Neoclassical transport in quasi-axially symmetric stellarators

The author presents a numerical and analytic assessment of the transport in two quasi-axially symmetric stellarators, including one variant of the MHH2 class of such devices, and a configuration they refer to as NHH2, closely related to MHH2. Monte Carlo simulation results are compared with expectations from established stellarator neoclassical theory, and with some empirical stellarator scalings, used as an estimate of the turbulent transport which might be expected. From the standpoint of transport, these may be viewed as either tokamaks with large ({delta} {approximately} 1%) but low-n ripple, or as stellarators with small ripple. For NHH2, numerical results are reasonably well explained by analytic neoclassical theory. MHH2 adheres less to assumptions made in most analytic theory, and its numerical results agree less well with theory than those for NHH2. However, for both, the non-axisymmetric contribution to the heat flux is comparable with the symmetric neoclassical contribution, and also falls into the range of the expected anomalous (turbulent) contribution. Thus, it appears effort to further optimize the thermal transport beyond the particular incarnations studied here would be of at most modest utility. However, the favorable thermal confinement relies heavily on the radial electric field. Thus, the present configurations will have a loss cone for trapped energetic ions, so that further optimization may be indicated for large devices of this type

Diffusive transport and self-consistent dynamics in coupled maps

The study of diffusion in Hamiltonian systems has been a problem of interest for a number of years. In this paper we explore the influence of self-consistency on the diffusion properties of systems described by coupled symplectic maps. Self-consistency, i.e. the back-influence of the transported quantity on the velocity field of the driving flow, despite of its critical importance, is usually overlooked in the description of realistic systems, for example in plasma physics. We propose a class of self-consistent models consisting of an ensemble of maps globally coupled through a mean field. Depending on the kind of coupling, two different general types of self-consistent maps are considered: maps coupled to the field only through the phase, and fully coupled maps, i.e. through the phase and the amplitude of the external field. The analogies and differences of the diffusion properties of these two kinds of maps are discussed in detail.Comment: 13 pages, 14 figure

Toward the automated analysis of plasma physics problems

A program (CALC) is described, which carries out nontrivial plasma physics calculations, in a manner intended to emulate the approach of a human theorist. This includes the initial process of gathering the relevant equations from a plasma knowledge base, and then determining how to solve them. Solution of the sets of equations governing physics problems, which in general have a nonuniform,irregular structure, not amenable to solution by standardized algorithmic procedures, is facilitated by an analysis of the structure of the equations and the relations among them. This often permits decompositions of the full problem into subproblems, and other simplifications in form, which renders the resultant subsystems soluble by more standardized tools. CALC's operation is illustrated by a detailed description of its treatment of a sample plasma calculation. 5 refs., 3 figs

Guiding-center Hamiltonian figure-8 particles in axisymmetric field-reversed configurations

The guiding-center Hamiltonian K is derived for so-called figure-8 particles which are present in field-reversed mirror configurations, using a formalism developed previously. For such particles, the gyro-orbit cannot be approximated by a circle, and standard approaches to guiding-center theory are thus totally inapplicable. K manifests this intrinsic difference by a quite different dependence on the gyroaction, and by familiar effects such as mirroring and magnetic-gradient drifts being controlled by the radial derivative of the magnetic field strength B at the point of field-reversal, rather than by B itself, as occurs in standard guiding-center theory

The generalized Balescu-Lenard collision operator: A unifying concept for tokamak transport

The generalization of the Balescu-Lenard collision operator to its fully electromagnetic counterpart in Kaufman's action-angle formalism is derived and its properties investigated. The general form may be specialized to any particular geometry where the unperturbed particle motion is integrable, and thus includes cylindrical plasmas, inhomogeneous slabs with nonuniform magnetic fields, tokamaks, and the particularly simple geometry of the standard operator as special cases. The general form points to the commonality between axisymmetric, turbulent, and ripple transport, and implies properties (e.g., intrinsic ambipolarity) which should be shared by them, under appropriate conditions. Along with a turbulent ''anomalous diffusion coefficient'' calculated for tokamaks in previous work, an ''anomalous pinch'' term of closely related structure and scaling is also implied by the generalized operator. 20 refs. (LSP

Anomalous energy exchange in the gBL and quasilinear theories

The rate of turbulence-induced energy exchange {dot W}{sub o} between species is computed in the framework of the quasilinear and gBL transport theories, and the relationship between these two theories, and the relationship between these two similar theories is thereby elucidated. For both theories, general formal expressions for {dot W}{sub o} are developed, and then applied to the trapped electron mode for illustration. The general expressions for {dot W}{sub o} in the two theories are formally closely related, but can yield predictions of very different magnitude in concrete applications. The fact that quasilinear theory is not valid for saturated steady-state turbulence gives rise to certain peculiarities in its predictions for this normal experimental situation, such as permitting energy to flow from the cooler to the hotter species, even in the limit of thermal equilibrium, where real-space gradients vanish. The gBL theory may be viewed as a modification of quasilinear theory to be valid for steady-state turbulence, keeping extra terms due to the self-consistent back reaction of particles on the fluctuations, which are just such as to eliminate these peculiarities

Transport of energetic ions by low-n magnetic perturbations

The stochastic transport of MeV ions induced by low-n magnetic perturbations is studied, focussing chiefly on the stochastic mechanism operative for passing particles in low frequency perturbations. Beginning with a single-harmonic form for the perturbing field, it iii first shown numerically and analytically that the stochastic threshold of energetic particles can be much lower than that of the magnetic field, contrary to earlier expectations, so that MHD perturbations could cause appreciable loss of energetic ions without destroying the bulk confinement. The analytic theory is then extended in a number of directions, to darity the relation of the present stochaistic mechanism to instances already found, to allow for more complex perturbations, and to consider the more general relationship between the stochasticity of magnetic fields, and that of particles of differing energies (and pitch angles) moving in those fields. It is shown that the stochastic threshold is in general a nonmonotonic function of energy, whose form can to some extent be tailored to achieve desired goals (e.g., burn control or ash removal) by a judicious choice of the perturbation. Illustrative perturbations are exhibited which are stochastic for low but not for high-energy ions, for high but not for low-energy ions, and for intermediate-energy ions, but not for low or high energy. The second possibility is the behavior needed for burn control; the third provides a possible mechanism for ash removal

Verification of the classical theory of helical transport in stellarators

The apparent discrepancies of the classical theory of helical transport in stellarators, versus two recent numerical studies of stellarator transport, are investigated. Numerical results are presented, verifying the classical theory, when the model for the magnetic field has the simple form assumed by the classical theory. When the helical contribution to the total transport is isolated numerically, and the different energy dependence of the particle distribution is accounted for, the results of one of the numerical studies is brought into substantial agreement with theory. It is argued that the anomalously favorable low collisionality results of the second numerical study are due partly to numerical procedure, and partly to a more complicated spatial dependence of the magnetic field. The latter may enable collisionless helical detrapping to dominate the usual collisional mechanism at low collisionality, thereby controlling transport