J. D. Callen

Neoclassical flows and transport in nonaxisymmetric toroidal plasmas

The moment equation approach to neoclassical transport theory has been generalized to nonaxisymmetric toroidal systems under the assumption of the existence of magnetic surfaces. In particular, the parallel plasma flows and bootstrap current are calculated in both the Pfirsch–Schluter and banana regimes. It is found that both parallel plasma flows and the bootstrap current can be reduced as the toroidal bumpiness increases in an otherwise axisymmetric system.

A pressure‐gradient‐driven tokamak ‘‘resistive magnetohydrodynamic’’ instability in the banana‐plateau collisionality regime

The moment equation approach to neoclassical processes is used to derive the linearized electrostatic perturbed flows, currents, and resistive MHD‐like equations for a tokamak plasma. The new features of the resultant ‘‘neoclassical magnetohydrodynamics,’’ which requires a multiple length scale analysis for the parallel eigenfunction, but is valid in the experimentally relevant banana‐plateau regime of collisionality, are: (1) a global Ohm’s law that includes a fluctuating bootstrap current resulting from the ‘‘parallel’’ electron viscous damping (at rate μe) of the poloidal flow due to the perturbed radial pressure gradient; (2) reduction of the curvature effects to their flux surface average because Pfirsch–Schluter currents cancel out the lowest‐order geodesic curvature effects: (3) an increased polarization drift contribution with B−2, replaced by B−2Θ where BΘ is the poloidal magnetic field component. An electrostatic eigenmode equation is determined from ∇⋅J=0. For the unstable fluid‐like eigenmode...

Nonlocal closures for plasma fluid simulations

The application of fluid models in studies of transport and macroscopic stability of magnetized, nearly collisionless plasmas requires closure relations that are inherently nonlocal. Such closures address the fact that particles are capable of carrying information over macroscopic parallel scale lengths. In this work, generalized closures that embody Landau, collisional and particle-trapping physics are derived and discussed. A gyro/bounce-averaged drift kinetic equation is solved via an expansion in eigenfunctions of the pitch-angle scattering operator and the resulting system of algebraic equations is solved by integrating along characteristics. The desired closure moments take the form of integral equations involving perturbations in the flow and temperature along magnetic field lines. Implementation of the closures in massively parallel plasma fluid simulation codes is also discussed. This implementation includes the use of a semi-implicit time advance of the fluid equations to stabilize the dominant ...

Toroidal flow and radial particle flux in tokamak plasmas

Many effects influence toroidal flow evolution in tokamak plasmas. Momentum sources and radial plasma transport due to collisional processes and microturbulence-induced anomalous transport are usually considered. In addition, toroidal flow can be affected by nonaxisymmetric magnetic fields; resonant components cause localized electromagnetic toroidal torques near rational surfaces in flowing plasmas and nonresonant components induce “global” toroidal flow damping torque throughout the plasma. Also, poloidal magnetic field transients on the magnetic field diffusion time scale can influence plasma transport. Many of these processes can also produce momentum pinch and intrinsic flow effects. This paper presents a comprehensive and self-consistent description of all these effects within a fluid moment context. Plasma processes on successive time scales (and constraints they impose) are considered sequentially: compressional Alfven waves (Grad–Shafranov equilibrium and ion radial force balance), sound waves (p...

Conductive electron heat flow along magnetic field lines

In this work, a unified closure for the conductive electron heat flux along magnetic field lines is derived and examined. Both free-streaming and collisional pitch-angle scattering of electrons are present in the drift kinetic equation which is solved using an expansion in pitch-angle eigenfunctions (Legendre polynomials). The closure takes the form of a generic integral operator involving the electron temperature variation along a magnetic field line and the electron speed. Derived for arbitrary collisionality, the heat flux closure may be written in forms resembling previous collisional and collisionless expressions. Electrons with two to three times the thermal speed are shown to carry heat for all collisionalities and thermal electrons make an important contribution to the heat flow in regimes of moderate to low collisionality. As a practical application, the flow of electron heat along a chaotic magnetic field is calculated in order to highlight the nonlocal nature of the closure which allows for heat to flow against local temperature gradients.

Transport equations in tokamak plasmas

Tokamak plasma transport equations are usually obtained by flux surface averaging the collisional Braginskii equations. However, tokamak plasmas are not in collisional regimes. Also, ad hoc terms are added for neoclassical effects on the parallel Ohm’s law, fluctuation-induced transport, heating, current-drive and flow sources and sinks, small magnetic field nonaxisymmetries, magnetic field transients, etc. A set of self-consistent second order in gyroradius fluid-moment-based transport equations for nearly axisymmetric tokamak plasmas has been developed using a kinetic-based approach. The derivation uses neoclassical-based parallel viscous force closures, and includes all the effects noted above. Plasma processes on successive time scales and constraints they impose are considered sequentially: compressional Alfven waves (Grad–Shafranov equilibrium, ion radial force balance), sound waves (pressure constant along field lines, incompressible flows within a flux surface), and collisions (electrons, parallel...

Structure and dynamics of current sheets at Alfvén resonances in a differentially rotating plasma

Alfven resonances, where the local flow speed relative to the boundary is equal to the local Alfven speed, introduce novel dynamical features in a differentially rotating plasma. The spatial structure and dynamics of current sheets in such plasmas is investigated analytically as well as numerically. The current sheets at Alfven resonances tend to power-law singularities. The growth of current sheets is algebraic in time in the linear regime and saturates in the presence of dissipation without the intervention of nonlinear effects. These results have significant implications for forced reconnection and Alfven wave dissipation in laboratory and space plasmas.

Kinetic approach to a pressure-gradient-driven tokamak resistive instability in the banana regime

A new resistive, low‐frequency (ω≪ωba ∼νa, where ω is the frequency of the mode and ωba and νa are the bounce frequency and collision frequency for species a) instability is found in a tokamak geometry. The mode is driven unstable by the parallel viscous (bootstrap) current induced by the radial pressure gradient. It has a growth rate γ∼(ω2*eνi)1/3 for νi≫ω*e, where ω*e is the electron diamagnetic drift frequency and νi is the ion–ion collision frequency. The frequency dependence of the parallel viscosity is also derived and utilized to show that drift wave branches of these modes are stable, but that this new mode remains unstable when the diamagnetic drift effects are included.

Paleoclassical transport in low collisionality toroidal plasmas

Radial electron heat transport in a low-collisionality, current-carrying resistive plasma confined in an axisymmetric toroidal magnetic field is hypothesized to be caused by the paleoclassical collisional processes of parallel electron heat conduction and radial magnetic-field diffusion. The electron distribution is Maxwellianized and the electron temperature equilibrated over a long length L (⪢ the poloidal periodicity half-length πR0q) along helical magnetic-field lines that are diffusing radially with the resistivity-induced magnetic-field diffusivity Dη≡η‖nc∕μ0≃νe(c∕ωp)2. This produces a paleoclassical radial electron heat diffusivity χepc that is a multiple M≃L∕(πR0q)∼10⪢1 of the magnetic-field diffusivity: χepc≃(3∕2)MDη. New paleoclassical model developments in this paper include full axisymmetric toroidal magnetic-field geometry, evolution of toroidal, poloidal, and helical magnetic fluxes, effects of temporally varying magnetic fluxes, introduction of electron guiding center radial diffusion effec...

Calculation of parallel viscosity in the plateau regime

A direct calculation of the parallel viscosity 〈B⋅∇⋅πa〉 in the plateau regime for a large‐aspect‐ratio, axisymmetric tokamak is presented.