A Hamiltonian guiding center drift orbit formalism is developed which permits the efficient calculation of particle trajectories in magnetic field configurations of arbitrary cross section with arbitrary plasma β. The magnetic field is assumed to be a small perturbation from a zero-order ‘‘equilibrium’’ field possessing magnetic surfaces. The equilibrium field, possessing helical or toroidal symmetry, can be modeled analytically or obtained numerically from equilibrium codes. The formalism is used to study trapped particle precession. Finite banana width corrections to the toroidal precession rate are derived, and the bounce averaged trapped particle motion is expressed in Hamiltonian form. Particle drift-pumping associated with the ‘‘fishbone’’ oscillation is investigated. A numerical code based on the formalism is used to study particle orbits in circular and bean-shaped tokamak configurations.

In toroidal plasmas, the toroidal magnetic field is nonuniform over a magnetic surface and causes coupling of different poloidal harmonics. It is shown bath analytically and numerically that the toraidicity not only breaks up the shear AlfvSn continuous spectrum, but also creates new, discrete, toroidicity-induced shear Alfven eigenmodes with frequencies inside the contincim gaps. Potential applications of the low-n toroidicity-induced shear Alfven eigenmodes on plasma heating and instabilities are addressed.

Ideal and resistive HHD equations for the shear Alfven waves are studied in a low-fj toroidal model by employing the high-n ballooning formalism. The ion sound effects are neglected. For an infinite shear slab, the ideal HHD model gives rise to a continuous spectrum of real frequencies and discrete eigenmodes (Alfven-Landau modes) with complex frequencies. With toroidal coupling effects due to nonuniform toroidal magnetic field, the continuum is broken up into small continuum bands and new discrete toroidal eigenmodes can exist inside the continuum gaps. Unstable ballooning eigenmodes are also introduced by the bad curvature when $ > 0 C. The* resistivity (r\) can be considered perturbatively for the ideal modes. In addition, four branches of resistive modes are induced by the resistivity: (1) Resistive entropy modes which are stable with frequencies going to zero with resistivity as n 1^3 , (2) Tearing modes which are stable (A' < 0) with frequencies approaching zero as H ' , (3) Resistive periodic shear Alfven waves which approach the finite frequency end points of the continuum bands as ti » an<^ (*) Resistive ballooning modes which are purely growing with growth rate proportional to ^1/3^2/3 a3 n + o and 8+0. DISTRIBUTION OF THIS DOCUMENT IS UMTEO * = i(i(+,e,6) exp[i x

The toroidicity-induced gaps of the shear Alfvén wave spectrum in tokamaks are shown to satisfy an envelope equation. The structure of these gaps, and the location of the high-n gap modes, which are localized modes with frequency in the gap, are studied for general numerically generated equilibria. The dependence of the frequencies of the gaps and the gap modes on the equilibrium properties, such as elongation, triangularity, and β of the plasma are explored.

A new type of axisymmetric magnetohydrodynamic equilibrium is presented. It is characterized by a region of pressure and safety factor variation with a short scale length imposed as a perturbation. The equilibrium consistent with these profile variations can be calculated by means of an asymptotic expansion. The flexibility obtained by generating such equilibria allows for a close examination of the mechanisms that are relevant to ballooning instabilities – ideal-MHD modes with large toroidal mode number. The so-called first and second regions of stability against these modes are seen well within the limits of validity of the asymptotic expansion. It appears that the modes must be localized in regions with small values of the local shear of the magnetic field. The second region of stability occurs where the local shear is large throughout the range where the magnetic-field-line curvature is destabilizing.

A three-dimensional (3-D) hybrid gyrokinetic-MHD (magnetohydrodynamic) simulation scheme is presented. To the 3-D toroidal MHD code, MH3D-K the energetic particle component is added as gyrokinetic particles. The resulting code, mh3d-k, is used to study the nonlinear behavior of energetic particle effects in tokamaks, such as the energetic particle stabilization of sawteeth, fishbone oscillations, and alpha-particle-driven toroidal Alfvén eigenmode (TAE) modes.

This is a preprint of a paper intended for publication in a journal or proceedings. Since changes may be made before publication, this preprint is made available with the understanding that it will not be cited or reproduced without the permission of the author.

Abstract. Recent DIII-D experiments show that ideal kink modes can be stabilized at high beta by a resistive wall, with sufficient plasma rotation. However, the resonant response by a marginally stable resistive wall mode to static magnetic field asymmetries can lead to strong damping of the rotation. Careful reduction of such asymmetries has allowed plasmas with beta well above the ideal MHD nowall limit, and approaching the ideal-wall limit, to be sustained for durations exceeding one second. Feedback control can improve plasma stability by direct stabilization of the resistive wall mode or by reducing magnetic field asymmetry. Assisted by plasma rotation, direct feedback control of resistive wall modes with growth rates more than 5 times faster than the characteristic wall time has been observed. These results open a new regime of tokamak operation above the free-boundary stability limit, accessible by a combination of plasma rotation and feedback control.