(Color) Top frame: Schematic slow shock structure in the tangential magnetic field showing the downstream wavetrain and the upstream Alfvén waves generated by the ion-ion streaming interaction. Middle and bottom frames: Results from a typical hybrid simulation of 1D slow shock with and . In the middle frame, the magnetic field profile is stacked in time (from bottom to top) during the time interval . The bottom frame displays the wave dispersion relation (on a log scale) in from the simulation. The low frequency, low phase velocity upstream-propagating waves are on the branch labeled “KAW.” A downstream wavetrain (seen on the left in the middle frame) also develops in the simulation.
(Color) KAW dispersion (bottom frame; on a log scale) and wave power spectrum as a function of wavenumber (top frame) obtained from parallel electric fields of a 1D PIC simulation of slow shock at and .
(Color) PIC (in color) and hybrid (black) simulations of a 1D slow shock at and . Displayed in (a) to (d) are profiles for the density as a function of , tangential magnetic field profiles and , and temperatures at . In (d), the upper three curves are parallel temperatures (black from hybrid and red from PIC) and (blue from PIC), whereas the lower three curves are perpendicular temperatures (black from hybrid and orange from PIC) and (green from PIC). Note that from the hybrid simulation (black) is covered for the most part by the lower orange and green curves. The bottom two frames in (e) and (f) are the phase-space distributions (on a log scale) for the electron and ion parallel velocities as function of at for the PIC shock, showing phase-space vortices in the ramp region between formed by electron resonant interactions with KAW and the slowing down of the backstreaming ions.
(Color) Top frame: Hybrid simulation of a 1D slow shock at with and . Displayed are the tangential magnetic field profiles during interval stacked in time (from the bottom to the top). Bottom frame shows ion and electron temperatures from a PIC simulation using the same slow shock parameters. Displayed are (upper black curve), (blue), (lower black), and (green) (at ).
(Color) PIC and hybrid simulations of a 1D slow shock at with low electron beta, . Displayed (black curves are from hybrid, curves in color are from PIC) from top to bottom are density as a function of , the magnetic field profiles and , and temperatures (at ). In the bottom frame, the upper three curves are parallel temperatures (black from hybrid and red from PIC) and (blue from PIC); the lower three curves are perpendicular temperatures (black from hybrid and orange from PIC) and (green from PIC).
(Color) Phase space vortices and velocity distributions from a PIC simulation of a slow shock at with . The middle two frames are electron and ion parallel velocity as function of at (on a log scale). The top and bottom frames are electron and ion velocity distributions reduced in the parallel direction (average over ), respectively, showing characteristic forms at various locations, as indicated at the top of each velocity distribution plot and marked near the axis of frame (f), at this time (overlaid with the initial distributions as shown by the dotted curves). Three forms of electron distributions are identified, i.e., the upstream-directed heat-flux distribution (a), the flat-topped (b), and the partially filled velocity space hole distribution (c), while the ion distribution exhibits a beamlet form due to the reduction of the backstreaming ion drift.
(Color) Phase-space vortices and velocity distributions from a highly oblique PIC 1D slow shock at with . The left four frames are electron and ion parallel velocities as function of at an early time and a later time (on a log scale). The right frames are electron (blue) and ion (red) parallel velocity distributions (overlaid with the initial distribution by the dotted curve) at various locations, as indicated at the top of each velocity distribution plot and marked near the axis of frames (a) and (c), at these two times (with the upper four frames at and the lower four at ). The flat-topped distribution (e), the partially filled velocity space hole distribution (f) and (i), and ion beamlet distributions (h), (k), and (l) are shown.
(Color) Wave dispersion relation from the parallel electric fields of the highly oblique PIC shock of Fig. 7. Displayed (on a log scale) are the upstream propagating KAWs (left-directed), as well as the downstream propagating (right-directed), higher frequency modes possibly generated from the velocity space hole distributions (see text for discussion of NEN).
Spiky structures in density and potential in the shock ramp from the simulation of Fig. 7. These profiles are nearly transverse to the local magnetic field in the shock ramp. Corresponding to the density maxima and minima in the shock ramp are the potential minima and maxima, respectively.
Article metrics loading...
Full text loading...