[en] This thesis deals with the development and verification of numerical methods for the kinetic stability analysis of compact toroidal plasmas. These methods are applicable to the low-frequency stability analysis of plasmas characterized by ion gyroradii that are comparable to the plasma scale length. Examples of such plasmas include spheromaks, field-reversed mirrors, and theta pinches, and ion rings and layers. Kinetic effects due to the finite ion Larmor radius may be crucial to the description of the stability of these plasmas. The quaSi-neutral hybrid model is used to describe the plasma dynamics. The ions are treated in a fully kinetic manner using particle in-cell techniques, while the electrons are described as a fluid. The displacement current is neglected in Maxwell's equations. The equations are linearized about an axisymmetrical equilibrium, enabling the analysis of the three-dimensional linear stability. The simulation model includes plasmas which are surrounded by a vacuum region. A computer code was developed to integrate the linearized equations in time to detect instabilities. This code was verified extensively against known analytic or independent numerical results

[en] In this paper, the authors present new theoretical results on stabilizing the internal tilting mode in a FRC which contains a minority energetic ion component. In contrast to previous results obtained in various asymptotic limits of geometry, mode structure, or beam parameters, the present results include all magnetoinductive effects self-consistently in a 3-D calculation representing a realistic FRC. The model developed here and implemented computationally is similar to previous models. Namely, the plasma is considered to consist of three components; thermal electrons, thermal ions, and energetic (beam) ions. The first two of these components are treated by fluid equations, while the energetic ions are treated as a collisionless Vlasov species. As far as the fluid equations are concerned, this model is a straightforward extension of earlier two-fluid calculations which include the Hall term in Ohm's law

[en] Many of the advances in our understanding of fusion plasmas over the past ten years has resulted from the application of techniques of large scale numerical simulation to three dimensional toroidal geometry. Since the dominant toroidal motions in a tokamak are generally long wavelength, finite Fourier series provides an efficient spatial representation for that coordinate. However, the next generation of numerical tokamak simulations will require that the poloidal cross section of actual experimental devices be more accurately represented. The authors address these difficulties by the application of an unstructured adaptive mesh to the representation of the poloidal plane, coupled with a finite Fourier representation of the toroidal coordinate. These meshes are not tied to a particular coordinate system, so that mesh points can be arbitrarily distributed to simulate the details of experimental apparatus. Since mesh points do not have a sequential orientation with their spatial neighbors, they can be easily added and deleted based on physical criteria. Evolving fine scale spatial structures are thus efficiently and accurately represented. The authors have derived an algorithm for the solution of the resistive MHD equations on these meshes. This algorithm is based on the triangulation of arbitrarily distributed points in the plane; hence the term triangular MHD. The algorithm preserves the solenoidal properties of B and J identically, and is a generalization of staggered mesh techniques used in structured, rectangular grids. A new 3-D MHD code, TRIM, based on this algorithm has been developed. Preliminary results from TRIM are presented

[en] The hot α-particles that are produced in a burning tokamak fusion plasma can significantly affect the stability of the background MHD activity. In particular, the toroidicity induced shear Alfven eigenmode, or TAE, has been shown to be linearly destabilized by an energetic particle distribution such as might arise from α-particles in a burning plasma, or an injected beam. This mode has been called the gap mode, since its real frequency lies in a toroidicity induced gap in the usual Alfven continuum. The nonlinear evolution of this mode is unknown at this time. In order to determine the hot α-particle influence on overall tokamak plasma confinement, it is important to assess the nonlinear consequences of the TAE in conjunction with the background MHD plasma. The authors have recently identified the stable TAE in nonlinear, three-dimensional, toroidal MHD codes. These codes have been modified to include the effect of an energetic species on the usual MHD evolution. Several models for the description of the beam dynamics have been considered, including fluid moment equations, a linearized gyrokinetic model, and full particle dynamics. In this paper they describe the coupling of the particle dynamics with the nonlinear MHD model. These methods have been previously successfully applied to FRC and RFP plasmas. Full details of numerical algorithms, and initial results pertaining to the TAE mode, are presented

[en] The ideal and resistive magnetohydrodynamic (MHD) model is used to examine the dynamics and structure of the solar corona. When the coronal magnetic field is deformed by photospheric flow it can evolve to states that become unstable to ideal MHD modes. The nonlinear evolution of these instabilities can lead to the generation of current sheets, field line reconnection, and energy release. The disruption of an arcade field and the kinking of coronal loops is described. The braiding of the large-scale coronal field by convective photospheric motions develops fine-scale structure in the magnetic field and leads to the development of intense current filaments. The resistive dissipation of these currents can provide an efficient coronal heating mechanism

[en] The numerical stability analysis of compact toroidal plasmas using implicit time differencing requires the solution of a set of coupled, 2-dimensional, elliptic partial differential equations for the field quantities at every timestep. When the equations are spatially finite-differenced and written in matrix form, the resulting matrix is large, sparse, complex, non-Hermitian, and indefinite. The use of the preconditioned bi-conjugate gradient method for solving these equations is discussed. The effect of block-diagonal preconditioning and incomplete block-LU preconditionig on the convergence of the method is investigated. For typical matrices arising in our studies, the eigenvalue spectra of the original and preconditioned matrices are calculated as an illustration of the effectiveness of the preconditioning. We show that the preconditioned bi-conjugate gradient method coverages more rapidly than the conjugate gradient method applied to the normal equations, and that it is an effective iterative method for the class of non-Hermitian, indefinite problems of interest

[en] A technique is presented for the linear three-dimensional stability analysis of plasmas in which ion kinetic effects are important. This technique is appropriate for the analysis of compact toroidal plasmas such as spheromaks, field-reversed mirrors and theta pinches, field-reversed configurations, and ion rings and layers. The plasma is modeled by the hybrid quasineutral model, in which the ions are represented by particles. An initial value approach is used to find the most rapid instabilities, in conjuction with the numerical integration of the equations. The model is verified against known analytic and numerical results for the linear stability of ion layers and theta pinches. The tilt instability in the spheromak is investigated, and comparison is made to magnetohydrodynamic (MHD) stability results for an equilibrium with a low ion beta

[en] Calculations of the long-term dynamical evolution of a solar coronal magnetic field arcade which is subjected to shearing photospheric flows are presented. The evolution is obtained by numerical solution of a subset of the resistive magnetohydrodynamic equations. For a simplified model of the bipolar magnetic field observed in the solar corona, it is found that photospheric flow produces a slow evolution of the magnetic field, with a buildup of magnetic energy. For certain photospheric shear profiles, the field configuration produced is linearly unstable to an ideal magnetohydrodynamic mode when the shear exceeds a critical value. The nonlinear evolution of this instability shows the spontaneous formation of current sheets. Reconnection of the magnetic field produces a rapid release of magnetic energy. The major fraction of the energy is dissipated resistively, while a small fraction is converted into kinetic energy of an ejected plasmoid. The relevance of these results to two-ribbon flares is discussed. 29 references

[en] Complete text of publication follows. We describe the latest applications of our global three-dimensional magnetohydrodynamic (MHD) model of the solar corona and the solar wind. The model uses boundary conditions based on observed photospheric magnetic fields. It has been used in the simplified, 'polytropic' approximation of the energy equation to study the geometrical and topological properties of the magnetic field (e.g., the location and evolution of corona holes, the reproduction of streamer structure, the location of the heliospheric current sheet, etc.). However, this approximation does not reproduce the density and temperature contrasts between open and closed field regions and does not address data from EUV and X-ray emission. Our improved MHD model that includes energy transport (radiative losses, anisotropic thermal conduction, and coronal heating) in the transition region and solar corona is capable of reproducing many emission properties as observed by SOHO and Hinode.

[en] The nonlinear evolution of a force-free magnetic field driven by slow shear flow on a boundary is investigated analytically and numerically. The Woltjer-Taylor theory is generalized to obtain the time-dependent magnetohydrodynamic (MHD) solution for the nonlinear force-free fields driven by shear flow. This solution agrees well with our resistive MHD simulations, which show that the force-free arcade field in a solar coronal plasma evolves quasi-statically through a series of force-free states before reconnection occurs. 14 refs., 2 figs