A multi-hierarchy simulation model aimed at magnetic reconnection studies has been developed, in which macroscopic and microscopic physics are solved self-consistently and simultaneously. In this work, the previous multi-hierarchy model by these authors is extended to a more realistic one with non-uniform space grids. Based on the domain decomposition method, the multi-hierarchy model consists of three parts: a magnetohydrodynamics algorithm to express the macroscopic global dynamics, a particle-in-cell algorithm to describe the microscopic kinetic physics, and an interface algorithm to interlock macro and micro hierarchies. For its verification, plasma flow injection is simulated in this multi-hierarchy model and it is confirmed that the interlocking method can describe the correct physics. Furthermore, this model is applied to collisionless driven reconnection in an open system. Magnetic reconnection is found to occur in a micro hierarchy by injecting plasma from a macro hierarchy.

The mechanism of plasma heating through magnetic reconnection with a guide magnetic field is investigated by means of two-dimensional electromagnetic particle simulations. These simulations mimic the dynamics of two torus plasmas merging through magnetic reconnection in a spherical tokamak (ST) device. It is found that a large part of protons, which behave as nonadiabatic, are effectively heated in the downstream because a ring-like structure of proton velocity distribution is observed at a local point in the downstream. The characteristic features of the velocity distribution can be explained as the following proton motion. Upon entering the downstream across the separatrix, nonadiabatic protons suddenly feel the strong electromagnetic field in the downstream and move in the outflow direction while rotating mainly around the guide magnetic field. The protons gain kinetic energy not only on the separatrix but also in the downstream. This effective heating process can be interpreted as the “pickup,” which, however, was thought to be responsible for only heavy ions. In this work, it is demonstrated that the pickup of protons is compatible with the known pickup theory in the cases in which the plasma beta is much less than 1, which is satisfied in STs.

The dependence of the ion effective heating on the poloidal (reconnection) and toroidal (guide) magnetic fields during magnetic reconnection in the presence of a guide magnetic field is investigated by means of particle simulations, which mimic merging plasmas in a spherical tokamak. In previous works, our simulations demonstrated that the ion temperature perpendicular to the magnetic field grows mainly in the downstream, in which ring-shaped velocity distributions are formed. This means that ions are effectively heated. The basic theory explains that the ring-shaped distribution is formed by the ions which rotate around the guide magnetic field while E × B drifting. In this work, the basic theory is extended to a more general theory including not only a ring-shaped distribution, but also a circular-arc-shaped distribution. The generalized theory explains that the effective temperature changes by the radius and the central angle of the arc-shaped velocity distribution and conjectures the dependence of the ion effective heating on the poloidal and toroidal magnetic fields. The simulations show that the ion heating energy is proportional to the square of the poloidal magnetic field, whereas the ion temperature decreases as the toroidal field is larger, but the toroidal field dependence becomes small for the regime of high toroidal field. These tendencies are consistent with those observed in experiments.

The motion of ultrarelativistic particles in an oblique plasma wave is theoretically studied. Making use of the relation vdγ/dt≫γdv/dt, where γ is the Lorentz factor, the zeroth-order velocity and energy increase rate are obtained. This solution is applicable to any particle species. The particle velocity is nearly parallel to the external magnetic field when vsh∼c cos θ, where vsh is the wave propagation speed and θ is the angle between the wave normal and the external magnetic field. The perturbed motions of ions and of positrons are then separately discussed. Their perturbations are both nearly perpendicular to the zeroth-order velocity. The ion perturbation is one dimensional with the frequency ω∼Ωi0γ−1/2, while that of the positrons is elliptic with ω∼Ωp0γ−1, where Ωi0 and Ωp0 are the nonrelativistic gyrofrequencies of ions and positrons, respectively.

The plasma heating mechanism during magnetic reconnection in the presence of guide magnetic field is investigated by means of particle simulations and test particle simulations. Particle simulations demonstrate that ring-like structures of ion velocity distributions are formed in the downstream, where a large percentage of ions are effectively heated. Furthermore, a single ion motion is focused upon by using test particle simulations. The ion moves in the downstream direction owing to the E × B drift while in gyromotion. Finally, it is reported that the profile of the ion temperature obtained by the particle simulation fits well with the profile observed in the TS-3 experiment.

The merging processes of spherical-tokamak-type plasmoids (STs), which are confined in a rectangular conducting vessel, are investigated by means of a two-dimensional particle-in-cell simulation. A series of simulation runs with different mass ratios clarify that a starting time of the ST merging is nearly given by a transit time for an ion sound wave to travel from an inner edge of each ST in an initial profile to a reconnection point and a part of poloidal magnetic energy is transferred to the ion thermal energy and the electron thermal energy at the approximate rate of 3:1 during the ST merging process, which is almost independent of the mass ratio except for the smallest mass ratio case of (M_i/M_e) = 100. This transfer process leads to the increases in a parallel component of electron temperature and a perpendicular component of ion temperature while keeping the other components almost constant. This is because the two-component electron distribution function with different velocity shifts along a toroidal magnetic field is formed around a reconnection point when two STs merge. On the other hand, an ion distribution function, consisting of three components with different velocity shifts perpendicular to the toroidal magnetic field, is formed around the reconnection point in the merging phase. It is also found that a sharp peak appears impulsively in the electron parallel temperature profile in the merging phase, which is consistent with the Mega Ampere Spherical Tokamak merging experiments [H. Tanabe et al., Nucl. Fusion 57, 056037 (2017)].