Boundary conditions for plasma fluid models at the magnetic presheath entrance

For the first time, a rigorous definition of the magnetic presheath entrance (MPSE) is provided, as the location where the drift-reduced approximation breaks down. We consider a weakly collisional electrostatic plasma with cold ions in contact with an absorbing wall in the presence of ExB drifts. We provide expressions at the MPSE for the parallel ion and electron velocities, the gradients of plasma density and potential, and the vorticity. In particular, we show that the plasma potential with respect to the wall increases when the angle of incidence of the magnetic field is smaller. A fully kinetic PIC code simulating the plasma wall transition has been developed to validate these local relations, showing an excellent agreement with the theory. This work represents a first step towards a complete formulation of the boundary conditions for fluid codes used to simulate the edge of magnetic confinement devices

A comparison between a refined two-point model for the limited tokamak SOL and self-consistent plasma turbulence simulations

A refined two-point model is derived from the drift-reduced Braginskii equations for the limited tokamak scrape-off layer (SOL) by balancing the parallel and perpendicular transport of plasma and heat and taking into account the plasma–neutral interaction. The model estimates the electron temperature drop along a field line, from a region far from the limiter to the limiter plates. Self-consistent first-principles turbulence simulations of the SOL plasma including its interaction with neutral atoms are performed with the GBS code and compared to the refined two-point model. The refined two-point model is shown to be in very good agreement with the turbulence simulation results

Sheath boundary conditions for plasma fluid models

A new definition of the sheath edge is rigorously derived taking into account the kinetic properties of the plasma, and a consistent set of local sheath edge conditions is presented for the case of a magnetic field perpendicular to the wall. These local boundary conditions give explicit expressions for the ion velocity, the electron velocity, and the electron heat flux at the sheath edge, which can be easily implemented in a fluid code. It is shown that in the case of positive current to the wall, the commonly used Bohm's relations well aproximate the proposed boundary conditions, while large discrepancies are observed for negative currents. A fully kinetic PIC code simulating the plasma wall transition has been developed to validate these local relations, showing an excellent agreement with the theory. This work represents a first step towards a complete formulation of the sheath edge local boundary conditions for a general magnetic geometry

Intrinsic toroidal plasma rotation in the scrape-off-layer

The origin and nature of intrinsic toroidal plasma rotation in the scrape-off-layer are theoretically investigated. We discuss and analytically estimate three mechanisms that give rise to SOL toroidal rotation: turbulent momentum transport associated with electrostatic instabilities, pressure gradients along the poloidal direction, and deviation of the plasma velocity at the sheath entrance with respect to the Bohm's value. The results of three-dimensional global fluid simulations of tokamak scrape-off-layer in a limiter configuration are shown and compared

Ideal ballooning modes in the tokamak scrape-off layer

A drift-reduced Braginskii fluid model is used to carry out a linear and non-linear study of ideal ballooning modes in the tokamak scrape-off layer. First, it is shown that the scrape-off layer finite connection length and boundary conditions modify the ideal stability limit with respect to the closed flux-surface result. Then, in a two-fluid description, it is found that magnetic induction effects can destabilize long wavelength resistive ballooning modes below marginal ideal stability. Non-linear simulations confirm a gradual transition from small scale quasi-electrostatic interchange turbulence to longer wavelength modes as the plasma beta is increased. The transition to global ideal ballooning modes occurs, roughly, at the linearly obtained stability threshold. The transport levels and the pressure gradient as a function of plasma beta obtained in non-linear simulations can be predicted using the non-linear flattening of the pressure profile from the linear modes as a turbulent saturation mechanism

Global scrape-off layer electromagnetic fluid turbulence simulations

Electromagnetic effects play a key role in tokamak edge turbulence. It has been suggested that the density limit and the L to H mode transition may both be due to an interplay between electromagnetic effects, diamagnetic flows and collisionality. (See, e.g., Ref [1].) The present paper discusses the results of scrape-off layer (SOL) non-linear 3D fluid turbulence simulations including finite beta effects in the shear-less limit. These simulations were carried out using the GBS code [2], which evolves the drift-reduced Braginskii equations for a collisional plasma with cold ions in circular (s-α) geometry with a toroidal limiter in the high-field side midplane. The GBS code has been used to study turbulence in linear devices and in a simple magnetized torus configuration [2, 3]. We have recently adapted the code for tokamak edge geometry, and introduced s-α curvature operators as well as magnetic shear, finite aspect ratio, and finite beta effects. The objective of our work is to describe the phase-space relevant to the tokamak SOL turbulence. In this paper, in particular, the role played by finite beta effects upon the characteristic lengths of the profile gradients, turbulence saturation levels, and other basic turbulence properties, is assessed in the context of fully global non-linear turbulence simulations. The non-linear steady-state turbulent plasma profiles are obtained as the result of a balance between plasma density and heat sources, turbulent fluctuations, and parallel losses at the limiter plates. The turbulence drive is a priori unknown and there is no separation between fluctuations and background profiles. Linear analysis of the fluid equations has been carried out for SOL relevant parameters. In the presence of finite beta effects, we recover three instabilities: drift waves, resistive ballooning modes, and ideal ballooning modes. The onset of ideal ballooning modes is known to correspond to the instability threshold α_MHD = q^2 β R/Lp ~ 1. In the non-linear simulations, however, we observe the onset of catastrophic transport well below the ideal limit. The saturated states in this regime are characterized by large transport due to global ideal modes. These modes are linearly subdominant but non-linearly dominant due to the underlying turbulence saturation mechanism