Magnetic reconnection during collisionless, stressed, X-point collapse was studied using kinetic, 2.5D, fully electromagnetic, relativistic Particle-in-Cell numerical code. Two cases of weakly and strongly stressed X-point collapse were considered. Here descriptors weakly and strongly refer to 20 % and 124 % unidirectional spatial compression of the X-point, respectively. In the weakly stressed case, the reconnection rate, defined as the out-of-plane electric field in the X-point (the magnetic null) normalised by the product of external magnetic field and Alfvén speeds, peaks at 0.11, with its average over 1.25 Alfvén times being 0.04. During the peak of the reconnection, electron inflow into the current sheet is mostly concentrated along the separatrices until they deflect from the current sheet on the scale of electron skin depth, with the electron outflow speeds being of the order of the external Alfvén speed. Ion inflow starts to deflect from the current sheet on the ion skin depth scale with the outflow speeds about four times smaller than that of electrons. Electron energy distribution in the current sheet, at the high-energy end of the spectrum, shows a power law distribution with the index varying in time, attaining a maximal value of −4.1 at the final simulation time step (1.25 Alfvén times). In the strongly stressed case, magnetic reconnection peak occurs 3.4 times faster and is more efficient. The peak reconnection rate now attains value 2.5, with the average reconnection rate over 1.25 Alfvén times being 0.5. Plasma inflow into the current sheet is perpendicular to it, with the electron outflow seeds reaching 1.4 Alfvén external Mach number and ions again being about four times slower than electrons. The power law energy spectrum for the electrons in the current sheet attains now a steeper index of −5.5, a value close to the ones observed near X-type region in the Earth's magneto-tail. Within about one Alfvén time, 2% and 20% of the initial magnetic energy is converted into heat and accelerated particle energy in the case of weak and strong stress, respectively. In the both cases, during the peak of the reconnection, the quadruple out-of-plane magnetic field is generated, hinting possibly to the Hall regime of the reconnection. These results strongly suggest the importance of the collisionless, stressed X-point collapse as an efficient mechanism of converting magnetic energy into heat and super-thermal particle energy. I. MOTIVATION OF THE STUDYMagnetic reconnection is an important physical process, which serves as one of the possible ways of converting energy stored in the magnetic field into heat and nonthermal, accelerated, motion of plasma particles. This process operates virtually in all extra-galactic, stellar, solar, space and laboratory plasmas with varied degree of importance. For example, in solar and stellar flares magnetic reconnection plays a key role. In addition, it can be one of the main contributing factors to solar coronal heating problem amongst other mechanisms such as wave dissi...

Recently, magnetic reconnection during collisionless, stressed, X-point collapse was studied using kinetic, 2.5D, fully electromagnetic, relativistic Particle-in-Cell numerical code [D. Tsiklauri and T. Haruki, Phys. Plasmas 14, 112905 (2007)]. Here we finalise the investigation of this topic by addressing key outstanding physical questions: (i) which term in the generalised Ohm's law is responsible for the generation of the reconnection electric field? (ii) how does the time evolution of the reconnected flux vary with the ion-electron mass ratio? (iii) what is the exact energy budget of the reconnection process, i.e. in which proportion initial (mostly magnetic) energy is converted into other forms of energy? (iv) are there any anisotropies in the velocity distribution of the accelerated particles? It has been established here that: (i) reconnection electric field is generated by the electron pressure tensor off-diagonal terms, resembling to the case of tearing unstable Harris current sheet studied by the GEM reconnection challenge; (ii) For mi/me ≫ 1 the time evolution of the reconnected flux is independent of ion-electron mass ratio; also, in the case of mi/me = 1 we show that reconnection proceeds slowly as the Hall term is zero; when mi/me ≫ 1 (i.e. the Hall term is non-zero) reconnection is fast and we conjecture that this is due to magnetic field being frozen into electron fluid, which moves significantly faster than ion fluid; (iii) within one Alfvén time, somewhat less than half (∼ 40%) of the initial total (roughly magnetic) energy is converted into the kinetic energy of electrons, and somewhat more than half (∼ 60%) into kinetic energy of ions (similar to solar flare observations); (iv) in the strongly stressed X-point case, in about one Alfvén time, a full isotropy in all three spatial directions of the velocity distribution is seen for super-thermal electrons (also commensurate to solar flare observations).

Previous studies of phase mixing of ion cyclotron (IC), Alfv\'enic, waves in the collisionless regime have established the generation of parallel electric field and hence acceleration of electrons in the regions of transverse density inhomogeneity. However, outstanding issues were left open. Here we use 2.5D, relativistic, fully electromagnetic PIC (Particle-In-Cell) code and an analytic MHD (Magnetohydrodynamic) formulation, to establish the following points: (i) Using the generalised Ohm's law we find that the parallel electric field is supported mostly by the electron pressure tensor, with a smaller contribution from the electron inertia term. (ii) The generated parallel electric field and the fraction of accelerated electrons are independent of the IC wave frequency remaining at a level of six orders of magnitude larger than the Dreicer value and approximately 20% respectively. The generated parallel electric field and the fraction of accelerated electrons increase with the increase of IC wave amplitude. The generated parallel electric field seems to be independent of plasma beta, while the fraction of accelerated electrons strongly increases with the decrease of plasma beta (for plasma beta of 0.0001 the fraction of accelerated electrons can be as large as 47%). (iii) In the collisionless regime IC wave dissipation length (that is defined as the distance over which the wave damps) variation with the driving frequency shows a deviation from the analytical MHD result, which we attribute to a possible frequency dependence of the effective resistivity. (iv) Effective anomalous resistivity, inferred from our numerical simulations, is at least four orders of magnitude larger than the classical Spitzer value.Comment: Final version, accepted for publication in Physics of Plasma

High-energy particles of a few hundred keV for electrons and up to MeV for ions were observed in a plasma focus device. Haruki et al. [Phys. Plasmas 13, 082106–1 (2006)] studied the mechanism of high-energy particle production in pinched plasma discharges by use of a 3D relativistic and fully electromagnetic particle-in-cell code. It was found that the pinched current is unstable against a sausage instability, and then becomes unstable against a kink instability. As a result high-energy electrons were observed, but protons with MeV energies were not observed. In this paper the same pinch dynamics as Haruki and co-workers is investigated, focusing on the shock formation and the shock acceleration during the pinched current. It is found that a fast magnetosonic shock wave is produced during the pinching phase which, after the maximum pinch occurs, is strongly enhanced and propagates outwards. Some protons trapped in the electrostatic potential produced near the shock front can be accelerated to a few MeV by the surfatron acceleration mechanism. It is also found that the protons accelerated along the pinched axis have a ring-shaped angular distribution that is observed from numerous experiments.

In an experimental plasma, high-energy particles were observed by using a plasma focus device, to obtain energies of a few hundred keV for electrons, up to MeV for ions. In order to study the mechanism of high-energy particle production in pinched plasma discharges, a numerical simulation was introduced. By use of a three-dimensional relativistic and fully electromagnetic particle-in-cell code, the dynamics of a Z-pinch plasma, thought to be unstable against sausage and kink instabilities, are investigated. In this work, the development of sausage and kink instabilities and subsequent high-energy particle production are shown. In the model used here, cylindrically distributed electrons and ions are driven by an external electric field. The driven particles spontaneously produce a current, which begins to pinch by the Lorentz force. Initially the pinched current is unstable against a sausage instability, and then becomes unstable against a kink instability. As a result high-energy particles are observed.