Anomalous plasma phenomena of hollow cathode arc discharge

Magnetically confined argon plasma produced by hollow cathode arc discharge has been studied in different experimental conditions, with discharge current from 10–50 A, vessel argon pressure between 10^–3 and 10^–4 torr (1 torr=133·32 Pa) and axial magnetic field up to 0·12 T. The plasma density measured by a cylindrical Langmuir probe is found to be 10¹⁹ to 4 × 10¹⁹ m^–3 and the electron temperatureT _e varies between 2·5 and 4·8 eV. When an external axial magnetic field is applied the plasma temperature decreases with the increase in the magnetic field intensity until it reaches a minimum value at 0·075T and then increases with the same rate. This has been interpreted as high frequency waves excitation due to electron beam-plasma interaction, which explains the electron density jumps with the magnetic field intensity. Enhanced plasma transport across the magnetic field is studied and classified as anomalous diffusion.     

Experimental Studies on Low-Pressure Plane-Parallel Hollow Cathode Discharges

Hollow cathode discharge (HCD) is widely used in material processing and plasma emission spectroscopy due to several advantages over other plasma sources. Basically, the HCD consists of a cathode with a hollow structure (cavity, hole, or parallel faces) and an anode of arbitrary shape. In this investigation, experimental studies on low-pressure plane-parallel HCD operated at different process conditions are reported. Herein, we investigate the dependence of the discharge current on the product of the gas pressure and inter-cathode distance (pD). In addition, the electron temperature and density were inferred from the current-voltage characteristics of a single cylindrical Langmuir probe positioned between the cathodes, on the discharge axis. The measurements were carried out at different gas pressures, magnetic field intensities, working gases, inter-cathode distances, cathode materials, and discharge voltages. The results showed that, at different gas pressures, the maximum discharge current (I_d,max) is not only a function of the product pD, but also of the pressure itself. Application of a uniform longitudinal magnetic field improved plasma confinement between cathodes, leading to a substantial increase in I_d,max in most of the situations considered in this study. However, for oxygen discharge, a strong discharge current reduction after the application of the magnetic field was observed. In relation to the Langmuir probe studies, it was observed that the uniform longitudinal magnetic field reduced the electron temperature, but this behavior depends strictly on pD. The typical values of electron density and electron temperature in the case of the nitrogen discharge were n_e?=?10¹⁷ m^?3 and T_e?=?2.5 eV, respectively. Finally, our experiments showed that the pD range for hollow cathode effects was between 0.2–5 Pa m.     

The Influence of Collisions in the Space Charge Sheath on the Ion current Collected by a Langmuir Probe

The current/voltage characteristics of a cylindrical Langmuir probe have been studied in Ar⁺/electron afterglow plasmas in helium carrier gas under truly thermal conditions at 300 K using our flowing afterglow/Langmuir probe (FALP) apparatus. The orbital motion limited (oml) ion and electron current regions of the probe characteristics have been explored over a wide range of the reduced probe voltage (up to ～ 100) and over a wide range of electron (n_e) and ion (n₊) number densities (1.6 × 10⁷ to 1.5 × 10¹⁰ cm^?3) at a constant pressure of the He carrier gas of 1.2 Torr. The observed increase of the probe ion currents above those predicted by collisionless oml theory, resulting in an apparent increase of the measured ion number density above n_e in the plasma, is explained by the enhancement in the ion current collection efficiency due to collisions of ions with neutral gas atoms in the space charge sheath surrounding the probe. The continuous change in the exponent, χ, of the power-law dependence,i₊ ∞ V of the ion current, i₊, on the probe voltage, V_p from 0.5 at the highest n₊ (smallest sheath) towards 1.0 at the lowest n₊ (large sheath) indicates that the ion current collection from the plasma changes from the oml current regime at the high n₊ to the continuum regime at the low n₊ when the ions undergo multiple collisions with the helium atoms in the space charge sheath and thus “drift” towards the probe.     

A contribution to the assessment of the influence of collisions on the measurements with Langmuir probes in the thick sheath working regime

In the present work we investigate theoretically and experimentally the influence of elastic collisions in a probe sheath on a cylindrical Langmuir probe. The analysed probe working regime covers conditions under which the following probe characteristic parameters are comparable: the probe radius, the Debye length and both the ion and electron mean free paths.The preliminary investigations under almost collisionless conditions show good agreement between theoretical and experimental values of the ion saturation currents and of the floating potentials only when the ion currents for the studied working regime of the cylindrical Langmuir probe are calculated according to the theory of Chen (Plasma Phys.7 (1965)47). These collisionless currents form the basis for the calculation of the collision-corrected probe characteristics according to the presented procedure by Talbot and Chou (Rarefied Gas Dynamics, Academic Press, New York, 1966, p. 1723).The applied theoretical analysis covers the influence of the collisions on the electron and ion current of the single probe characteristic and on the estimation of the space potential. The results of the calculations are presented in graphical overviews for the series of cases of practical importance. The other working regimes can be covered using the calculating procedure presented.For comparison of the calculated collision-corrected characteristics with those from an experiment we used the positive column plasma of the He glow discharge where the electron density is known and the space potential can be experimentally estimated from the lowest excitation potential of He. The comparison was carried out for the ion and electron currents, the floating potential and the zero-cross of the probe characteristic second derivative.The estimation of the secondary electron current contribution to the total probe current shows that it limits the applicability of the collision-corrected probe characteristic to the plasma diagnostic in the transition to the collision-determined working regime.     

Theory of ion extraction from plasma by an external electric field in systems of laser isotope separation

A refined model of processes taking place in electrostatic extractors is proposed. The model is based on the analysis of the present-day state of theoretical studies in this field and takes into account both the Langmuir and Bohm mechanisms of ion transport, calculations of initial profile of ionic current to the cathode, and the integrated contribution of ionic current to the anode. The Bohm mechanism is shown to make the dominant contribution to ion extraction for typical values of initial ionic densityn _i ⁰ ≥10¹⁰ cm^?3. Under these conditions, this mechanism not only causes a considerable (by more than an order of magnitude) decrease in plasma relaxation time τ _R in comparison with the values determined by the usual Langmuir mechanism, but also substantially modifies the main structural dependences of the relaxation time, which are found to be now in good agreement with the experimental power dependences. The new results obtained in the work favor the view that electrostatic (nonmagnetic) ion extraction systems provide a rather high efficiency at an increased (n _i ⁰ ～10¹¹ cm^?3) plasma density and, correspondingly, at a high power density.     

A Collisional Model of the Positive Ion Collection by a Cylindrical Langmuir Probe

This article presents a new theoretical model of ion collection by a cylindrical Langmuir probe at medium and higher pressures which we call the “modified Talbot and Chou model”. The model makes use of the following theories; (a) the kinetic theory by Chou, Talbot and Willis [6, 7] and (b) the theory by Zakrzewski and Kopiczynski [10, 11]. The basic idea is to calculate the decrease of probe ion current due to collisions with neutrals according [6, 7] and the increase of the ion current due to destruction of an orbital motion according [10, 11]. The computed results are presented in the form of graphs suitable for probe data interpretation at medium and higher pressures. The applicability of the results at particular plasma conditions is also discussed.     

Influence of Plasma Resistance and Fluctuation on Probe Characteristics in Detached Recombining Plasmas

In order to find the causes of the strong anomaly of current‐voltage characteristics of Langmuir probe observed in detached recombining plasmas in a linear divertor plasma simulator, NAGDIS‐II, we have investigated plasma resistance along a magnetic field and potential fluctuations in the detached recombining plasmas. Simple calculation on the ratio between the plasma length, at which plasma resistance and resistance of ion sheath formed around a probe tip become equal, and an electron collection length indicates that the evaluation of electron temperature T_e becomes inaccurate at T_e of less than 0.6 eV when plasma density and neutral pressure are 1.0 × 10¹⁸ m^—3 and 10 mtorr, respectively. The potential fluctuation in detached recombining plasmas was found to be so large compared to T_e/e, which can also modify the probe characteristics.     

The Effect of Rotating Cylindrical Langmuir Probes in Magnetron Plasmas

Using a cylindrical Langmuir probe, the plasma properties (ion density, electron temperature, floating and plasma potentials) in a magnetron sputter source have been investigated, along one particular line‐of‐sight, but for different probe‐orientations with respect to the B‐field. The plasma in the region hosen for observation is haracterised by electrons, which are magnetised (Larmor radius r_le < both the electron mean‐free‐path λ_e, and plasma extension L) and ions, which are not (their Larmor radius r_I > L, λ_I). Through the development of a simple expression for the electron saturation current at different probe angles relative to the local B‐field, it is possible to correct for the diminished electron currents due to their restricted transport across the field. The results indicate that the measured ion density, electron temperature, floating and plasma potentials are unaffected by the probe orientation, however the electron saturation current is attenuated when the probe is aligned along the B‐field. A simple model for the collection of electrons indicates that classical electron diffusion may not operate in the magnetron, with cross‐field electron transport dominated by anomalous, possibly Bohm, diffusion.     

Negative Ions in a Glow Discharge of Tetrafluoromethane

The Langmuir — probe measurements in a CF₄ — glow discharge reveal a large number of negative ions (10¹⁰ cm^?3) in the plasma between the planar C-electrodes. Under special conditions the density of them exceeds the electron density at several orders of magnitude and sustains a quasi — electron free plasma. The ratio depends on the residence time of the molecular gas in the discharge reactor. It is due to dissociative electron attachment to highly molecular gas components arising from the plasmachemical conversion of CF₄. F^? and CF₃^? are the most important negative ions.     

Anomalous Diffusion in a Linear Plasma Generator

Plasma production and particle transport of the magnetized plasma in the linear device PSI‐2 are investigated by analyzing the radial density and electron temperature pro.les obtained from Langmuir probe measurements. Additional information on the atomic (H) and proton temperatures is obtained from high resolution Doppler spectroscopy. The density profiles are found to be hollow, but do extend radially far beyond the visible rim with an exponential decay length of 3 cm. They can be explained by parallel and perpendicular diffusion in combination with a cylindrical source extending along the magnetic field all over the device. A large perpendicular diffusion coefficient in the range of 5 m²/s is inferred from the experimental results. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Influence of magnetic field on cesium thermionic energy converter

This article deals with the calculation of the influence of the magnetic field upon the electric current of a thermionic converter presupposing the approach to conditions in a low-pressure cesium converter. The distribution of the starting velocities of the emitted electrons is considered firstly as independent of the angle from the perpendicular to the emitter plane, and secondly according to the cosine law.The magnetic field effect from the converter current is calculated and compared with the calculations in the papers by Schock [1] and Block [2]; the effect of the external magnetic field is verified by measurements on a solar thermionic converter prototype.Symbols F=I/I ₀ factor of current reduction from magnetic field effect - ¯F value of factorF (when the magnetic field is not constant) - I [A/m²] density of collector current (real current influenced by magnetic field) - I ₀ [A/m²] theoretical density of collector current (in ideal case equals electron emission current) - T _e [°K] electron gas temperature; assumed equal to emitter temperatureT _E [°K] - B[Wb/m²] magnetic induction (field) - D[m] distance from emitter to collector - R[m] radius of electrodes, emitter and collector - r[m] variable radius in the limits 0 toR - V [m/s] random velocity of electron - v _xz [m/s] component of the vectorV inx-z plane - v _m =2kT _E /m most probable velocity in the velocity distribution according to Maxwell and Boltzmann - w-v _xz /v _m relatively expressed electron velocityv _xz - the angle of any vectorV - [m] radius of circular electron path - n [m^–3] number (density) of electrons with certain value of random velocity - n ₀ [m^–3] total electron number (density) - n ₁ [m^–3] number of electrons returned to emitter by means of magnetic field - N ₀ [m^–2s^–1] total flow of thermionic electrons emitted from a unit surface - N ₁ [m^–2s^–1] partial flow of electrons returned to emitter - P=N ₁/N₀ relatively expressed flow of electrons returned to emitter (whenB = const.) - ¯P mean value ofP (whenB const.) - F _cos, ,P _cos, values asF,¯F,P,¯P in case of velocity distribution according to cosine law - m=9·107×10^–31 [gk] electron mass - e=1·60×10^–19 [C] electron charge - k×1·38×10^–23 [J/grad] Boltzmann's constant - ₀ 1·257×10^–6 [H/Vs] permeability of vacuum     

Electrostatic ion cyclotron wave dispersion relation in a steady-state toroidal plasma

Summary Electrostatic ion cyclotron wave dispersion relation has been studied in the experiment THORELLO, a steady-state magnetized toroidal plasma, produced in different neutral gases by hot-filament electron emission and acceleration by a bias voltage. Electron temperature and density, evaluated by Langmuir probes, are of the order of 5eV and 10¹⁰ cm⁻³, respectively. The maximum toroidal magnetic field on the axis is about 2kG. The waves are excited by a pair of thin metallic blades, fed with opposite phase by a low power (<10 W) RF signal, and detected by a movable RF probe. An interferometric method allows the evaluation of the perpendicular wave number, for any given frequency. The fit of experimental data with theoretical curves gives the possibility to evaluate the order of magnitude of the ion temperature. To speed up publication, the authors of this paper have agreed to not receive the proofs for correction.     

Characteristics of a reflex discharge in hydrogen in a magnetic field

The properties of an extensive reflex discharge of large power with one heated and one cold cathode in a magnetic field of 10 to 1500 Gauss were measured. At a neutral hydrogen pressure of 10^–4 to 10^–3 torr a plasma column was obtained which was 100 cm long, 10 cm in diameter and had a density greater than 10^–11 cm^–3. The dependence of the radial profile of the potential in the plasma was measured by a heated probe, and the temperature and electron density by Langmuir probes calibrated by a microwave interferometer.The dependence of the origin of low-frequency rotational instability on the parameters of the discharge was studied and the measured critical magnetic field was compared with theory. Apart from this low-frequency instability, intensive oscillations were also found in the discharge current in a frequency band up to 30 MHz, and the dependence of their spectrum on the magnetic field was measured.     

Plasma losses in a toroidal theta-pinch with superposed hexapole

A toroidal theta-pinch discharge with superposed non-helical hexapole field is investigated. The characteristic data of the discharge are: major diameter 52 cm, minor inner diameter of the vacuum vessel 6 cm, maximum magnetic field between 10 and 21 kG, rise time (quarter-cycle) 3.0 μs, maximum temperature between 40 and 100 eV, maximum density between 1 and 3×10¹⁶ cm^?3, beta-values between 0.3 and 1. The plasma confinement times are determined by measuring particle density, temperature and plasma radius. The confinement times are compared with those of models which account for cusp losses, resistive losses, and Bohm diffusion. Measured confinement times are consistent with those expected from cusp losses with a cusp slit-width of one ion gyro-radius. Above electron temperatures of 20 eV, resistive losses are negligible. Bohm diffusion is not consistent with measurements, but is of the same order of magnitude.     

A Rb-magnetometer for a wide range and high sensitivity

A Rb-magnetometer was constructed for a wide range of application. It uses a very small optically pumped resonance cell with an active volume of less than 0.1 cm³ as the sensor element. The cell is housed in a small probe containing polarizer, rf-coil, heater and photoelement. The pumping light is brought to the resonance cell by use of a 3 m long fibre optics. The magnetometer allows continuous monitoring or stabilizing magnetic fields from about 3·10^?8T to beyond 0.3T. The ultimate sensitivity of the instrument is of the order of 10^?10T. Observing the Hanle signal in the transverse mode of optical pumping the instrument can be used for zero field detection and for the measurement for weak fields by means of field compensation.     

Diagnosis of a low pressure capacitively coupled argon plasma by using a simple collisional-radiative model

This paper proposes a simple collisional-radiative model to characterise capacitively coupled argon plasmas driven by conventional radio frequency in combination with optical emission spectroscopy and Langmuir probe measurements. Two major processes are considered in this model, electron-impact excitation and the spontaneous radiative decay. The diffusion loss term, which is found to be important for the two metastable states (4s[3/2]₂, 4s'[1/2]₀), is also taken into account. Behaviours of representative metastable and radiative states are discussed. Two emission lines (located at 696.5 nm and 750.4 nm) are selected and intensities are measured to obtain populated densities of the corresponding radiative states in the argon plasma. The calculated results agree well with that measured by Langmuir probe, indicating that the current model combined with optical emission spectroscopy is a candidate tool for electron density and temperature measurement in radio frequency capacitively coupled discharges.     

Experimental and theoretical study of density,potential, and current structures of a helium plasma in front of an radio frequency antenna tilted with respect to the magnetic field lines

Potential and density structures in the vicinity of an radio frequency (RF) electrode/antenna in a magnetized plasma are investigated using an RF-compensated cylindrical Langmuir probe. These measurements were performed in the ALINE plasma device in which only electrons can be considered well magnetized. Very precise 2-D maps of the plasma parameters are drawn thanks to a 3-D automatic manipulator on which the probe is mounted. The effect of the tilted magnetic angle between the RF-biased surface and the magnetic lines is also studied thanks to a tilting electrode. Comparison of several simplistic models with the experiments proved the reliability of simple Langmuir probe measurements in such an RF and magnetized environment (space potential vs. tilting angle of the antenna with respect to magnetic field lines and recovery of the floating potential structure using measured currents). A fluid model based on total current density and ion diffusion equations over the biased flux tube provides the same density structures in front of the electrode as the measurements. Those density structures display a “bunny ears” shape and can be explained using transverse RF and collisional current behaviour: In front of the antenna, the transverse ion currents deplete the magnetized flux tube, while at the edge of the biased flux tube, the same currents increase the density.     

An experimental check of the electron distribution function in a current carrying plasma

The local current density obtained by means of Thomson scattering measurements (with a component of the scattering vector k along the current direction) [1] has been compared with the local current density obtained by means of magnetic field measurements made using a magnetic probe inserted in the plasma. A better agreement has been found between the two kinds of measurements when the scattered signals have been treated on the assumption of the Spitzer-Härm electron distribution function than on the assumption of the displaced Maxwellian one for the current carrying plasma.     

Collisionless Currents for Cylindric Probes in a Plasma with non-Maxwellian Distribution of the Electron Energy

The radial model developed by Allen, Boyd, Reynolds and Chen [1, 2] for the ion collection of Langmuir probes is extended to describe the case of a non-Maxwellian distribution of the electron energy. Assuming standard distributions, showing with respect to the Maxwell distribution an increasing deficite of fast electrons as the parameter k of the distribution increases, the electron-retarded current characteristic, the potential distribution and the density profiles for electrons and ions in the probe sheath, ion-current characteristics as well as graphs for the ion-density determination are calculated for different k. It is shown, that the application of the Chen model (k = 1) in plasma with k > 1 leads only to a small error in the ion-density measurement.