Nonlinear saturation of resistive tearing modes in a cylindrical tokamak with and without solving the dynamics

We show that the saturation of resistive tearing modes in a cylindrical tokamak, as well as the corresponding island width, can be directly calculated with an MHD equilibrium code without solving the dynamics and without considering resistivity. The results are compared to initial value resistive MHD simulations and to an analytical nonlinear theory. For small enough islands, the agreement is remarkable. For sufficiently large islands, the equilibrium calculations, which assume a flat current profile inside the island, overestimate the saturation amplitude. On the other hand, excellent agreement between nonlinear resistive MHD simulations and nonlinear theory is observed for all the considered tearing unstable equilibria

Properties of a new quasi-axisymmetric configuration

A novel, compact, quasi-axisymmetric configuration is presented which exhibits low fast-particle losses and is stable to ideal MHD instabilities. The design has fast-particle loss rates below 8\% for flux surfaces within the half-radius, and is shown to have an MHD-stability limit of a normalised pressure of $\langle\beta\rangle=3\%$ where $\langle\beta\rangle$ is volume averaged. The flux surfaces at various plasma betas and currents as calculated using the SPEC equilibrium code are presented. Neoclassical transport coefficients are shown to be similar to an equivalent tokamak, with a distinct banana regime at half-radius. An initial coil design study is presented to assess the feasibility of this configuration as a fusion-relevant experiment

Potential of a plasma bound between two biased walls

An analytical study is presented for an one-dimensional, steady-state plasma bound between two perfectly absorbing walls that are biased with respect to each other. Starting from a description of the plasma sheaths formed at both walls, an expression relating the bulk plasma potential to the wall currents is derived, showing that the plasma potential undergoes an abrupt transition when currents cross a critical value. This result is confirmed by numerical simulations performed with a particle-in-cell code. [http://dx.doi.org/10.1063/1.4745863

Validation of GBS plasma turbulence simulation of the TJ-K stellarator

We present a validation of a three-dimensional, two-fluid simulation of plasma turbulence in the TJ-K stellarator, a low temperature plasma experiment ideally suited for turbulence measurements. The simulation is carried out by the GBS code, recently adapted to simulate 3D magnetic fields. The comparison shows that GBS retrieves the main turbulence properties observed in the device, namely the fact that transport is dominated by fluctuations with low poloidal mode number. The poloidal dependence of the radial $\text{E}\times\text{B}$ turbulent flux is compared on a poloidal plane with elliptical flux surfaces, where a very good agreement between experiment and simulation is observed, and on another with triangular flux surfaces, which shows a poorer comparison. The fluctuation levels in both cases are underestimated in the simulations. The equilibrium density profile is well retrieved by the simulation, while the electron temperature and the electrostatic potential profiles, which are very sensitive to the strength and localization of the sources, do not agree well with the experimental measurements

Magnetic islands and singular currents at rational surfaces in three-dimensional magnetohydrodynamic equilibria

Using the recently developed multiregion, relaxed MHD (MRxMHD) theory, which bridges the gap between Taylor's relaxation theory and ideal MHD, we provide a thorough analytical and numerical proof of the formation of singular currents at rational surfaces in non-axisymmetric ideal MHD equilibria. These include the force-free singular current density represented by a Dirac δ-function, which presumably prevents the formation of islands, and the Pfirsch-Schlüter 1/x singular current, which arises as a result of finite pressure gradient. An analytical model based on linearized MRxMHD is derived that can accurately (1) describe the formation of magnetic islands at resonant rational surfaces, (2) retrieve the ideal MHD limit where magnetic islands are shielded, and (3) compute the subsequent formation of singular currents. The analytical results are benchmarked against numerical simulations carried out with a fully nonlinear implementation of MRxMHD

Boundary conditions for plasma fluid models at the magnetic presheath entrance

The proper boundary conditions at the magnetic presheath entrance for plasma fluid turbulence models based on the drift approximation are derived, focusing on a weakly collisional plasma sheath with Ti≪Te and a magnetic field oblique to a totally absorbing wall. First, the location of the magnetic presheath entrance is rigorously derived. Then boundary conditions at the magnetic presheath entrance are analytically deduced for v||i, v||e, n, ϕ, Te, and for the vorticity ω = ∇⊥2ϕ. The effects of E × B and diamagnetic drifts on the boundary conditions are also investigated. Kinetic simulations are performed that confirm the analytical results. Finally, the new set of boundary conditions is implemented in a three-dimensional global fluid code for the simulation of plasma turbulence and, as an example, the results of a tokamak scrape-off layer simulation are discussed. The framework presented can be generalized to obtain boundary conditions at the magnetic presheath entrance in more complex scenarios