Magnetized Plasma-wall Transition Research Articles

Effect of a non-uniform magnetic field on two ion species plasma-wall transition

Fluid theory has been employed to investigate the magnetized plasma-wall transition properties for two ion species plasmas with a uniform background of neutral gas density in the presence of an external magnetic field. The external applied magnetic field is parallel to the surface and its magnitude varies in the direction perpendicular to the surface. The governing equations of ion and electron fluids include ionization and collision with neutral atoms. A comparative study of transition parameters for non-uniform and uniform magnetic fields is performed at equal values of the magnetic flux density at x = 0. This study shows that the sheath region shrinks for the non-uniform magnetic field case, essentially in reason of the lower value of the average magnetic field intensity in the plasma-wall transition region. We introduce a figure of merit to quantify the nonuniformity of the magnetic field , and show that for its value 0.21 it is possible to model the plasma-wall transition region considering the magnetic field as uniform and equal to its average value. Furthermore, we find that the density distribution of electrons close to the surface deviates from the Boltzmann distribution due to the influence of a strong magnetic field.

Presheath-sheath coupling for kinetic trajectory simulation of a magnetized plasma sheath

The coupling of presheath-sheath parameters is extended for the study of magnetized plasma sheath using the kinetic trajectory simulation (KTS) method, in which the final self-consistent states are obtained iteratively by solving the kinetic equations. In our case, it is assumed that the ion and electron velocity distribution functions are cut-off Maxwellians at the sheath entrance. The results show that the cut-off and Maxwellian maximum velocities have equal magnitudes at the sheath entrance and at wall. The presheath electron temperature has a considerable effect on the self-consistent potential profile which affects the Child sheath thickness. The latter increases from 3.8320 μm to 5.4190 μm when the presheath electron temperature increases from 10 eV to 20 eV. It is found that the number of ions reaching wall is higher than that of the electrons and hence the space charge density has its maximum value there. Furthermore, the temperature of ions in the sheath region increases with the increase in presheath ion temperature. Moreover, the cut-off distribution causes our simulation result to deviate from the theoretical result found for the Boltzmann distribution by about 3%. The coupling scheme presented here provides a basis for smooth transition of plasma parameters at the presheath-sheath interface. The proper understanding of the magnetized plasma-wall transition plays a vital role for further exploring the plasma sheath characteristics which has useful applications in fusion and industrial plasma devices.

Self-consistent one dimension in space and three dimension in velocity kinetic trajectory simulation model of magnetized plasma-wall transition

We have developed a self-consistent 1d3v (one dimension in space and three dimension in velocity) Kinetic Trajectory Simulation (KTS) model, which can be used for modeling various situations of interest and yields results of high accuracy. Exact ion trajectories are followed, to calculate along them the ion distribution function, assuming an arbitrary injection ion distribution. The electrons, on the other hand, are assumed to have a cut-off Maxwellian velocity distribution at injection and their density distribution is obtained analytically. Starting from an initial guess, the potential profile is iterated towards the final time-independent self-consistent state. We have used it to study plasma sheath region formed in presence of an oblique magnetic field. Our results agree well with previous works from other models, and hence, we expect our 1d3v KTS model to provide a basis for the studying of all types of magnetized plasmas, yielding more accurate results.

A self-consistent two-fluid model of a magnetized plasma-wall transition

A self-consistent one-dimensional two-fluid model of the magnetized plasma-wall transition is presented. The model includes magnetic field, elastic collisions between ions and electrons, and creation/annihilation of charged particles. Two systems of differential equations are derived. The first system describes the whole magnetized plasma-wall transition region, which consists of the pre-sheath, the magnetized pre-sheath (Chodura layer), and the sheath, which is not neutral, but contains a positive space charge. The second system of equations describes only the neutral part of the plasma-wall transition region—this means only the pre-sheath and the Chodura layer, but not also the sheath. Both systems are solved numerically. The first system of equations has two singularities. The first occurs when ion velocity in the direction perpendicularly to the wall drops below the ion thermal velocity. The second occurs when the electron velocity in the direction perpendicularly to the wall exceeds the electron thermal velocity. The second system of differential equations only has one singularity, which has also been derived analytically. For finite electron to ion mass ratio, the integration of the second system always breaks down before the Bohm criterion is fulfilled. Some properties of the first system of equations are examined. It is shown that the increased collision frequency demagnetizes the plasma. On the other hand, if the magnetic field is so strong that the ion Larmor radius and the Debye length are comparable, the electron velocity in the direction perpendicularly to the wall reaches the electron thermal velocity before the ion velocity in the direction perpendicularly to the wall reaches the ion sound velocity. In this case, the integration of the model equations breaks down before the Bohm criterion is fulfilled and the sheath is formed.

Stability of the magnetized plasma-wall transition layer

Under the condition λD≪ρi≪ℓ (where λD is the Debye length, ρi is the ion gyro-radius, and ℓ is the smallest relevant collision length) and for the case of the obliquity of the magnetic field to the wall, the magnetized plasma-wall transition layer can be split into the following sub-layers: the Debye sheath (DS), the magnetic pre-sheath (MPS), and the collisional pre-sheath (CPS). Thanks to the above-mentioned condition, it is possible to investigate these sublayers independently of each other. In this paper, the kinetic theory of the stability of the MPS and the CPS is presented (for the DS, a small parameter, relevant for the development of the linear theory, is not found). The ion gas was assumed to move with a constant velocity, and the presence of such an ion beam made it necessary to modify the form of the Bohm–Chodura criterion and the behavior of the electric potential in the CPS. The instability rate was found to be proportional to the square root of the time.

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 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.

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

The magnetized plasma-wall transition (MPWT) layer at the presence of the obliquity of the magnetic field to the wall consists of three sub-layers: the Debye sheath (DS), the magnetic pre-sheath (MPS), and the collisional pre-sheath (CPS) with characteristic lengths λD (electron Debye length), ρi (ion gyro-radius), and ℓ (the smallest relevant collision length), respectively. Tokamak plasmas are usually assumed to have the ordering λD≪ρi≪ℓ, when the above-mentioned sub-layers can be distinctly distinguished. In the limits of εDm(λD/ρi)→0 and εmc(ρi/ℓ)→0 (“asymptotic three-scale (A3S) limits”), these sub-layers are precisely defined. Using the smallness of the tilting angle of the magnetic field to the wall, the ion distribution functions are found for three sub-regions in the analytic form. The equations and characteristic length-scales governing the transition (intermediate) regions between the neighboring sub-layers (CPS – MPS and MPS – DS) are derived, allowing to avoid the singularities arising from the εDm→0 and εmc→0 approximations. The MPS entrance and the related kinetic form of the Bohm–Chodura condition are successfully defined for the first time. At the DS entrance, the Bohm condition maintains its usual form. The results encourage further study and understanding of physics of the MPWT layers in the modern plasma facilities.

Magnetized plasma-wall transition layer with cold ions

AbstractThe magnetized plasma-wall transition (MPWT) layer occurring, for example near a tokamak diverter, typically consists of three distinct sublayers: the Debye sheath (DS), the magnetic presheath (MPS) and the collisional presheath (CPS), with characteristic lengths λD (electron Debye length), ρi (ion gyroradius) and λ (smallest relevant ion collision length), respectively. For analytical simplicity one usually assumes the ordering λD ≪ ρi ≪ λ, or, equivalently, $\varepsilon _{Dm} \equiv \frac{{\lambda _D }}{{\rho _i }} \to 0$ and $\varepsilon _{mc} \equiv \frac{{\rho _i }}{\lambda } \to 0$ (‘asymptotic three-scale (A3S) limit’), in which the three sublayers are precisely defined. In the present work the equations and length scales governing the transition, or the ‘intermediate’ regions between neighboring sublayers (DS–MPS, MPS–CPS), in the A3S limit are derived, allowing one to avoid the singularities arising from the ϵDm → 0 and ϵmc → 0 approximations. The MPS entrance and the related Bohm–Chodura condition is defined in a natural way. It is found that in the hydrodynamic Ti = 0 approximation the intermediate scales and equations have a universal form and a similar structure not only for the MPS–DS and CPS–MPS transitions but also for the DS–CPS transition in the non-magnetized case.

The magnetized plasma–wall transition (PWT) and its relation to fluid boundary conditions

The magnetized plasma–wall transition (PWT) region typically exhibits three characteristic subregions: the “Debye sheath”, the “magnetic presheath”, and the “collisional presheath”. The fluid boundary conditions for transport codes (simulating, e.g., the scrape-off layer (SOL) of a tokamak) are usually applied at the “magnetic presheath entrance”, where in the simplest model the ion velocity parallel to the magnetic field equals the local sound velocity. After reviewing the basic time-independent and collisionless models of the magnetized PWT, various extensions will be discussed which are due to E × B , ∇ B and diamagnetic drifts, nonuniformity of the electric field parallel to the wall, and turbulence effects. In practically all cases considered, quantitative results can be obtained only by massive application of numerical methods of solution.

Boundary conditions for the multi-ion magnetized plasma-wall transition

Properties of the multi-ion magnetized plasma-wall transition (PWT) are investigated. The corresponding boundary conditions are derived for the case when different ions species have similar gyro-radii.