typical dynamic range of EDF measurement unaffected by I i is approximately three orders of magnitude corresponding to an energy range about of 6Te. It seems that is enough to determine the electron temperature from the slope of I e T e e = ΔU ΔlnI e (1) where e is the electron charge, Te is the electron temperature, and ΔU is the voltage interval in which electron current is a logarithmic function of the voltage.

7 Experiments In our experiments, pulsed glow discharge with current ranged from 10 to 200 ma in helium at a pressure of Torr with the duration of the active phase of 50 mks and afterglow phase of 350 mks was ignited in a glass cylindrical tube with a radius of 1.6 cm and distance between electrodes 23 cm. Cylindrical probe with radius of 0.01 cm and length of 1 cm was immersed into the plasma at discharge axis. The plasma diagnostics were carried out using a special electronic circuit capable of measuring the I(U) curve and its second derivative I (U) Measurements of electron temperature were carried out in the afterglow of the discharge, when the EDF is Maxwellian.

8 Probe current-voltage characteristics Fig. CVC in the afterglow of helium: 1 - I = 130mA, P = 0.4 Torr, t = 270 mks; 2 - I = 70mA, P = 0.7 Torr, t = 200 mks; 3 - I = 30mA, P = 2.4 Torr, t = 200 mks.

9 Second derivatives of probe current This difference of Te is paradoxically: with decreasing current Te increases its value. Fig. The dependence of I "(U) in the afterglow of helium. P = 0.7 Torr, time delay 200 ms. Discharge current pulse: 1-70 ma, Te = 0.04 ev; 2-40 ma, Te = 0.07 ev; 3 - approximating curve Const/U^(3/2).

10 Discussion The experimental results give a paradoxical increase in the electron temperature with increasing gas pressure and decreasing energy deposited in the discharge. P, (Torr) Discharge current (ma) Delay time (ms) T e, ev

11 Influence of probe circuit resistance When making probe measurements, one usually assumes that the voltage applied to the probe is localized in the probe sheath around the probe tip. In reality, this voltage is distributed along different parts of the probe current path including not only the voltage drop across the probe sheath V but also the voltage drops across the external resistor, the voltage across the internal resistance and the residual voltage. The probe circuit resistance significantly affects the probe I/V characteristic near the plasma potential, which corresponds to the low-energy electrons of the distribution, where the probe current reaches its maximum and the probe-sheath resistance its minimum.

12 Influence of probe circuit resistance EEPF distortion depends on the ratio Rc/Rpo, where Rc is the total probe circuit resistance and Rpo is the minimal probe differential resistance (at plasma potential) Rpo = Te/eIeo and Ieo is the electron saturation current. Fig. Second derivative of the probe electron current for Maxwellian EEDF for different parameters δ = Rpo/Rc.

13 Discussion In the presence of both distorting factors (ion current and probe circuit resistance) the actual dynamic range of the EDF is reduced. This leads to errors in determining electron temperature on the slope probe CVC. For correct determination of electron temperature should be carried out a particular accounting procedure. In practice to reduce the resistance of the probe circuit is difficult, so the first step may be to try to take into account the effect of ion current.

14 Discussion Fig. The procedure to correct the EEPF measurements affected by the ion current A standart method to eliminate Ii is the subtraction from the total probe current Ip(V ) of the ion current Ii(V ) extrapolated from a large negative probe voltage (where Ii >> Ie) to a lower probe voltage (where Ii and Ie are comparable). To extrapolate to the lowpotential can use a graphical subtraction or the analytic relationship I i (V) = const V 1 2, which gives the second derivative I i "(V) = const V 3 2

15 Discussion After subtracting the contribution of the ion current agreement between the experimental data is satisfactory. P, (Torr) Discharge current (ma) Delay time (ms) T e, ev T e,(corr), ev

16 Conclusion The measurement of the electron temperature by probe method is justified only for Maxwell EDF. We have carried out probe measurements in afterglow helium plasma in at pressures of Torr. It has been established that the electron temperature Te determined from the slope of the second derivative of the probe current are overstated. By taking into account the ion current contribution, it is possible to correct the Te values.

17 Acknowledgments This work was supported by the DOE OFES (Contract No. DE- SC ) and SPbGU.