Structure of the quasi‐parallel bow shock: Results of numerical simulations

Quasi‐parallel bowshock structures are simulated by using a one‐dimensional nonperiodic hybrid code in which the ion dynamics are treated exactly while the electron dynamics are omitted by neglecting the electron inertia ( m e = 0) and pressure. The simulations are initialized with the upstream condition specified by θ 1 = 10°, β 1 = 0.5, and M A1 = 2 to 4 with 0.5 increment while the downstream condition is obtained from the Rankine‐Hugoniot relations, where θ 1 is the angle between the shock normal and the magnetic field, β 1 is the ratio of kinetic to magnetic pressures, and M A1 is the Alfvén Mach number. The main results of our simulations follow: (1) For M A1 , < 3, the magnetic field profile of the shock is laminar or quasi‐laminar. The upstream waves are right‐hand polarized whistlers with ω ≃ 3.2Ω ni in the plasma frame, where Ω ni is the ion gyrofrequency based on the normal field component B n . This corresponds to a wave frequency ƒ ≃ 0.25 Hz and wavelength λ ≃ 310 km under solar wind conditions. The downstream waves are absent or low in amplitudes. (2) For M A1 > 3, the magnetic field profile of the shock is turbulent. The upstream waves are again right‐hand polarized whistlers with wavelengths varying from λ ∼ 310 km upstream to λ ≳ 1250 km downstream. The downstream waves are predominantly the right‐hand polarized fast magnetosonic waves (ω ≲ Ω i ). (3) The transition from the laminar (subcritical) to the turbulent (supercritical) shock structures is shown to result from the firehose instability which occurs when M A1 ≳ 3. (4) The dissipation mechanism for the quasi‐parallel shock in our simulation is identified with the nonadiabatic compression of ions streaming through the low frequency whistler waves (ω ≳ Ω i ), resulting in conversion of ion streaming energy to ion thermal energy. (5) Significant ion heat flux flowing upstream occurs when M A1 ≳ 3 due primarily to the backscattering of highly nonadiabatically heated ions.

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