TransROTA: A code for solving collisionality-extended Braginskii's closure formalism for toroidally-rotating plasmas with nonlinear successive overrelaxation

Abstract

TransROTA (Transport analysis based on ROTAtions) is a code that solves the axisymmetric version of Stacey-Sigmar extended plasma rotation model based on a collisionality-extended Braginskii's closure formalism with realistic d-shaped flux surface geometry in toroidally-confined plasmas [Nucl. Fusion 53 (2013) 043,011]. The Stacey-Sigmar model is unique in rotation and transport calculations by retaining all the terms in the angular momentum balance and by considering the first-order poloidal asymmetries in density, velocity, and electrostatic potential, for a higher accuracy in rotation calculations. TransROTA code evolves out of an earlier two-ion code GTROTA [Comp. Phys. Comm. 184 (2013) 2571–2587] and is developed for more practical studies on rotation and transport of up to five ion species (including deuterium and carbon). The main practical application is focused on intrinsic rotation studies. TransROTA requires a well-calibrated radial velocity profile of carbon impurity as one of the 21 required inputs. Once provided, TransROTA stably converges its nonlinear iterations with locally-optimized Successive Overrelaxation (SOR) scheme only, which is a remarkable improvement from GTROTA. This stable convergence is achieved by both modified application of the model equations and improvement in the numerical method. The new numerical scheme successfully removes the numerical instability issues commonly observed in GTROTA to make TransROTA not only to robustly converge the solutions but also to be faster and user-friendly. Program SummaryProgram title: A_TransROTA2023aCPC Library link to program files: https://doi.org/10.17632/3hnht4j94k.1Licensing provisions: CCO 1.0Programming language: Matlab2023aSupplementary material: Quick Test Run guide, User's Manual, and input preparation templates (available in the provided package)Journal Reference of previous version: C. Bae, W.M. Stacey, and T.D. Morley, GTROTA: A code for the solution of the coupled nonlinear extended neoclassical rotation equations in tokamak plasmas using successive over-relaxation and simulated annealing. Computer Physics Communications, 2013. 184(11): p. 2571-2587.Does the new version supersede the previous version?: YesReasons for the new version: Velocity and transport calculations of previous two-ion model of GTROTA extended to five ions with a robust convergence. Faster and user-friendly code. Upgraded for intrinsic (or spontaneous) rotation and impurity transport studies.Summary of revisions: TransROTA can calculate the velocities and transport parameters of up to five ion species in tokamaks. The numerical iterations are much more stable than GTROTA code and robustly find converged solutions. Two practical extensions are also added for the studies of intrinsic rotation and for the investigation of relative torque contributions of residual stress and neoclassical toroidal viscosity torques.Nature of problem: Rotation velocities of toroidally-confined plasmas and consequent plasma transport properties are calculated from a coupled set of nonlinear equations based on Stacey-Sigmar plasma rotation theory with collisionality-extended Braginskii's closure formalism. The consequent coupled set of equations in orthogonal toroidal coordinates (radial, poloidal, and toroidal) are extremely nonlinear in nature, thus its numerical iterations can easily grow unstable. Its numerical model has many inherent sources of singularities in their system coefficients. There is a need to remodel the formalism so that the resultant model is more resilient against such singularity effects.Solution method: The final numerical model solved by TransROTA has been reformulated to yield a more robust convergence with less singularity effects. The key to this success is based on the lessons learned from GTROTA code that all iterations of the unknown variables approach their solutions at vastly-different rates. Thus, while keeping a similar functional decomposition of the entire system of unknowns, application of locally-optimized SOR relaxation schemes to each functional subsystem can allow the nonlinear iterations of all the functional subsystems to approach their solutions at a synchronized rate for a successful convergence of the entire system.Additional comments including restrictions and unusual features: The theoretical model and the code are not developed for a good accuracy in the plasma edge region where the normalized radial radius is beyond 0.80. TransROTA is designed to use TRANSP code to prepare many of its required inputs although any tools can be used. TransROTA provides two MS Excel input templates for user-friendly preparation of all inputs. The provided templates are specifically customized for EAST tokamak coordinates and their positive directions. Refer to User's Manual on how to customize the positive coordinate directions for other tokamaks.