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Plasma potential is a key parameter in plasma discharge or fusion plasma to control plasma–wall interaction or ExB drift. The magnitude of plasma potential depends on the overall energy transmitted to the plasma via direct current (dc) or radio frequency (RF) devices such as electrodes or antennas. Knowing the plasma potential from the exciting source is useful to prevent high energetic fluxes to the wall or to improve the plasma confinement or explaining shear velocity. The aim of the present model is to calculate this plasma potential with respect to a dc or RF source in a magnetized or unmagnetized plasma. This double saturated probe (DSP) model takes into account the electron saturation current and is able to derive the plasma potential as a function of the electrode/wall area ratio for a dc or RF discharge in a helium/argon plasma with or without a magnetic field. The results of the model are compared with Aanesland’s model in the case of unmagnetized capacitive sheath and particle-in-cell (PIC) simulations. The magnetized model is applied to a plasma column with a perpendicular capacitive current in an RF discharge. It appears that the plasma potential can increase to almost the RF potential value at a low wall/electrode area ratio ($A_{\text {wall}}/A_{\text {el}}$ lower than 5), while the same potential collapses as soon as the area ratio (perpendicular over the parallel current area) is higher than the electron/ion saturation current ratio. This is directly due to the saturation of electron current, preventing the plasma potential from following the imposed RF potential by the electrode, so that the maximum value can be as lower as the floating potential. The perpendicular current involved is mainly a conduction current modeled as a resistive collisional current. In fusion plasma, the maximum plasma potential can rise to higher values than in plasma discharges, but the collapse of the potential still occurs for long collisional biased flux tubes. [ABSTRACT FROM AUTHOR]

The sheath properties are studied by using 1d3V particle-in-cell simulations in a plasma bounded by two conductive electrodes between which is applied a constant voltage, Vw. A magnetic field tilted by θ with respect to the wall is considered in the simulations. Elastic collisions with neutrals are modeled by an operator that randomly reorients ions and electrons in the velocity space. The ratio between the ion mean-free-path and the Larmor radius is chosen such that λ c i R > 1 , ≃ 0.5 or < 1, whereas the same ratio for electrons is always ≫ 1. For low ion collisionality ( λ c i R > 1) and incidences such that sin θ > R λ c i , the sheath size is shown to scale with sin θ and depends on Vw according to the Child–Langmuir law, with a 3/4 exponent. For larger collisionalities, the sin θ dependence of the sheath size disappears because ions are demagnetized by collisions. Then, for incidences θ > 5 ° , the sheath size varies with a 3/5 exponent of the wall potential, as expected in moderate collisional sheaths. More interestingly, for grazing incidences and λ c i R ≃ 0.5 , an inverse sheath, i.e., an electro-negative space charge, arises at the wall vicinity in order to screen the positive wall potential (instead of the negative one). Its size, comparable to a classical Debye sheath, is shown to vary with a 2/3 exponent of the wall potential. Finally, our simulation results show that the Child–Langmuir law is a good way to evaluate the sheath size for a large range of collisionality at any magnetic field incidence as long as the exponent is chosen accordingly. [ABSTRACT FROM AUTHOR]

The small layer oscillating in front of a radio frequency (rf) biased electrode in an asymmetric rf plasma discharge without a magnetic field is diagnosed using an rf compensated cylindrical probe. Thanks to this probe (0.15 mm in diameter), the floating potential is measured in this area. Radio frequency plasmas and sheath properties are then derived from the I-V characteristics measured by the probe at different rf power levels in both capacitive and direct couplings. In direct coupling, the plasma biasing is, as expected, nearly equal to the applied rf potential except at high power levels for which the current collected by the electrode saturates and the sheath potential gap is reversed. In capacitive coupling, the self-biasing of the electrode is strongly negative due to the matching box used. From the difference between the plasma potential and the floating potential, we found a sheath thickness of about 3 λDe. Within the rf power scan performed, the sheath thicknesses deduced from the potential and density profiles are 3 times higher than those from the Child–Langmuir law both in direct and capacitive coupling in a low collisional helium plasma. [ABSTRACT FROM AUTHOR]

Particle in cell simulations were carried out with a plasma bounded by two absorbing walls and a magnetic field applied parallel to them. Both the sheath extent and the potential drop in it were derived from simulations for different plasma parameters, such as the electron and ion temperature Ti, particle density, and ion mass. Both of them exhibit a power law dependent on the Larmor to plasma ion pulsation ratio Xi. For increasing values of the magnetic field, the potential drop within the sheath decreases from a few Ti=e down to zero, where e stands for the electron charge. The space charge extent increases with Xi and saturates to 2.15 ion Larmor radius. A simple model of sheath formation in such a magnetic field configuration is presented. Assuming strongly magnetized electrons, and neglecting collisions and ionizations, a new typical length is evidenced, which depends on the ratio Xi. The charge separation sheath width is theoretically found to increase from a combination of the electron gyroradius and the ion Debye length for low Xi ratios up to several ion gyroradii for strongly magnetized ions. Both the calculated sheath extent and plasma potential show a fair agreement with the numerical simulations. [ABSTRACT FROM AUTHOR]

A minimal two-field fluid approach is followed to describe the radio-frequency (RF) wave propagation in the bounded scrape-off layer plasma of magnetic fusion devices self-consistently with direct current (DC) biasing of this plasma. The RF and DC parts are coupled by non-linear RF and DC sheath boundary conditions at both ends of open magnetic field lines. The physical model is studied within a simplified framework featuring slow wave (SW) only and lateral walls normal to the straight confinement magnetic field. The possibility is however kept to excite the system by any realistic 2D RF field map imposed at the outer boundary of the simulation domain. The self-consistent RF + DC system is solved explicitly in the asymptotic limit when the width of the sheaths gets very large, for several configurations of the RF excitation and of the target plasma. In the case of 3D parallelepipedic geometry, semi-analytical results are proposed in terms of asymptotic waveguide eigenmodes that can easily be implemented numerically. The validity of the asymptotic treatment is discussed and is illustrated by numerical tests against a quantitative criterion expressed from the simulation parameters. Iterative improvement of the solution from the asymptotic result is also outlined. Throughout the resolution, key physical properties of the solution are presented. The radial penetration of the RF sheath voltages along lateral walls at both ends of the open magnetic field lines can be far deeper than the skin depth characteristic of the SW evanescence. This is interpreted in terms of sheath-plasma wave excitation. Therefore, the proper choice of the inner boundary location is discussed as well as the appropriate boundary conditions to apply there. The asymptotic scaling of various quantities with the amplitude of the input RF excitation is established. [ABSTRACT FROM AUTHOR]

The plasma-wall transition is studied by means of a particle-in-cell (PIC) simulation in the configuration of a parallel to the wall magnetic field (B), with collisions between charged particles vs. neutral atoms taken into account. The investigated system consists of a plasma bounded by two absorbing walls separated by 200 electron Debye lengths (λd). The strength of the magnetic field is chosen such as the ratio λ d / r l , with rl being the electron Larmor radius, is smaller or larger than unity. Collisions are modelled with a simple operator that reorients randomly ion or electron velocity, keeping constant the total kinetic energy of both the neutral atom (target) and the incident charged particle. The PIC simulations show that the plasma-wall transition consists in a quasi-neutral region (pre-sheath), from the center of the plasma towards the walls, where the electric potential or electric field profiles are well described by an ambipolar diffusion model, and in a second region at the vicinity of the walls, called the sheath, where the quasi-neutrality breaks down. In this peculiar geometry of B and for a certain range of the mean-free-path, the sheath is found to be composed of two charged layers: the positive one, close to the walls, and the negative one, towards the plasma and before the neutral pre-sheath. Depending on the amplitude of B, the spatial variation of the electric potential can be non-monotonic and presents a maximum within the sheath region. More generally, the sheath extent as well as the potential drop within the sheath and the pre-sheath is studied with respect to B, the mean-free-path, and the ion and electron temperatures. [ABSTRACT FROM AUTHOR]

Abstract: Using numerical simulation, a first estimate is made of power fluxes caused by radio-frequency sheaths on plasma facing components surrounding the ITER Ion Cyclotron Range of Frequencies wave launcher. Three toroidal strap phasings were considered, and four plasma scenarios covering a broad range of Scrape-Off Layer densities. Parallel heat fluxes up to ∼16MW/m2 are obtained, localized in poloidal peaks whose radial extension (initially 4–35mm) increases when nearby flux tubes are coupled by exchanging RF currents. Quantitative results strongly depend on the local density, both via the unperturbed input profiles and via subsequent RF-induced modifications by E × B 0 convection. Sources of uncertainty and aspects requiring further validation are identified. [Copyright &y& Elsevier]