Structure-preserving algorithms for guiding center dynamics based on the slow manifold of classical Pauli particle

The classical Pauli particle(CPP) serves as a slow manifold, substituting the conventional guiding center dynamics. Based on the CPP, we utilize the averaged vector field(AVF) method in the computations of drift orbits. Demonstrating significantly higher efficiency, this advanced method is capable of accomplishing the simulation in less than one-third of the time of directly computing the guiding center motion. In contrast to the CPP-based Boris algorithm, this approach inherits the advantages of the AVF method, yielding stable trajectories even achieved with a tenfold time step and reducing the energy error by two orders of magnitude. By comparing these two CPP algorithms with the traditional RK4 method, the numerical results indicate a remarkable performance in terms of both the computational efficiency and error elimination. Moreover, we verify the properties of slow manifold integrators and successfully observe the bounce on both sides of the limiting slow manifold with deliberately chosen perturbed initial conditions. To evaluate the practical value of the methods, we conduct simulations in non-axisymmetric perturbation magnetic fields as part of the experiments,demonstrating that our CPP-based AVF method can handle simulations under complex magnetic field configurations with high accuracy, which the CPP-based Boris algorithm lacks. Through numerical experiments, we demonstrate that the CPP can replace guiding center dynamics in using energy-preserving algorithms for computations, providing a new, efficient, as well as stable approach for applying structure-preserving algorithms in plasma simulations.

Adaptive energy-preserving algorithms for guiding center system

We develop two types of adaptive energy preserving algorithms based on the averaged vector field for the guiding center dynamics,which plays a key role in magnetized plasmas.The adaptive scheme is applied to the Gauss Legendre’s quadrature rules and time stepsize respectively to overcome the energy drift problem in traditional energy-preserving algorithms.These new adaptive algorithms are second order,and their algebraic order is carefully studied.Numerical results show that the global energy errors are bounded to the machine precision over long time using these adaptive algorithms without massive extra computation cost.

Non-Perturbative Guiding Center and Stochastic Gyrocenter Transformations:Gyro-Phase Is the Kaluza-Klein 5^(th) Dimension also for Reconciling General Relativity with Quantum Mechanics

The non perturbative guiding center transformation is extended to the relativistic regime and takes into account electromagnetic fluctuations. The main solutions are obtained in covariant form: the gyrating particle and the guiding particle solutions, both in gyro-kinetic as in MHD orderings. Moreover, the presence of a gravitational field is also considered. The way to introduce the gravitational field is original and based on the Einstein conjecture on the feasibility to extend the general relativity theory to include electromagnetism by geometry, if applied to the extended phase space. In gyro-kinetic theory, some interesting novelties appear in a natural way, such as the exactness of the conservation of a magnetic moment, or the fact that the gyro-phase is treated as the non observable fifth dimension of the Kaluza-Klein model. Electrodynamics becomes non local, without the inconsistency of self-energy. Finally, the gyrocenter transformation is considered in the presence of stochastic e.m. fluctuations for explaining quantum behaviors via Nelson’s approach. The gyrocenter law of motion is the Schrödinger equation.

Calculations of the Ion Orbit Loss Region at the Plasma Edge of EAST

In divertor tokamak plasma, the energetic ion losses of edge plasma are considered to be responsible for the negative radial electric field. In the present paper, a guiding center approximation orbit equation is found by assuming the conservation of three integrals of motion, i.e. the total ion energy E, the magnetic moment # and toroidal angular momentum Pc, and it is used to calculate expediently the ion orbit loss region. The direct ion orbit losses in the initial velocity space near the plasma edge of EAST with SN （single null） divertor configuration are analyzed systematically. The ion loss regions are obtained by solving the guiding center approximation orbit equation of critical ions with the effect of the radial electric field taken into account. Under the influence of plasma current Ip, the type of ions, the toroidal field Bt and the changes of the loss regions are analyzed and calculated accordingly.