T. Gyergyek

Experimental study of the creation of a fire-rod I: Temporal development of the electron energy distribution function

Positive voltage steps are applied to a planar electrode (collector) immersed in a magnetized discharge plasma column with its surface perpendicular to the magnetic field lines. If the voltage step and the neutral gas pressure are high enough additional ionization occurs in front of the collector and a fire-rod is created. Time resolved measurements of the plasma response are performed by a one-sided plane Langmuir probe using standard boxcar technique. The temporal development of the electron energy distribution function after the application of a positive voltage step to the collector is measured by a one-sided plane Langmuir probe. In a magnetized plasma the electron energy distribution function is proportional to the first derivative of a plane Langmuir probe characteristics. It is found that immediately (1 μs) after the application of a positive voltage step to the collector a short lifetime electron population is created. This electron population disappears in approximately 2 μs. It is related to the anomalously large initial electron current collected by the collector current overshoot. When the initial current overshoot to the collector is terminated, a high potential (anode) plasma starts to form in front of the collector if the voltage step and the pressure are high enough. The formation of the anode plasma electron population is followed experimentally.

Potential formation in front of an electron emitting electrode immersed in a plasma that contains a monoenergetic electron beam

A one-dimensional fluid model of the sheath formation in front of a large, planar electron emitting electrode (collector) immersed in a plasma that contains a monoenergetic electron beam is presented. Expressions for the Bohm criterion, the total electric current to the collector, and for the zero electric field at the collector are derived. When there is no electron emission, the model predicts, in some cases, up to three different solutions. The low and the high solutions correspond to the fact that the presheath potential drop can be determined either by thermal or by the beam electrons. The middle solution between them has no physical meaning. When the electron emission is space charge limited, the model may have up to five solutions because the low solution can sometimes split into three parts. The current-voltage characteristic of the collector that exhibits triple floating potential is calculated and it shows qualitative similarity with experimental ones [C.-H. Nam et al., J. Appl. Phys. 63, 5674 (...

An investigation of the electrode current oscillations caused by the potential relaxation instability in a weakly magnetized discharge plasma

Oscillations of the electrode current, plasma density and plasma potential, caused by the potential relaxation instability in a weakly magnetized discharge plasma are studied. The oscillations appear when the electrode bias exceeds the plasma potential. As long as the difference between the electrode bias and the plasma potential is below approximately 2 V, that is approximately kTe/e0 in our experiment, the oscillations are periodic. When the electrode bias is increased above this value, the oscillations become irregular. The limit cycle in the phase space disappears, the power spectrum becomes broader and the autocorrelation time shorter. Presence of f- alpha noise is observed in the power spectra. Distribution of Fourier phases for electrode current, plasma density and plasma potential oscillations is shown. Dimensional analysis of the signals is performed using the Grassberger-Procaccia algorithm. The correlation dimension is found to be between 1.2 and 2.0 for low electrode biases and no saturation of the In(C(r)) versus In(r/r0) plots is found for higher electrode biases. Entropy K2 is plotted versus r/r0. The largest Lyapunov exponent is calculated using two different methods, one developed by Rosenstein and co-workers and the second by Wolf and co-workers. It appears that the largest Lyapunov exponent is positive and close to zero. An attempt to calculate the complete Lyapunov spectrum with the method of Kruel and co-workers is also made.

Potential formation in a one-dimensional bounded plasma system containing a two-electron temperature plasma: Kinetic model and PIC simulation

Potential formation in a bounded plasma system that contains electrons with a two-temperature velocity distribution and is terminated by a floating, electron emitting electrode (collector) is studied by a one-dimensional kinetic model. A method on how to determine the boundary conditions at the collector for the numerical solution of the Poisson equation is presented. The difference between the regular and the irregular numerical solutions of the Poisson equation is explained. The regular numerical solution of the Poisson equation fulfills the boundary conditions at the source and can be computed for any distance from the collector. The irregular solution does not fulfill the source boundary conditions and the computation breaks down at some distance from the collector. An excellent agreement of the values of the potential at the inflection point found from the numerical solution of the Poisson equation with the values predicted by the analytical model is obtained. Potential, electric field, and particle ...

Fluid model of the sheath in front of a floating electrode immersed in a magnetized plasma with oblique magnetic field: Some comments on ion source terms and ion temperature effects

A one-dimensional fluid model of the magnetized plasma-wall transition region in front of a floating electrode immersed in a magnetized plasma with oblique magnetic field is presented. The Boltzmann relation is assumed for the electrons, while the positive ions obey the ion continuity and momentum exchange equation. The ions are assumed to be isothermal. By comparison with a two-fluid model, it is shown that assuming the Boltzmann relation for the electrons implies that there is no creation or annihilation of the electrons. Consequently, there should not be any creation and annihilation of the positive ions either. The models that assume the Boltzmann relation for the electrons and a non-zero ion source term at the same time are therefore inconsistent, but such models have nevertheless been used extensively by many authors. So, in this work, an extensive comparison of the results obtained using the zero source term on one hand and three different non-zero source terms on the other hand is made. Four diffe...

Mode suppression of a two-dimensional potential relaxation instability in a weakly magnetized discharge plasma

Abstract A potential relaxation instability (PRI) is modulated by an external signal using an additional grid to modulate the radial plasma potential profile in a magnetized plasma column in a linear magnetized discharge plasma device. It is observed that the electrode current oscillations follow the van der Pol equation with an external forcing term, and the linear growth rate of the instability is measured.

Advances in Langmuir probe diagnostics of the plasma potential and electron-energy distribution function in magnetized plasma

Advanced Langmuir probe techniques for evaluating the plasma potential and electron-energy distribution function (EEDF) in magnetized plasma are reviewed. It is shown that when the magnetic field applied is very weak and the electrons reach the probe without collisions in the probe sheath the second-derivative Druyvesteyn formula can be used for EEDF evaluation. At low values of the magnetic field, an extended second-derivative Druyvesteyn formula yields reliable results, while at higher values of the magnetic field, the first-derivative probe technique is applicable for precise evaluation of the plasma potential and the EEDF. There is an interval of intermediate values of the magnetic field when both techniques—the extended second-derivative and the first-derivative one—can be used. Experimental results from probe measurements in different ranges of magnetic field are reviewed and discussed: low-pressure argon gas discharges in the presence of a magnetic field in the range from 0.01 to 0.08 T, probe measurements in circular hydrogen plasmas for high-temperature fusion (magnetic fields from 0.45 T to 1.3 T) in small ISTTOK and CASTOR tokamaks, D-shape COMPASS tokamak plasmas, as well as in the TJ-II stellarator. In the vicinity of the last closed flux surface (LCFS) in tokamaks and in the TJ-II stellarator, the EEDF obtained is found to be bi-Maxwellian, while close to the tokamak chamber wall it is Maxwellian. The mechanism of the appearance of a bi-Maxwellian EEDF in the vicinity of the LCFS is discussed. Comparison of the results from probe measurements with those obtained from calculations using the ASTRA and EIRENE codes shows that the main reason for the appearance of a bi-Maxwellian EEDF in the vicinity of the LCFS is the ionization of the neutral atoms.

Comparison of measured and simulated electron energy distribution functions in low-pressure helium plasmas

Knowledge of the electron energy distribution function (EEDF) is of great interest in different branches of plasma physics ranging from laboratory to fusion plasmas. In the frame of this work systematic measurements of the EEDF in low temperature helium plasmas (Te ≈ 2 eV) at different working gas pressures and discharge currents (Idis between 1 and 2 A) will be presented and compared with numerical particle-in-cell (PIC) code simulations. The experiments were conducted in the Innsbruck double plasma machine and in the Ljubljana linear magnetic plasma device with helium as the working gas. The EEDF was obtained by the second derivative of the characteristic of a Langmuir probe. The PIC code was used to simulate the EEDF by taking into account most of the physical parameters in the plasma vessel.

Determination of plasma parameters from plane-probe characteristics in a current-carrying plasma

The authors present an approximate method of determining the temperature and the drift velocity of electrons in a current-carrying plasma. An approximate expression for the determination of plasma density is also derived. The authors consider the probe characteristics obtained by a one-sided plane probe in a plasma in which the electron distribution may be assumed to be a shifted Maxwellian. The method they propose for analysing such characteristics can be regarded as a generalization of the standard probe method for the determination of plasma parameters in a Maxwellian plasma. Application of the method is illustrated by experimental examples. A confirmation of the method is performed by comparing the results with those obtained by other techniques.

Ion temperature profiles in front of a negative planar electrode studied by a one-dimensional two-fluid model

Plasma-wall transition is studied by a one-dimensional steady state two-fluid model. Continuity and momentum exchange equations are used for the electrons, while the continuity, momentum exchange, and energy transport equation are used for the ions. Electrons are assumed to be isothermal. The closure of ion equations is made by the assumption that the heat flux is zero. The model equations are solved for potential, ion and electron density, and velocity and ion temperature as independent variables. The model includes coulomb collisions between ions and electrons and charge exchange collisions between ions and neutral atoms of the same species and same mass. The neutral atoms are assumed to be essentially at rest. The model is solved for finite ratio e=λDL between the Debye length and λD and ionization length L in the pre-sheath and in the sheath at the same time. Charge exchange collisions heat the ions in the sheath and the pre-sheath. Even a small increase of the frequency of charge exchange collisions ...