Test particle simulations for transport in toroidal plasmas

Abstract

The authors derive the guiding center equations of motion from the phase space Euler–Lagrange formulation for the 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. The 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. The 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 the diffusion processes through both the orbit squeezing and the Er×B shear flow of the poloidal velocity.

Drift wave test particle transport in reversed shear profile

“…Park et al [4] the exact ion orbits in full toroidal geometry are followed and these results complement the present study by maps. As a practical matter, however, only with maps can one follow orbits accurately for the lo6 time steps required to go from the wave correlation time scale T~ -1/Aws to the transport time scale of rtra 2 / D -1 -10 s.…”

“…In contrast, the results for @02 shows that ET generates enough shear in the E x B poloidal velocity to suppress the transport induced by the drift wave electrostatic fluctuations, as first proposed by Biglari et al [ll] and numerically confirmed for the global toroidal system in Ref. [4] by solving the coupled ordinary differential equations for the exact guiding-center trajectories. When we use the Er profiles in Fig.…”

Global drift wave map test particle simulations

“…Assuming that small angle Coulomb scattering changes the direction, but not the magnitude, of the velocity, the collisional scattering map for the change of velocity was derived in Ref. 23 and is given by the following:…”

Explicit Runge–Kutta integrator with Hamiltonian correction for long-time simulations of guiding-center orbit in tokamak configurations

“…The exact canonical Hamiltonian formalism was then developed by White and Zakharov, 5 Wang, 6 and Cooper et al 7 It is necessary to make long-time simulations, for example, for the purpose of studying plasma transport physics. 8,9 Any increase of computing speed in guidingcenter codes is an important improvement in predictive capability due to the large number of necessary simulations; e.g., rapid guiding-center calculations are proposed. 10 The key point of numerically modeling the long-time behavior of guiding-center is to keep the Hamiltonian characteristics, e.g., conservation of energy and momentum, etc.…”