Yukiharu Ohsawa

Parallel electric fields in nonlinear magnetosonic waves

The electric field parallel to the magnetic field, E‖, in nonlinear magnetosonic waves is studied theoretically and numerically. In the calculation of E‖ based on the conventional reductive perturbation method, the terms related to the magnetic pressure cancel, and E‖ is proportional to the electron temperature Te. With a modified perturbation scheme assuming that the wave amplitude is in the range (me∕mi)1∕2<ϵ<1, an expression for E‖ is obtained that is proportional to the magnetic pressure in a cold plasma. Its integral along the magnetic field, F=−∫E‖ds, is proportional to ϵ2mivA2. One-dimensional, fully kinetic, electromagnetic particle simulations verify the theoretical predictions for small-amplitude waves. Further, they demonstrate that eF becomes of the order of ϵ(mivA2+ΓeTe) in large-amplitude [ϵ∼O(1)] oblique shock waves. These theory and simulations indicate that E‖ in magnetosonic waves can be strong in a strong magnetic field.

Parallel electric fields in nonlinear magnetosonic waves in an electron-positron-ion plasma

The electric field E∥ along the magnetic field B in nonlinear magnetosonic waves in a three-component plasma is studied with theory based on a three-fluid model and with fully kinetic, electromagnetic, particle simulations. The theory for small-amplitude (ϵ⪡1) pulses shows that the integral of E∥ along B, F=−∫E∥ds, is proportional to ϵ(pe0−pp0) in warm plasmas, where pe0 and pp0 are, respectively, the electron and positron pressures, and proportional to ϵ2mivA2∕(1+vA2∕c2)3 in cold plasmas, where vA is the Alfven speed. These predictions are verified with simulations. Furthermore, for shock waves with ϵ∼O(1), simulation values are consistent with the phenomenological relation ne0eF∼ϵ(ρvA2+Γepe0)(ni0∕ne0), where ρ is the mass density and Γe is the specific heat ratio. These results indicate that E∥ can be strong in strong magnetic fields.

The effect of parallel electric field in shock waves on the acceleration of relativistic ions, electrons, and positrons

The effect of an electric field E∥ parallel to the magnetic field B on particle acceleration in shock waves is studied. With test particle calculations, for which the electromagnetic fields of shock waves are obtained from one-dimensional, fully kinetic, electromagnetic, particle simulations, the motions of relativistic ions, electrons, and positrons are analyzed. In these simulations, the shock speed vsh is taken to be close to cu2009cosu2009θ, where θ is the angle between the external magnetic field and wave normal, and thus strong particle acceleration takes place. Test particle motions calculated in two different methods are compared: In the first method the total electric field E is used in the equation of motion, while in the second method E∥ is omitted. The comparison confirms that in the acceleration of relativistic ions E∥ is unimportant for high-energy particles. For the acceleration of electrons and positrons, however, E∥ is essential.

Effect of ion composition on ion acceleration by magnetosonic shock waves

The study of heavy-ion acceleration by magnetosonic shock waves in multi-ion-species plasmas [M. Toida and Y. Ohsawa, Solar Physics 171, 161 (1997)] is extended to the case in which the ion masses are of the same order of magnitude; specifically, the effect of mass and density ratios is examined for H-T and D-T plasmas with three-dimensional, electromagnetic, particle simulations. The frequency difference Δω, where Δω=(ω+0−ω−r)∕ω+0 with ω+0 the cut-off frequency of the high-frequency magnetosonic mode and ω−r the resonance frequency of the low-frequency mode, is a key parameter in the generation of shock waves from a disturbance. In H-T plasmas with nH⪡nT and with nH⪢nT and in D-T plasmas with any density ratio, Δω is small, and the high-frequency-mode shock wave is mainly generated and plays a central role in ion energization processes. In H-T plasmas with nH=nT, for which Δω is much greater, both the high- and low-frequency-mode shock waves are generated and contribute to the acceleration.

Effect of Ion Composition on Magnetosonic Waves

The propagation of the two types of fast magnetosonic waves, i.e., low- and high-frequency modes, in a two-ion-species plasma is studied theoretically and numerically. It is analytically found that the KdV equation for the low-frequency mode is valid for amplitudes e 2Δ ω . With electromagnetic particle simulations, the evolution of the low- and high-frequency-mode pulses is investigated for various density and cyclotron frequency ratios and is compared with theoretical predictions. In particular, it is shown that high-frequency-mode pulses are generated from a long-wavelength low-frequency-mode pulse if its amplitude e exceeds 2Δ ω .

Damping of magnetohydrodynamic disturbances in multi-ion-species plasmas

The evolution of macroscopic magnetohydrodynamic disturbances across a magnetic field is studied, with particular attention to the effect of multiple ion species. Analyses are carried out on disturbances where the initial magnetic profiles are sinusoidal. Both the theory and electromagnetic simulations show that, in a single-ion-species plasma, the disturbance is undamped, with its energy oscillating between the magnetic field and ion velocity. In a multi-ion-species plasma, however, it is initially damped, owing to the phase mixing of the magnetosonic mode and the modes having ion-ion hybrid cutoff frequencies. Furthermore, it is found from long-time simulations that the amplitude of the disturbance continues to decrease in a multi-ion-species plasma. This is due to nonlinear mode couplings. The magnetic energy is irreversibly transferred to the ions.

Detrapping of Energetic Electrons from Curved Shock Front

The effect of the curvature of a shock front on electron trapping is investigated by means of a two-dimensional, fully kinetic, relativistic, electromagnetic particle code. Electron trapping and acceleration are observed even in a cylindrical shock wave in an external magnetic field B 0 . Furthermore, unlike that in the case of planar shock waves in a uniform B 0 , a significant fraction of trapped electrons can escape from the wave maintaining their ultrarelativistic energies. Such detrapping is due to the curvature of the shock front, i.e., the angle between the wave normal and B 0 varies along the trajectory of a trapped particle. The detrapping in a planar shock wave in a nonuniform magnetic field is also shown with one-dimensional simulations.

Shock Formation in a Collision of Two Plasmas with Their Relative Velocity Oblique to the Magnetic Field

Shock formation processes arising from a collision of two plasmas in an external magnetic field B 0 are studied with electromagnetic particle simulations, for the case in which one plasma (exploding plasma) has a high velocity v 0 while the other (surrounding plasma) is at rest with a lower density; the ion gyroradius for the speed v 0 is much greater than the width of the shock transition region. The ion motion across B 0 induces strong electric field in the direction - v 0 × B 0 , which accelerates the surrounding ions in this direction in the early phase. Then, the change in the velocities of the two groups of ions due to the magnetic force leads to the formation of two pulses near the front of the exploding ions, which evolve into forward and reverse shock waves. The effect of the angle θ between v 0 and B 0 on plasma behavior is examined. The two pulses appear in time of the order of the ion gyroperiod. As θ decreases from 90°, however, it takes a longer time for the two pulses to form.

Evolution of Magnetohydrodynamic Waves and Acceleration of Particles in a Collision of Two Plasmas

Electron acceleration in magnetohydrodynamic waves produced by a collision of two high-temperature plasmas in an external magnetic field B 0 is studied with particle simulations. First, possible particle motions that traverse multiple layers with alternating magnetic polarity are illustrated. Then, it is shown with one-dimensional, fully kinetic, relativistic, electromagnetic particle simulations that as a result of plasma collision, a large-amplitude Alfven wave packet can be formed behind a magnetosonic shock wave. In the wave packet with alternating magnetic polarity, some electrons exhibit orbits predicted by the physical considerations and are accelerated to high energies such that γ>100. It is thus found that the Alfven wave packet as well as the magnetosonic shock wave can create ultrarelativistic particles with its strong wave fields.

Numerical studies on ultrarelativistic ion motions in an oblique magnetosonic shock wave

The motion of ultrarelativistic ions in an oblique magnetosonic shock wave is studied analytically and numerically. The zeroth-order theory predicts that an oblique shock wave can accelerate ions in the direction nearly parallel to the magnetic field if the shock speed is vsh∼cu2009cosu2009θ, where θ is the angle between the wave normal and the magnetic field, while the perturbation is a one-dimensional oscillation nearly perpendicular to the zeroth-order motion. The perturbation frequency ω is of the order of Ωi0γ−1/2, where γ is the Lorentz factor of the zeroth-order velocity. These theoretical predictions are examined with test particle simulations, in which the test particle orbits are calculated with use of the electromagnetic fields of a shock wave obtained from an electromagnetic particle simulation. The zeroth-order and perturbed motions in the simulations are explained by the theory.