научная статья по теме ANALYSIS OF CYLINDRICAL LANGMUIR PROBE USING EXPERIMENT AND DIFFERENT THEORIES Физика

Текст научной статьи на тему «ANALYSIS OF CYLINDRICAL LANGMUIR PROBE USING EXPERIMENT AND DIFFERENT THEORIES»

ФИЗИКА ПЛАЗМЫ, 2013, том 39, № 3, с. 289-296

ДИАГНОСТИКА ПЛАЗМЫ

УДК 533.9

ANALYSIS OF CYLINDRICAL LANGMUIR PROBE USING EXPERIMENT AND DIFFERENT THEORIES

© 2013 г. M. A. Hassouba1, 2, A. R. Galaly3, 4,U. M. Rashed5

1 Physics Department, Faculty of Science, Benha University, Egypt

2 Applied Physics Department, Faculty of Applied Sciences, Taibah University, KSA

3 Engineering Science Dept, Faculty of Community, Umm Al-Qura University, KSA

4 Physics Department, Faculty of Science, Beni-Suef University, Egypt 5 Physics Department, Faculty of Science, Alazhar University, Egypt e-mail: hassouba@yahoo.com Поступила в редакцию 24.02.2012 г. Окончательный вариант получен 21.07.2012 г.

Cylindrical probe data have been analyzed using different theories in order to determine some plasma parameters (electron temperature and electron and ion densities). Langmuir probe data are obtained in a cylindrical DC glow discharge in the positive column plasma at argon gas pressures varied from 0.5 to 6 Torr and at constant discharge current equal to 10 mA. The electron density has calculated from the electron current at the space potential and from Orbital Motion Limited (OML) collisionless theory. Ion density has obtained from the OML analysis of the ion saturation currents. In addition, the electron temperature has measured by three different methods using probe and electrons currents. Electron temperature Te, plasma density ne, and space potential Vs, have been obtained from the measured single cylindrical probe I—Vcharacteristic curves. The radial distribution of the electron temperature and plasma density along the glow discharge are measured and discussed. Using the collisionless theories by Langmuir cylindrical probe and up to several Torr argon gas pressures the differences between the values of electron temperature and electron and ion densities stay within reasonable error limits.

DOI: 10.7868/S0367292113030037

1. INTRODUCTION

Langmuir and Mott-Smith [1—5] firstly showed that it is possible to analyze properly the current-voltage probe characteristic in order to determine the plasma parameters near the probe. In particular, it is possible to determine the plasma potential, the electron and ion densities and the electron energy distribution function. Assuming that the energy distribution of electrons is Maxwellian it is possible to determine the electron temperature too. The most widely used technique to measure electron temperature and electron density is the Langmuir probe due to its easy manufactory and implementation.

There are several potentially serious sources of errors in measurement of the probe characteristics in

DC plasma without the magnetic field. Some of them are coupled with the processing of the signal from the probe; some are effects that are coupled with the interaction of the probe and the plasma being investigated. Of the apparatus, effects are worthy to mention the magnitude of the resistance in the probe circuit that should be much lower than the lowest differential resistance of the probe characteristic; the effect has been discussed in [6]. Among the second group one can list

(i) too high probe collection area [7—9], (ii) the change of the work function over the probe surface (es-

pecially due to contamination of the probe surface) [10], (iii) the secondary emission of electrons from the probe surface and (iv) the collisions of charged particles with neutrals atoms within the space charge sheath. If a magnetic field is applied to plasma, then, in addition, (v) the orientation of the probe to the direction of the magnetic field is of prior importance. The effects (i, ii, v) cause rounding off the probe characteristic near the plasma potential and subsequently uncertainty in determination of the plasma potential and electron energy distribution function (EEDF). The effects (iii, iv) are at low-to-medium pressures mostly important in the positive-ion-current part of the probe characteristic and can cause changes of the measured value of the floating potential and of the estimated values of the plasma density [10].

Sudit and Woods [11] have measured ion and electron densities in long, low pressure, cylindrical nitrogen and helium DC discharge using computer-controlled Langmuir probes. Electron densities were obtained from the electron saturation currents using orbital motion limited (OML) theories, and from the electron retardation region of the probe trace by integration of the second derivative of the probe current. Ion densities were obtained from both OML and radial motion analysis of the ion saturation currents. While

needle valve

rn S N

Ar Ar

^ J

gas

regulator

Fig. 1. Experimental set up.

both probe electron density methods agree very well with each other and reasonably well with the independent density measurements, the OML theory applied to the ions overestimates the plasma density by up to a factor of 10. The radial motion theory yields ion densities that show considerably better agreement with the electron densities than the OML theory.

Bilyk et al. [12] compare several probe theories that described the collection of charged particles by Lang-muir probe with that obtained from measurements of recombination rates of positive ions with electrons in stationary afterglow system. They compare apparent electron density calculated from the probe data using different theories with the reference electron density that obtained from the known rate of recombination.

Demidov et al. [13] have reviewed the electric probe methods for diagnostics of plasmas with emphasis on the link between the appropriate probe theories and the instrumental design. The starting point is an elementary discussion of the working principles and a discussion of the physical quantities that can be measured by the probe method. This is followed by a systematic classification of the various regimes of probe operation and a summary of theories and methods for measurements of charged particle distributions. Application of a single probe and probe clusters for measurements of fluid observables is discussed. Probe clusters permit both instantaneous and time-averaged measurements without sweeping the probe voltage.

The purpose of present work is to compare plasma parameters determined from the measured probe characteristic using various well-known probe analysis techniques in glow discharge. Electron temperature Te, plasma density ne, and space potential Vs, have obtained from the measured probe I—V characteristic curves using the following techniques:

(a) Classical Langmuir procedure applied to the electron retardation region of the single probe characteristics corresponding to electron collection when the probe potential Vp is less than the plasma potential [2];

(b) Orbital motion limit (OML) theory for electron collection in the electron saturation region of the probe characteristic (Vp > Vs,) [3];

(c) OML theory for ion collection in the ion saturation region of the probe characteristic [5, 14].

2. EXPERIMENTAL SET UP

Fig. 1 shows a schematic diagram of the experimental setup. The cylindrical discharge cell is a Pyrex glass tube of 23 cm length and 7 cm diameter. Two parallel, circular and movable electrodes made of stainless steel are enclosed in the discharge cell. The distance between the two electrodes is fixed at 3 cm and each of them has a diameter of 5 cm. The discharge cell is evacuated using two stage rotary pump to a base pressure of 7 mTorr then the gas is allowed to fill the tube at the desired flow rate. Pure Ar gas is used as working gas and fills the discharge cell under continuous flow through needle valve. A vacuum gauge is connected to the discharge tube to measure the inside gas pressure. The applied voltage is controlled by a DC power supply which can produce potential up to 1000 V and current up to 100 mA.

Single cylindrical Langmuir probe made of molybdenum wire of 0.3 mm diameter and length of 2 mm is used. The wire is isolated by a thin glass tube and the tip of a probe is immersed inside the positive column of the glow discharge plasma.

The axis of the cylindrical Langmuir probe should always be positioned perpendicular to the electric field otherwise changes of the space potential along of the

probe may distort the probe characteristic, especially in the vicinity of the space potential (it may round off the knee of the probe characteristic). The probe was periodically cleaned by ion bombardment to remove all possible hysteresis effects of the probe characteristic.

3. THEORETICAL CONSIDERATIONS 3.1. Introduction

The working regime of the probe in a plasma without the magnetic field is usually described by two parameters [15] namely by the Knudsen number for ions and electrons K, e = X , e/rp, (where X;, e is the mean free path for ions/electrons and rp is the probe radius) and by the Debye number Dx = rp/XD, XD = = (s0kTe/q2ne)1/2 is the Debye length, s0 is the permittivity of vacuum, k is the Boltzmann constant, Te is the electron temperature, q is the elementary charge and ne, is the electron density). Another parameter which influences the collection of charged particles by a probe is the "anisothermicity parameter" of a plasma namely the ratio of the electron to ion temperature, t = TJTi. The introduction of this parameter (and also of XD) already implies the Maxwellian distribution of electron and (for the case T > 0) of ion energies [15]. The Maxwellian distribution of electron and ion energies is assumed also throughout the present paper except where stated otherwise. We restrict ourselves further to the case of a cylindrical probe which is easy to manufacture and is applicable in all cases where the distribution of electron and ion energies can be assumed isotropic. Also one assumes anisothermic plasma for which t > 1.

A completely general theory describing the collection of charged particles by a probe does not exist. The appropriate theory depends on the pa

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