This paper uses the implicit Monte–Carlo full-orbit-following parallel program ISSDE to calculate the prompt loss and slowing down process of neutral beam injection(NBI)-generated fast ions due to Coulomb collisions ...This paper uses the implicit Monte–Carlo full-orbit-following parallel program ISSDE to calculate the prompt loss and slowing down process of neutral beam injection(NBI)-generated fast ions due to Coulomb collisions in the equilibrium configuration of Experimental Advanced Superconducting Tokamak(EAST).This program is based on the weak equivalence of the Fokker–Planck equation under Rosenbluth Mac Donald Judd(RMJ)potential and Stratonovich stochastic differential equation(SDE).The prompt loss with the LCFS boundary and the first wall(FW)boundary of the two co-current neutral injection beams are studied.Simulation results indicate that the loss behavior of fast ions using the FW boundary is very different from that of the LCFS boundary,especially for fast ions with a large gyration radius.According to our calculations,about 5.11%of fast ions generated by perpendicular injection drift out of the LCFS and then return inside the LCFS to be captured by the magnetic field.The prompt loss ratio of fast ions and the ratio of orbital types depend on the initial distribution of fast ions in the Pζ–Λspace.Under the effect of Coulomb collisions,the pitch-angle scattering and stochastic diffusion happens,which will cause more fast ion loss.For short time scales,among the particles lost due to collisions,the fraction of banana ions reaches 92.31%in the perpendicular beam and 58.65%in the tangential beam when the fraction of banana ions in the tangential beam is 3.4%of the total ions,which means that the effect of Coulomb collisions on banana fast ions is more significant.For long time scales,the additional fast ion loss caused by Coulomb collisions of tangential and perpendicular beams accounted for 16.21%and 25.05%of the total particles,respectively.We have also investigated the slowing down process of NBI fast ions.展开更多
A Monte Carlo implicit simulation program,Implicit Stratonovich Stochastic Differential Equations(ISSDE),is developed for solving stochastic differential equations(SDEs)that describe plasmas with Coulomb collision.The...A Monte Carlo implicit simulation program,Implicit Stratonovich Stochastic Differential Equations(ISSDE),is developed for solving stochastic differential equations(SDEs)that describe plasmas with Coulomb collision.The basic idea of the program is the stochastic equivalence between the Fokker-Planck equation and the Stratonovich SDEs.The splitting method is used to increase the numerical stability of the algorithm for dynamics of charged particles with Coulomb collision.The cases of Lorentzian plasma,Maxwellian plasma and arbitrary distribution function of background plasma have been considered.The adoption of the implicit midpoint method guarantees exactly the energy conservation for the diffusion term and thus improves the numerical stability compared with conventional Runge-Kutta methods.ISSDE is built with C++and has standard interfaces and extensible modules.The slowing down processes of electron beams in unmagnetized plasma and relaxation process in magnetized plasma are studied using the ISSDE,which shows its correctness and reliability.展开更多
基金the National MCF Energy Research and Development Program(Grant No.2018YFE0304100)the National Key Research and Development Program of China(Grant Nos.2016YFA0400600,2016YFA0400601,2016YFA0400602,and 2019YFE0302004)the National Natural Science Foundation of China(Grant Nos.11805273 and 11905220)。
文摘This paper uses the implicit Monte–Carlo full-orbit-following parallel program ISSDE to calculate the prompt loss and slowing down process of neutral beam injection(NBI)-generated fast ions due to Coulomb collisions in the equilibrium configuration of Experimental Advanced Superconducting Tokamak(EAST).This program is based on the weak equivalence of the Fokker–Planck equation under Rosenbluth Mac Donald Judd(RMJ)potential and Stratonovich stochastic differential equation(SDE).The prompt loss with the LCFS boundary and the first wall(FW)boundary of the two co-current neutral injection beams are studied.Simulation results indicate that the loss behavior of fast ions using the FW boundary is very different from that of the LCFS boundary,especially for fast ions with a large gyration radius.According to our calculations,about 5.11%of fast ions generated by perpendicular injection drift out of the LCFS and then return inside the LCFS to be captured by the magnetic field.The prompt loss ratio of fast ions and the ratio of orbital types depend on the initial distribution of fast ions in the Pζ–Λspace.Under the effect of Coulomb collisions,the pitch-angle scattering and stochastic diffusion happens,which will cause more fast ion loss.For short time scales,among the particles lost due to collisions,the fraction of banana ions reaches 92.31%in the perpendicular beam and 58.65%in the tangential beam when the fraction of banana ions in the tangential beam is 3.4%of the total ions,which means that the effect of Coulomb collisions on banana fast ions is more significant.For long time scales,the additional fast ion loss caused by Coulomb collisions of tangential and perpendicular beams accounted for 16.21%and 25.05%of the total particles,respectively.We have also investigated the slowing down process of NBI fast ions.
基金Project supported by the National MCF Energy R&D Program of China(Grant No.2018YFE0304100)the National Key Research and Development Program of China(Grant Nos.2016YFA0400600,2016YFA0400601,and 2016YFA0400602)the National Natural Science Foundation of China(Grant Nos.NSFC-11805273 and NSFC-11905220).
文摘A Monte Carlo implicit simulation program,Implicit Stratonovich Stochastic Differential Equations(ISSDE),is developed for solving stochastic differential equations(SDEs)that describe plasmas with Coulomb collision.The basic idea of the program is the stochastic equivalence between the Fokker-Planck equation and the Stratonovich SDEs.The splitting method is used to increase the numerical stability of the algorithm for dynamics of charged particles with Coulomb collision.The cases of Lorentzian plasma,Maxwellian plasma and arbitrary distribution function of background plasma have been considered.The adoption of the implicit midpoint method guarantees exactly the energy conservation for the diffusion term and thus improves the numerical stability compared with conventional Runge-Kutta methods.ISSDE is built with C++and has standard interfaces and extensible modules.The slowing down processes of electron beams in unmagnetized plasma and relaxation process in magnetized plasma are studied using the ISSDE,which shows its correctness and reliability.
