Improved Unlike-Particle Collision Operator for delta-f Drift-Kinetic Particle Simulations

Plasmas in modern tokamak experiments contain a significant fraction of impurity ion species in addition to main deuterium background. A new unlike-particle collision operator for δf particle simulation has been developed to study the nonlocal effects of impurities due to finite ion orbits on neoclassical transport in toroidal plasmas. A new algorithm for simulation of cross-collisions between different ion species includes test-particle and conserving field-particle operators. An improved field-particle operator is designed to exactly enforce conservation of number, momentum and energy.

Irreducible tensor form of three-particle operator for open-shell atoms

A three-particle operator in a second quantized form is studied systematically and comprehensively. The operator is transformed into irreducible tensor form. Possible coupling schemes, identified by the classes of symmetric group S6, are presented. Recoupling coefficients that make it possible to transform a given scheme into another are produced by using the angular momentum theory combined with quasispin formalism. The classification of the three-particle operator which acts on n = 1, 2,..., 6 open shells of equivalent electrons of atom is considered. The procedure to construct three-particle matrix elements are examined.

Coupled tensorial form for atomic relativistic two-particle operator given in second quantization representation

General formulas of the two-electron operator representing either atomic or effective interactions are given in a coupled tensorial form in relativistic approximation. The alternatives of using uncoupled, coupled and antisymmetric two-electron wave functions in constructing coupled tensorial form of the operator are studied. The second quantization technique is used. The considered operator acts in the space of states of open-subshell atoms.

IMPLEMENTATION OF ENDOMORPHISMS OF THE CAR ALGEBRA

The implementation of non-surjective Bogoliubov transformations in Fock states over CAR algebras is investigated. Such a transformation is implementable by a Hilbert space of isometries if and only if the well-known Shale-Stinespring condition is met. In this case, the dimension of the implementing Hilbert space equals the square root of the Watatani index of the associated inclusion of CAR algebras, and both are determined by the Fredholm index of the corresponding one-particle operator. Explicit expressions for the implementing operators are obtained, and the connected components of the semigroup of implementable transformations are described.