M. Yu. Isaev

Full-field drift Hamiltonian particle orbits in 3D geometry

A Hamiltonian/Lagrangian theory to describe guiding centre orbit drift motion which is canonical in the Boozer coordinate frame has been extended to include full electromagnetic perturbed fields in anisotropic pressure 3D equilibria with nested magnetic flux surfaces. A redefinition of the guiding centre velocity to eliminate the motion due to finite equilibrium radial magnetic fields and the choice of a gauge condition that sets the radial component of the electromagnetic vector potential to zero are invoked to guarantee that the Boozer angular coordinates retain the canonical structure. The canonical momenta are identified and the guiding centre particle radial drift motion and parallel gyroradius evolution are derived. The particle coordinate position is linearly modified by wave–particle interactions. All the nonlinear wave–wave interactions appear explicitly only in the evolution of the parallel gyroradius. The radial variation of the electrostatic potential is related to the binormal component of the displacement vector for MHD-type perturbations. The electromagnetic vector potential projections can then be determined from the electrostatic potential and the radial component of the MHD displacement vector.

Neoclassical transport and α particle confinement in novel 3-D reactor systems

Neoclassical transport and α particle confinement are analysed for three 3-D reactor designs—the QAS3, the ST/sphellamak hybrid and the sphellamak—using the VENUS code. It is observed that neither the QAS3 nor the ST/sphellamak is truly a quasi-axisymmetric configuration. Thus the transport is governed by the helical deformation of the magnetic field strength, and these configurations do not effectively confine the trapped α particles. On the other hand, the sphellamak is a nearly isodynamic structure in the plasma core, which leads to almost perfect α confinement, and the neoclassical transport is very similar to that obtained in a 2-D equivalent tokamak.

Exact canonical drift Hamiltonian formalism with pressure anisotropy and finite perturbed fields

A Hamiltonian formulation of the guiding center drift orbits is extended to pressure anisotropy and field perturbations in axisymmetric systems. The Boozer magnetic coordinates are shown to retain canonical properties in anisotropic pressure plasmas with finite electrostatic perturbations and electromagnetic perturbed fields that solely affect the parallel component of the magnetic vector potential. The equations of motion developed in the Boozer coordinate frame are satisfied by direct verification of the drift velocities. A numerical application illustrates the significance of retaining all second order terms.

Moment approach to the bootstrap current in nonaxisymmetric toroidal plasmas using δf Monte Carlo methods

To evaluate the bootstrap current in nonaxisymmetric toroidal plasmas quantitatively, a δf Monte Carlo method is incorporated into the moment approach. From the drift-kinetic equation with the pitch-angle scattering collision operator, the bootstrap current and neoclassical conductivity coefficients are calculated. The neoclassical viscosity is evaluated from these two monoenergetic transport coefficients. Numerical results obtained by the δf Monte Carlo method for a model heliotron are in reasonable agreement with asymptotic formulae and with the results obtained by the variational principle.

Relativistic Hamiltonian guiding center drift formalism in anisotropic pressure magnetic coordinates

A Hamiltonian formulation of the relativistic guiding center drifts is extended to anisotropic pressure plasmas. The magnetic coordinates devised by Boozer are adapted to the anisotropic pressure model and retain canonical properties for two-dimensional and three-dimensional toroidal plasma equilibria including finite electrostatic perturbations provided that any electromagnetic perturbation only alters the parallel component of the vector potential. A mapping technique from arbitrary flux coordinates is outlined. A direct evaluation of the relativistic drift velocity recovers the equations of motion derived from the Hamiltonian formalism except for ignorable higher order terms in the evolution of the canonical angular variables and the effective parallel gyroradius.

The pseudo-symmetric optimization of the National Compact Stellarator Experiment

A new experiment, the National Compact Stellarator Experiment (NCSX) [Monticello et al. “Physics Consideration for the Design of NCSX,” Proceedings of 25th EPS Conference on Controlled Fusion and Plasma Physics, Prague, 1998 (European Physical Society, Petit-Lancy), paper 1.187], hopes to overcome the deleterious ripple transport usually associated with stellarators by creating a quasi-axisymmetric configuration. A quasi-axisymmetric configuration is one in which the Fourier spectrum of the magnetic field strength in so-called Boozer coordinates is dominated by the toroidal angle averaged (n=0) components. In this article the concept of pseudosymmetry is used to improve ripple transport in a four-period variant of NCSX. By definition, pseudosymmetric magnetic configurations have no locally trapped particles. To obtain a pseudosymmetric configuration, different target functions are considered. It is found that a target function equal to the area of ripple of the magnetic field magnitude along the field lin...

Plasma stability in Heliac-like quasi-helically symmetric stellarators

An attempt is made to find an optimal quasi-helically symmetric (QHS) four period magnetic configuration with a Heliac-like structure of the magnetic surface cross-sections. This means that the cross-sections rotate in phase with the magnetic axis principal normal in contrast to the Helias-like systems where the magnetic surface cross-sections rotate half as fast as the principal normal. The equilibrium and local stability are studied with the VMEC and TERPSICHORE codes. It is shown that, in the configuration found, the equilibrium beta limit is about 9%, the Mercier beta limit is about 4% and the ballooning modes restrict the beta value to 1%. The accuracy of the fulfilment of the QHS condition is given by X~3 (i.e. the largest amplitude of the magnetic field strength B harmonic that violates the quasi-symmetry is a third that of the main helical harmonic of B in Boozer co-ordinates)

Bootstrap current calculations with the SPBSC and the VENUS+δf codes for the Large Helical Device

Total bootstrap current calculations with the updated VENUS+δf code that incorporates energy convolution and the momentum correction technique have been performed for the reference tokamak JT-60U cases and for the experimental Large Helical Device (LHD, NIFS, Japan) configurations with different magnetic axis positions. The VENUS+δf results have been compared with the corresponding tokamak results of the neoclassical bootstrap current models for the general axisymmetric equilibria and arbitrary collisionality regime, as well as with the corresponding 3D SPBSC code numerical predictions and with the LHD experimental tendency.

A new class of quasi-omnigenous configurations

An approximation to a quasi-omnigenous structure of the magnetic field strength has been numerically obtained by optimization of the magnetic configuration of a conventional heliotron/torsatron. This configuration shows very good collisionless confinement of the guiding centre orbits of fusion alpha-particles for values of up to 0.05.

Ideal MHD stability calculations for compact stellarators

Stability results for high-n ideal local pressure-driven instabilities (ballooning and interchange modes) are calculated from the COBRA and TERPSICHORE codes and compared for several low aspect ratio stellarators. Such a comparison is important because of the predominant roles that these codes are playing in the design of compact stellarators at several laboratories around the world. The code development required to reach the levels of convergence and accuracy needed for reliable operation at low aspect ratios is also described.