Test particle simulations for transport in toroidal plasmas

Abstract

To investigate the transport in toroidal plasmas, we use two sets of equations of motion. The first is the set of guiding center equations of motion derived from the phase space Euler-Lagrange formulation for motion of a charged particle in toroidal magnetic confinement geometry. The guiding center equations are numerically solved together with the Monte Carlo Coulomb collisional pitch angle scattering. Numerically calculated microscopic diffusion coefficients for various values of collisionality $ν_*$ in the case of no electrostatic potential agree well with the results of neoclassical theory. Diffusion coefficient is then measured in the presence of a model electrostatic drift wave fluctuation and an equilibrium potential. The diffusion coefficient increases with increasing fluctuation amplitude while the equilibrium potential diminishes diffusion processes through both the orbit squeezing and the $\vec{E}_r × \vec{B}$ shear flow of poloidal velocity. We also apply the test particle simulation method for neocalssical transport in core region of a reversed shear plasma. The results indicate that the radial transport is not diffusive in the core region where the orbit topology is much different from what is assumed in standard neoclassical theory. It seems that the unusual orbit topology and steep gradients in density and q profiles are not sufficient to explain the very low ion thermal conductivity observed in the ERS experiments. We also derive a set of symplectic map equations that have the same Hamiltonian structure of the underlying flows and allow long time integration of the orbits. By the calculation using the drift wave map equations we show that a dramatic improvement in particle confinement from the $\vec{E} × \vec{B}$ turbulence can happen in a favorable electric or magnetic field profile, for example, in the reversed q(r) profile, without necessarilly a significant change in the turbulence level.