Speaker
Description
In this work, an implicit scheme for electromagnetic particle-in-cell/Fourier simulations is developed using the v_∥ formula and applied to studies of Alfvén waves in one dimension and in tokamak plasmas on structured meshes. While the “particle enslavement” scheme has been introduced for reducing the degree of freedom of particles in the field-particle system, in this work, we focus on the theoretical analyses of the convergence of the system. An analytical treatment is introduced to achieve efficient convergence of the iterative solution of the implicit field-particle system. The essence of this scheme is to represent the particle moments such as the density and the parallel current as functions of field variables. Then the correction matrix of the implicit field-particle system can be obtained analytically. As a result, this treatment is termed with “moment enslavement”. Its application to the one-dimensional uniform plasma demonstrates the applicability in a broad range of β/m_e values. The simulation results and the theoretical results agree well in our studied regime where β_e m_i/m_e∈[1/16,32], k_⊥ ρ_ti=0.2, where β_e is the electron beta, k_⊥ is the perpendicular (to B) wave vector, ρ_ti is the Larmor radius of thermal ions, m_i and m_e are ion and electron masses. The toroidicity induced Alfvén eigenmode (TAE) is simulated using the widely studied case defined by the ITPA Energetic particle (EP) Topical Group. The real frequency and the growth (or damping) rate of the TAE with (or without) EPs agree with previous results reasonably well. The full f electromagnetic particle scheme established in this work provides a natural choice for EP transport studies where large profile variation and arbitrary distribution need to be captured in kinetic simulations. By combining recent developments with the applications to mode structure symmetry breaking studies, the ongoing work focuses on the simulations of kinetic ballooning mode simulations and EP driven Alfvén modes in realistic tokamak geometry, with the capability of including the plasma separatrix. The full f and delta f simulations are compared, demonstrating their features in performance and the capabilities of the full f scheme in treating specific problems.
