Comprehensive kinetic analysis of the plasma-wall transition layer in a strongly tilted magnetic field

Tskhakaya, D.; Kos, L.

doi:10.1063/1.4900765

Cited by 22 publications

(10 citation statements)

References 18 publications

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“…9 Recently, a rather comprehensive kinetic analysis, where the boundaries of the Chodura layer have been precisely defined, has been published. 10 In the last years, the use of the Boltzmann relation for the electrons when there is a magnetic field present has been reexamined by several authors. [11][12][13] Also, in recent years, many other specific aspects of the sheath in an oblique magnetic field have been analyzed.…”

Section: Introductionmentioning

confidence: 99%

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

Gyergyek

Kovačič

2015

Physics of Plasmas

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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 twofluid 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 different ion source terms are considered in total: the zero source term and three different non-zero ion source terms. When the zero source term is used, the model becomes very sensitive to the boundary conditions, and in some cases, the solutions exhibit large amplitude oscillations. If any of the three non-zero ion source terms is used, those problems are eliminated, but also the consistency of the model is broken. The model equations are solved numerically in the entire magnetized plasma-wall transition region. For zero ion temperature, the model can be solved even if a very small ion velocity is selected as a boundary condition. For finite ion temperature, the system of equations becomes stiff, unless the ion velocity at the boundary is increased slightly above the ion thermal velocity. A simple method how to find a solution with a very small ion velocity at the boundary also for finite ion temperature in the entire magnetized plasma-wall transition region is proposed. V C 2015 AIP Publishing LLC.

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Section: Introductionmentioning

confidence: 99%

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

Gyergyek

Kovačič

2015

Physics of Plasmas

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“…The resulting ion distribution functions exhibit an interesting and involved structure with singularities, which are expected to be smeared out by unstable ion cyclotron modes (Daube, Riemann & Schmitz 1998) and finite neutral temperature. Tskhakaya Sr & Kos (2014) analysed the plasma-wall boundary layers using an asymptotic scale separation and an asymptotic expansion in α 1. They considered the ion gyro-orbits to have zero spatial extent, but retained all other kinetic effects.…”

Section: Introductionmentioning

confidence: 99%

Large gyro-orbit model of ion velocity distribution in plasma near a wall in a grazing-angle magnetic field

Geraldini

2021

J. Plasma Phys.

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A model is presented for the ion distribution function in a plasma at a solid target with a magnetic field $\boldsymbol {B}$ inclined at a small angle, $\alpha \ll 1$ (in radians), to the target. Adiabatic electrons are assumed, requiring $\alpha \gg \sqrt {Zm_{e}/m_{i}}$ , where $m_{e}$ and $m_{i}$ are the electron and ion mass, respectively, and $Z$ is the charge state of the ion. An electric field $\boldsymbol {E}$ is present to repel electrons, and so the characteristic size of the electrostatic potential $\phi$ is set by the electron temperature $T_{e}$ , $e\phi \sim T_{e}$ , where $e$ is the proton charge. An asymptotic scale separation between the Debye length $\lambda _{D} = \sqrt {\epsilon _0 T_{{e}} / e^{2} n_{{e}} }$ , the ion sound gyro-radius $\rho _{s} = \sqrt { m_{i} ( ZT_{e} + T_{i} ) } / (ZeB)$ and the size of the collisional region $d_{c} = \alpha \lambda _{\textrm {mfp}}$ is assumed, $\lambda _{D} \ll \rho _{s} \ll d_{c}$ . Here $\epsilon _0$ is the permittivity of free space, $n_{e}$ is the electron density, $T_{i}$ is the ion temperature, $B= |\boldsymbol {B}|$ and $\lambda _{\textrm {mfp}}$ is the collisional mean free path of an ion. The form of the ion distribution function is assumed at distances $x$ from the wall such that $\rho _{s} \ll x \ll d_{c}$ , that is, collisions are not treated. A self-consistent solution of the electrostatic potential for $x \sim \rho _{s}$ is required to solve for the quasi-periodic ion trajectories and for the ion distribution function at the target. The large gyro-orbit model presented here allows to bypass the numerical solution of $\phi (x)$ and results in an analytical expression for the ion distribution function at the target. It assumes that $\tau =T_{i}/(ZT_{e})\gg 1$ , and ignores the electric force on the quasi-periodic ion trajectory until close to the target. For $\tau \gtrsim 1$ , the model provides an extremely fast approximation to energy–angle distributions of ions at the target. These can be used to make sputtering predictions.

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“…Other studies emphasized the role of the magnetic field angle and strength on the different regions since the original work of Chodura 12,13 .…”

Section: Introductionmentioning

confidence: 99%

The plasma-wall transition with collisions and an oblique magnetic field: Reversal of potential drops at grazing incidences

et al. 2019

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The plasma-wall transition is studied by using 1d3V particle-in-cell (PIC) simulations in the case of a one dimensional plasma bounded by two absorbing walls separated by 200 Debye lengths (λ d). A constant and oblique magnetic field is applied to the system, with an amplitude such that r < λ d < R, where r and R are the electron and ion Larmor radius respectively. Collisions with neutrals are taken into account and modelled by an energy conservative operator, which randomly reorients ion and electron velocities. The plasma-wall transition (PWT) is shown to depend on both the angle of incidence of the magnetic field with respect to the wall θ, and on the ion mean-free-path to Larmor radius ratio, λ ci /R. In the very low collisionality regime (λ ci R) and for a large angle of incidence, the PWT consists in the classical trilayer structure (Debye sheath / Chodura sheath / Pre-sheath) from the wall towards the center of the plasma. The drops of potential within the different regions are well consistent with already published models. However, when sin θ ≤ R/λ ci or with the ordering λ ci < R , collisions can not be neglected, leading to the disappearance of the Chodura sheath. In these case, a collisional model yields analytic expressions for the potential drop in the quasi-neutral region, and explains, in qualitative and quantitative agreement with the simulation results, its reversal below a critical angle derived in the paper, a regime possibly met in the SOL of tokamaks. It is further shown that the potential drop in the Debye sheath slightly varies with the collisionality for λ ci R. However, it tends to decrease with λ ci in the high collisionality regime, until the Debye sheath finally vanishes.

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Comprehensive kinetic analysis of the plasma-wall transition layer in a strongly tilted magnetic field

Cited by 22 publications

References 18 publications

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

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

Large gyro-orbit model of ion velocity distribution in plasma near a wall in a grazing-angle magnetic field

The plasma-wall transition with collisions and an oblique magnetic field: Reversal of potential drops at grazing incidences

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