Ken-Ichi Nishikawa

Three-dimensional Relativistic Magnetohydrodynamic Simulations of Magnetized Spine-Sheath Relativistic Jets

Numerical simulations of weakly and strongly magnetized relativistic jets embedded in a weakly magnetized and strongly magnetized stationary or weakly relativistic (v = c/2) sheath have been performed. A magnetic field parallel to the flow is used in these simulations performed by the new general relativistic magnetohydrodynamic numerical code RAISHIN used in its relativistic magnetohydrodynamic (RMHD) configuration. In the numerical simulations, the Lorentz factor ? = 2.5 jet is precessed to break the initial equilibrium configuration. In the simulations, sound speeds are c/ in the weakly magnetized simulations and 0.3c in the strongly magnetized simulations. The Alfv?n wave speed is 0.07c in the weakly magnetized simulations and 0.56c in the strongly magnetized simulations. The results of the numerical simulations are compared to theoretical predictions from a normal mode analysis of the linearized RMHD equations capable of describing a uniform axially magnetized cylindrical relativistic jet embedded in a uniform axially magnetized relativistically moving sheath. The theoretical dispersion relation allows investigation of effects associated with maximum possible sound speeds, Alfv?n wave speeds near light speed, and relativistic sheath speeds. The prediction of increased stability of the weakly magnetized system resulting from c/2 sheath speeds and the stabilization of the strongly magnetized system resulting from c/2 sheath speeds is verified by the numerical simulation results.

Production of Magnetic Turbulence by Cosmic Rays Drifting Upstream of Supernova Remnant Shocks

We present results of two- and three-dimensional particle-in-cell simulations of magnetic turbulence production by isotropic cosmic-ray ions drifting upstream of supernova remnant shocks. The studies aim at testing recent predictions of a strong amplification of short-wavelength magnetic field and at studying the subsequent evolution of the magnetic turbulence and its back-reaction on cosmic-ray trajectories. For our parameters an oblique filamentary mode grows more rapidly than nonresonant parallel modes analytically found in the limit -->? ?i, and the growth rate is slower than is estimated for the parallel plane wave mode. The evolved oblique filamentary mode was also observed in MHD simulations to dominate in the nonlinear phase, when the structures are already isotropic. We thus confirm the generation of the turbulent magnetic field due to the drift of cosmic-ray ions in the upstream plasma, but as our main result find that the amplitude of the turbulence saturates at about -->?B/B ~ 1. The back-reaction of the magnetic turbulence on the particles leads to an alignment of the bulk flow velocities of the cosmic rays and the background medium, which accounts for the saturation of the instability at moderate amplitudes of the magnetic field. Previously published MHD simulations have assumed a constant cosmic-ray current and no energy or momentum flux in the cosmic rays, which excludes a back-reaction of the generated magnetic field on cosmic rays, and thus the saturation of the field amplitude is artificially suppressed. This may explain the continued growth of the magnetic field in the MHD simulations. A strong magnetic field amplification to amplitudes -->?B B0 has not been demonstrated yet.

THE INFLUENCE OF AN AMBIENT MAGNETIC FIELD ON RELATIVISTIC COLLISIONLESS PLASMA SHOCKS

Plasma outflows from gamma-ray bursts, supernovae, and relativistic jets, in general, interact with the surrounding medium through collisionless shocks. The microphysics of such shocks are still poorly understood, which, potentially, can introduce uncertainties in the interpretation of observations. It is now well established that the Weibel two-stream instability is capable of generating strong electromagnetic fields in the transition region between the jet and the ambient plasma. However, the parameter space of collisionless shocks is vast and still remains unexplored. In this Letter, we focus on how an ambient magnetic field affects the evolution of the electron Weibel instability and the associated shock. Using a particle-in-cell code, we have performed three-dimensional numerical experiments on such shocks. We compare simulations in which a jet is injected into an unmagnetized plasma with simulations in which the jet is injected into a plasma with an ambient magnetic field both parallel and perpendicular to the jet flow. We find that there exists a threshold of the magnetic field strength below which the Weibel two-stream instability dominates, and we note that the interstellar medium magnetic field strength lies well below this value. In the case of a strong magnetic field parallel to the jet, the Weibel instability is quenched. In the strong perpendicular case, ambient and jet electrons are strongly accelerated because of the charge separation between deflected jet electrons and less deflected jet ions. Also, the electromagnetic topologies become highly nonlinear and complex with the appearance of antiparallel field configurations.

THREE-DIMENSIONAL RELATIVISTIC MAGNETOHYDRODYNAMIC SIMULATIONS OF CURRENT-DRIVEN INSTABILITY. I. INSTABILITY OF A STATIC COLUMN

We have investigated the development of current-driven (CD) kink instability through three-dimensional relativistic magnetohydrodynamic simulations. A static force-free equilibrium helical magnetic configuration is considered in order to study the influence of the initial configuration on the linear and nonlinear evolution of the instability. We found that the initial configuration is strongly distorted but not disrupted by the kink instability. The instability develops as predicted by linear theory. In the nonlinear regime, the kink amplitude continues to increase up to the terminal simulation time, albeit at different rates, for all but one simulation. The growth rate and nonlinear evolution of the CD kink instability depend moderately on the density profile and strongly on the magnetic pitch profile. The growth rate of the kink mode is reduced in the linear regime by an increase in the magnetic pitch with radius and reaches the nonlinear regime at a later time than the case with constant helical pitch. On the other hand, the growth rate of the kink mode is increased in the linear regime by a decrease in the magnetic pitch with radius and reaches the nonlinear regime sooner than the case with constant magnetic pitch. Kink amplitude growth in the nonlinear regime for decreasing magnetic pitch leads to a slender helically twisted column wrapped by magnetic field. On the other hand, kink amplitude growth in the nonlinear regime nearly ceases for increasing magnetic pitch.

Solar wind-magnetosphere interaction as simulated by a 3-D EM particle code

We have studied the solar wind-magnetosphere interaction using a 3-D electromagnetic particle code. The results for an unmagnetized solar wind plasma streaming past a dipole magnetic field show the formation of a magnetopause and a magnetotail, the penetration of energetic particles into cusps and radiation belt and dawn-dusk asymmetries. The effects of interplanetary magnetic field (IMF) have been investigated in a similar way as done by MHD simulations. The simulation results with a southward IMF show the shrunk magnetosphere with great particle entry into the cusps and nightside magnetosphere. This is a signature of a magnetic reconnection at the dayside magnetopause. After a quasi-stable state is established with an unmagnetized solar wind we switched on a solar wind with an northward IMF. In this case the significant changes take place in the magnetotail. The waving motion was seen in the magnetotail and its length was shortened. This phenomena are consistent with the reconnections which occur at the high latitude magnetopause. In our simulations kinetic effects will determine the self-consistent anomalous resistivity in the magnetopause that causes reconnections.

THREE-DIMENSIONAL RELATIVISTIC MAGNETOHYDRODYNAMIC SIMULATIONS OF CURRENT-DRIVEN INSTABILITY WITH A SUB-ALFVENIC JET: TEMPORAL PROPERTIES

We have investigated the influence of a velocity shear surface on the linear and nonlinear development of the current-driven (CD) kink instability of force-free helical magnetic equilibria in three dimensions. In this study, we follow the temporal development within a periodic computational box and concentrate on flows that are sub-Alfvenic on the cylindrical jets axis. Displacement of the initial force-free helical magnetic field leads to the growth of CD kink instability. We find that helically distorted density structure propagates along the jet with speed and flow structure dependent on the radius of the velocity shear surface relative to the characteristic radius of the helically twisted force-free magnetic field. At small velocity shear surface radius, the plasma flows through the kink with minimal kink propagation speed. The kink propagation speed increases as the velocity shear radius increases and the kink becomes more embedded in the plasma flow. A decreasing magnetic pitch profile and faster flow enhance the influence of velocity shear. Simulations show continuous transverse growth in the nonlinear phase of the instability. The growth rate of the CD kink instability and the nonlinear behavior also depend on the velocity shear surface radius and flow speed, and the magnetic pitch radial profile. Larger velocity shear radius leads to slower linear growth, makes a later transition to the nonlinear stage, and with larger maximum amplitude than that occuring for a static plasma column. However, when the velocity shear radius is much greater than the characteristic radius of the helical magnetic field, linear and nonlinear development can be similar to the development of a static plasma column.

THREE-DIMENSIONAL RELATIVISTIC MAGNETOHYDRODYNAMIC SIMULATIONS OF CURRENT-DRIVEN INSTABILITY. III. ROTATING RELATIVISTIC JETS

We have investigated the influence of jet rotation and differential motion on the linear and nonlinear development of the current-driven (CD) kink instability of force-free helical magnetic equilibria via three-dimensional relativistic magnetohydrodynamic simulations. In this study, we follow the temporal development within a periodic computational box. Displacement of the initial helical magnetic field leads to the growth of the CD kink instability. We find that, in accordance with the linear stability theory, the development of the instability depends on the lateral distribution of the poloidal magnetic field. If the poloidal field significantly decreases outward from the axis, then the initial small perturbations grow strongly, and if multiple wavelengths are excited, then nonlinear interaction eventually disrupts the initial cylindrical configuration. When the profile of the poloidal field is shallow, the instability develops slowly and eventually saturates. We briefly discuss implications of our findings for Poynting-dominated jets.

THREE-DIMENSIONAL RELATIVISTIC MAGNETOHYDRODYNAMIC SIMULATIONS OF CURRENT-DRIVEN INSTABILITY. II. RELAXATION OF PULSAR WIND NEBULA

We have investigated the relaxation of a hydrostatic hot plasma column containing toroidal magnetic field by the current-driven (CD) kink instability as a model of pulsar wind nebulae. In our simulations, the CD kink instability is excited by a small initial velocity perturbation and develops a turbulent structure inside the hot plasma column. We demonstrate that, as envisioned by Begelman, the hoop stress declines and the initial gas pressure excess near the axis decreases. The magnetization parameter σ, the ratio of the Poynting to the kinetic energy flux, declines from an initial value of 0.3 to about 0.01 when the CD kink instability saturates. Our simulations demonstrate that axisymmetric models strongly overestimate the elongation of the pulsar wind nebulae. Therefore, the previous requirement for an extremely low pulsar wind magnetization can be abandoned. The observed structure of the pulsar wind nebulae does not contradict the natural assumption that the magnetic energy flux still remains a good fraction of the total energy flux after dissipation of alternating fields.

Coalescence of two parallel current loops in a nonrelativistic electron–positron plasma

The coalescence of two parallel current loops in an electron–positron plasma is investigated by a three‐dimensional electromagnetic relativistic particle code. Instead of mixing uniformly in the dissipation region as observed for current coalescence in an electron–ion plasma, electrons and positrons initially in the loops are driven to move separately by the magnetic gradient drift. Redistribution of the current‐carrying electrons and positrons creates new current loops, which coalesce again, if the initial drift velocities remain greater than a critical value after coalescence. It was found that the energy stored in the current loops dissipates gradually through several coalescences. Consequently, the electrons and positrons near the current loops are heated through the coalescence. This process is qualitatively different from the explosive energy release during coalescence in an electron–ion plasma.

MAGNETIC-FIELD AMPLIFICATION BY TURBULENCE IN A RELATIVISTIC SHOCK PROPAGATING THROUGH AN INHOMOGENEOUS MEDIUM

We perform two-dimensional relativistic magnetohydrodynamic simulations of a mildly relativistic shock propagating through an inhomogeneous medium. We show that the postshock region becomes turbulent owing to preshock density inhomogeneity, and the magnetic field is strongly amplified due to the stretching and folding of field lines in the turbulent velocity field. The amplified magnetic field evolves into a filamentary structure in two-dimensional simulations. The magnetic energy spectrum is flatter than the Kolmogorov spectrum and indicates that a so-called small-scale dynamo is occurring in the postshock region. We also find that the amount of magnetic-field amplification depends on the direction of the mean preshock magnetic field, and the timescale of magnetic-field growth depends on the shock strength.