S.A. Galkin

Multi-fluid MHD model and calculations of Alfvén wave spectrum and dissipation in tokamaks

The numerical method is developed for calculations of wave excitation and dissipation in Alfven and in Ion Cyclotron Range of Frequency (ICRF) in axisymmetric tokamaks. Multi-fluid magneto-hydrodynamic plasma model is used and two-dimensional inhomogeneity of plasma parameters with arbitrary cross section of magnetic surfaces is considered. The difference scheme for the wave equation is not connected to magnetic field geometry and is suitable for the method extensions to nonlinear and three-dimensional case. Special care is taken to avoid the spectrum distortion and pollution. Relevant benchmark cases are presented. Finally, the results of numerical calculations of Alfven wave absorption are presented for the experimental conditions foreseen for the Tokamak Chauffage Alfven wave experiment in Brazil (TCABR) [Nucl. Fusion 30 (1996) 503]. In particular, the effect of toroidal mode coupling on the power deposition of Global Alfven Wave (GAW) eigenmodes is demonstrated.

Calculations of alfvén wave heating in TCABR tokamak

A two dimensional code ALTOK, which is designed for calculating plasma heating due to radio frequency fields in the Alfven and in Ion Cyclotron Ranges of Frequencies in axisymmetric tokamaks, is used to analyze Alfven wave absorption in multi species plasmas in TCABR (Tokamak Chauffage Alfven Brasilien) [Nucl.Fusion 30, 503 (1996)]. A good agreement between the results obtained with ALTOK code calculations and with a two dimensional kinetic code [Phys. Plas., 6 (1999) 2437] is shown for Alfven wave dissipation in hydrogen plasmas. The global Alfven wave resonance of the m = 0 mode is found to be the best candidate to explain some heating regimes in TCABR.

Hybrid Iterative Approach for Simulation of Radio-frequency Fields in Plasma

A novel iterative approach for solving discretized linear wave equations in a frequency domain, which combines time evolution with iterative relaxation schemes, is presented. In this hybrid approach, each iteration cycle consists of evolution of electromagnetic (EM) fields in time over a specified number of field periods followed by several iterative relaxations. Provided that there is sufficient dissipation, both the time evolution and the iterative relaxations contribute to the convergence of the EM fields to the solution of the formulated full wave boundary value problem. Time evolution rapidly distributes EM fields, propagating with group velocity, over the simulation domain, while the iterative relaxations smooth the fields, reducing the numerical errors such that iteration cycles converge to a steady state solution, approximating the solution of the formulated problem. This approach is intended for large scale simulations which are beyond the capabilities of direct solvers presently used for solving wave equations in the frequency domain. The technique is demonstrated for solving wave equations on a regular grid using a cold plasma dielectric model with collisions for 2D modeling of EM fields in tokamak in an electron cyclotron frequency range.A novel iterative approach for solving discretized linear wave equations in a frequency domain, which combines time evolution with iterative relaxation schemes, is presented. In this hybrid approach, each iteration cycle consists of evolution of electromagnetic (EM) fields in time over a specified number of field periods followed by several iterative relaxations. Provided that there is sufficient dissipation, both the time evolution and the iterative relaxations contribute to the convergence of the EM fields to the solution of the formulated full wave boundary value problem. Time evolution rapidly distributes EM fields, propagating with group velocity, over the simulation domain, while the iterative relaxations smooth the fields, reducing the numerical errors such that iteration cycles converge to a steady state solution, approximating the solution of the formulated problem. This approach is intended for large scale simulations which are beyond the capabilities of direct solvers presently used for solving...

3D hybrid meshless adaptive algorithm and code for ion extraction problem

We present progress on the development of a new 3D hybrid electrostatic code, IonEx3D, for simulating ion extraction from plasma. The code is based on the meshless, adaptive Particle-In-Cloud-Of-Points (PICOP)1 approach. The ions are treated fully kinetically whereas electrons are described as a neutralizing fluid obeying the Boltzmann distribution. Steady state ion trajectories are found in the self-consistent electrostatic field and the given magnetic field. The semi-linear Poissons equation is solved on a meshless cloud of points, which is iteratively adapted to the field and the beam structure. The algorithm conserves both the full energy and the angular momentum. 3D effects on the ion beam formation will be presented. An effective algorithm for the code parallelization on petascale computers will be also discussed.

Comparison of the calculations of the stability properties of a specific stellarator equilibrium with different MHD stability codes

A particular configuration of the LHD stellarator with an unusually flat pressure profile has been chosen to be a test case for comparison of the MHD stability property predictions of different three-dimensional and averaged codes for the purpose of code comparison and validation. In particular, two relatively localized instabilities, the fastest growing modes with toroidal mode number n = 2 and n = 3 were studied using several different codes, with the good agreement that has been found providing justification for the use of any of them for equilibria of the type considered.