Plasma In Toroidal Geometry Research Articles

The relationship between flux coordinates and equilibrium-based frames of reference in fusion theory

The properties of two local reference frames based on the magnetic field and the current density are investigated for magnetized plasmas in toroidal geometry with a symmetric angle. The magnetic field-based local frame of reference has been well-studied, for example, by Dewar and colleagues [Phys. Fluids 27, 1723 (1984)]. An analogous frame based on the current density vector is possible because it is also divergence free and perpendicular to the gradient of the poloidal flux. The concept of straightness of a vector is introduced and used to elucidate the Boozer and Hamada coordinate systems. The relationship of these local frames to the more well-known Frenet frame of reference, which specifies a curve in terms of curvature and torsion, is given. As an example of the usefulness of this formal relationship, we briefly review the ideal MHD theory and its use. We also present a new annihilation operator, useful for eliminating shorter time scales than the time scale of interest, for deriving the inner layer equations of Glasser et al. [Phys. Fluids 18, 875 (1975)]. Compared to the original derivation that is based on the local frame of reference in terms of the magnetic field, the new annihilation operator that is based on the local frame of reference in terms of the current density simplifies the derivation.

Proper orthogonal decomposition methods for noise reduction in particle-based transport calculations

Proper orthogonal decomposition techniques to reduce noise in the reconstruction of the distribution function in particle-based transport calculations are explored. For two-dimensional steady-state problems, the method is based on low rank truncations of the singular value decomposition of a coarse-grained representation of the particle distribution function. For time-dependent two-dimensional problems or three-dimensional time-independent problems, the use of a generalized low-rank approximation of matrices technique is proposed. The methods are illustrated and tested with Monte Carlo particle simulation data of plasma collisional relaxation and guiding-center transport with collisions in a magnetically confined plasma in toroidal geometry. It is observed that the proposed noise reduction methods achieve high levels of smoothness in the particle distribution function by using significantly fewer particles in the computations.

Non-neutral Plasma Confinement in Toroidal Geometry

Studying non-neutral plasma is a long and established field however the majority of these studies utilized cylindrical traps. The newly constructed Lawrence Non-Neutral Torus (LNT) II apparatus will study non-neutral plasmas in toroidal geometry. The LNT II features an improved toroidal magnetic field magnitude (∼1 kG) and base vacuum pressure (<10−9Torr) from the previous apparatus. A segmented Au-plated Al electrode shell contributes to the reduction in field asymmetries and enables enhanced diagnostics. Additionally, the electron source is located on a retractable bellows for study of confinement dynamics in a complete torus. Confinement times on the order of 1 second would represent more than an order of magnitude improvement over measurements made with the previous apparatus.

Poloidal momentum transport due to drift-waves in toroidal geometry

The aim of this paper is to provide the theoretical framework for a quasi-linear drift-wave model of poloidal and toroidal momentum transport in magnetically confined plasmas in toroidal geometry. Axisymmetry is not required. The new feature is the inclusion of poloidal flow in the coupled equations for linear drift-wave stability and quasilinear mean field transport. It is shown how both toroidal and poloidal rotations can be included in a distribution function which is an equilibrium of the Vlasov equation in a rotating reference frame. The equations for the fluctuation driven toroidal and poloidal viscous stresses are determined and the toroidal form of the E×B and parallel velocity shear terms are found. In order to be able to follow the electric field evolution during a transport bifurcation, the neoclassical constraint on the poloidal rotation is not imposed. Instead, the common poloidal flow is evolved as part of the system of transport equations.

A nonlinear two-fluid model for toroidal plasmas

A nonlinear numerical model for the two-fluid (electron and ion fluid) description of the evolution of a plasma in toroidal geometry, MH3D-T, is described. The model extends the “drift” ordering for small perturbations to arbitrary perturbation size. It is similar, but not identical, to the collisional Braginskii equations. The ion gyroviscous stress tensor, Hall terms, temperature diamagnetic drifts, and a separate electron pressure evolution are included. The model stresses the (fluid) parallel dynamics by solving the density evolution together with the temperature equations, including the thermal equilibration along the magnetic field. It includes the neoclassical, collisional parallel viscous forces for electrons and ions. The model has been benchmarked against the stabilizing effects of the ion diamagnetic drift ω*i on the m=1, n=1 reconnecting mode in a cylinder. The stabilization mechanism is shown to be poloidal rotation of the global kink flow of the plasma mass vi within q&amp;lt;1, relative to the location of the magnetic field X-point within the reconnection layer. The ion ω*i-drift is also shown to cause frequency-splitting for the toroidal Alfvén eigenmode (TAE). Basic diamagnetic and neoclassical magnetohydrodynamic (MHD) effects on magnetic island evolution and rotation are discussed. The dynamics of the plasma along the magnetic field, when compressibility, parallel thermal conductivity, plasma density evolution, and full toroidal geometry are kept, are found to have strong effects on both linear growth rates and nonlinear evolution. The nonlinear coupling of magnetic islands, driven by perturbations of different toroidal mode number, is enhanced by the density evolution in both MHD and two-fluids.

Spectral Analysis of Resistive MHD in Toroidal Geometry

A code, SPECTOR, has been developed to determine the complete spectrum (both stable and unstable modes) for a resistive plasma in toroidal geometry described by the linearized, compressible, magnetohydrodynamic, single fluid equations. The structure of the code is explained and comparisons with other codes are presented which test its validity. Some applications to both cylindrical and tokamak-like plasmas are presented to illustrate the scope of the code particularly for the stable part of the spectrum. A study is made of the effect of resistivity on a typical toroidal Alfvén eigenmode.

Modelling heating and current drive in the ion cyclotron frequency range

Numerical simulation of heating and current drive in the ion cyclotron frequency range has progressed to the point that both the propagation and absorption of IC waves on the one hand, and the evolution of ion and electron distribution functions due to interaction with the HF fields on the other hand, can be described in realistic geometry and to some extent consistently with each other. The author reviews work in this field, with particular emphasis on the derivation and numerical solution of adequate equations to describe wave propagation in hot plasmas in toroidal geometry. Codes solving the quasilinear kinetic equations and their interface to wave propagation codes are also briefly mentioned. The complete problem is so complex, however, that in most cases simplified models must be used for extensive numerical studies of IC heating and current drive scenarios. Plane stratified models are appropriate to investigate antenna loading and global power balance; ray tracing gives excellent results in large hot plasmas and are easily interfaced to quasilinear kinetic codes. Full-wave codes in toroidal geometry are often simplified by neglecting either finite Larmor radius effects or the poloidal component of the static magnetic field, or both.

Equilibrium of non-neutral plasma in toroidal geometry with applied electric field

The equilibrium and stability of non-neutral plasma in toroidal geometry with applied electric field is studied. The calculations are done in a large aspect ratio, thin ring approximation, using a circuit model. Toroidal corrections to the l=1 (l is the poloidal mode number) mode are obtained. These corrections reduce the l=1 cylindrical diocotron frequency. It is shown that under certain conditions, the external electric field can stabilize dissipative l=1 diocotron oscillations.

Numerical analysis of equilibria with islands in magnetohydrodynamics

In this paper we shall describe extensions and refinements of a numerical method we have developed to calculate the equilibrium of a plasma in toroidal geometry without axial symmetry. The method is based on a classical variational principle of ideal magnetohydrodynamics which characterizes equilibria as stationary points of the potential energy.

High β and toroidal effects in three dimensions

The resistive MHD equations for toroidal plasma configurations are reduced by expanding to second order in ϵ, the inverse aspect ratio, allowing for high β = μ 0 p/ B 2 of order ϵ. The result is a closed system of nonlinear, three-dimensional equations where the fast magnetohydrodynamic time scale is eliminated. In particular, the equation for the toroidal velocity remains decoupled. These equations generalize reduced equations derived earlier. They are now solved numerically. As a first step, various types of axisymmetric equilibria are found by relaxing a given initial configuration. Then, three-dimensional perturbations are introduced and followed in time to investigate the linear and nonlinear properties of tearing modes, etc., for high-β plasmas in toroidal geometry.

A nonconforming finite element method to compute the spectrum of an operator relative to the stability of a plasma in toroidal geometry

In this paper we describe a nonconforming finite element method to compute the MHD spectrum of a plasma in a toroidal configuration. We show that this method leads to a good approximation of the spectrum.

Numerical studies of new stellarator concepts

A three-dimensional computer code has been developed to study the magnetohydrodynamic equilibrium and stability of a diffuse or sharp boundary plasma in toroidal geometry. It is shown how equilibria with net toroidal current identically zero can be determined and how growth rates of instabilities can be calculated. Applications are made to an l = 2, 3 stellarator configuration that offers the possibility of achieving a critical value as high as 10% for the plasma parameter β.

Stationary Equilibrium of a Toroidal Plasma

Studies are made of the effects of resistivity, inertial forces, viscosity, pressure anisotropy, and especially gyroviscosity on the stationary equilibrium of a low-density plasma in toroidal geometry. The conditions imposed by viscosity on the two arbitrary functions occurring in the expression for the zero-order velocity vector have been derived. It is shown that gyroviscosity does not impose conditions on these two arbitrary functions. It is suggested that among the perturbing forces considered, dissipative forces such as the collision-dominated viscosity and resistivity will give rise to conditions on the two arbitrary functions at the higher approximations.

Equilibrium of a Toroidal Plasma with Finite Resistivity and Inertia

A theoretical study of the equilibrium of a dilute plasma in toroidal geometry with rotational transform has been carried out, taking into account finite resistivity and finite inertia. If an additional nonvanishing density gradient drift of the plasma perpendicular to the magnetic field is assumed, the plasma drifts out of the toroid. The characteristic time of this process is found to be a factor of 2 r/R (where R and r are the major and minor radii of the toroid, respectively) smaller than the time which is associated with the mere diffusion from a toroid.