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.

We study the kinetic plasma dynamics in collisionless relativistic jets with velocity shear, by carrying out particle-in-cell simulations in the transverse plane of a jet. It is discovered that intermittent magnetic reconnections (MRs) are driven by mushroom instability (MI), which is an important kinetic-scale plasma instability in the plasma shear flows with relativistic bulk speed. We refer to this sequence of kinetic plasma phenomena as “MI-driven MR.” The MI-driven MRs intermittently occur with moving the location of the reconnection points from the vicinity of the initial velocity-shear surface toward the center of the jet. As a consequence, the number density of high-energy electrons that are accelerated by MI-driven MRs increases with time in the region inside the initial velocity-shear surface with the accompanying generation and subsequent amplification of magnetic fields by MI. The maximum Lorentz factor of electrons increases with initial bulk Lorentz factor of the jet. A possible relation of MI-driven MR to the bright synchrotron emission in the jet spine of an active galactic nucleus jet is also discussed.

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)].

The role of magnetic islands in collisionless driven reconnection has been investigated from the standpoint of a kinetic approach to multi-scale phenomena by means of two-dimensional particle-in-cell (PIC) simulation. There are two different types of the solutions in the evolution of the reconnection system. One is a steady solution in which the system relaxes into a steady state, and no island is generated (the no-island case). The other is an intermittent solution in which the system does not reach a steady state, and magnetic islands are frequently generated in the current sheet (the multi-island case). It is found that the electromagnetic energy is more effectively transferred to the particle energy in the multi-island case compared with the no-island case. The transferred energy is stored inside the magnetic island in the form of the thermal energy through compressional heating, and is carried away together with the magnetic island from the reconnection region. These results suggest that the formation of a magnetic island chain may have a potential to bridge the energy gap between macroscopic and microscopic physics by widening the dissipation region and strengthening the energy dissipation rate.

A theoretical model and an analytic theory of current sheet structure are presented for understanding anti-parallel driven magnetic reconnection in 2-1/2 dimension in collisionless plasmas. The theoretical model provides formulation to compute the current sheet y-profiles by specifying the profiles of electron and ion flow velocities $V_{ex}(x,y)$ and $V_{ix}(x,y)$ . The current sheet solutions depend on the plasma density n_in, merging magnetic field B₀, ion velocity v_i, and electron velocity v_e in the upstream and the $S_{\mathit{evz}}=V_{ez}/V_{dz}$ parameter where V_ez is the electron velocity accelerated by the reconnection electric field E_z in the electron orbit meandering region, $V_{dz}\simeq c{E}_y/B_x$ is the $\overrightarrow{E}\times \overrightarrow{B}$ drift velocity as electrons enter the orbit meandering region, B_x is the merging magnetic field, and E_y is the electrostatic electric field. With simplifying assumptions on the y-profiles of V_ex and V_ix, we have also developed an analytic theory of the current sheet structure. Analytic expressions for the anomalous resistivity, the electrostatic potential drop, and the maximum E_y amplitude E_max are obtained. The analytic results agree reasonably well with both the particle-in-cell simulation results and the numerical solutions of the theoretical model. The ions energy gain due to the potential drop is $\propto B_0^2/n_{in}$ . The electron energy gain is $\propto (B_0^2/8\pi n_{in})S_{\mathit{evz}}$ . The $B_0^2/n_{in}$ scaling of the average ion and electron energy gains are consistent with laboratory experiments and space plasma observations.

Multi-hierarchy simulation models aimed at analysis of magnetic reconnection were developed. Based on the real-space decomposition method, the simulation domain consists of three parts: a magnetohydrodynamics (MHD) domain, a particle-in-cell (PIC) domain, and an interface domain to communicate MHD and PIC data. In this paper, the previous model (the 1D interlocking with the upstream condition) by the authors is improved to three types of new models, i.e., two types of the 1D interlocking with the downstream condition and one type of the 2D interlocking with the upstream condition. For their verification, simulations of plasma propagation across the multiple domains were performed in the multi-hierarchy models, and it was confirmed that the new interlocking methods are physically correct.