Energy time dispersion of a new class of magnetospheric ion events observed near the Earth’s bow shock
We have analyzed high time resolution (≥6 s) data during the onset and the decay phase of several energetic (≥35 keV) ion events observed near the Earth’s bow shock by the CCE/AMPTE and IMP-7/8 spacecraft, during times of intense substorm/geomagnetic activity. We found that forward energy dispersion at the onset of events (earlier increase of middle energy ions) and/or a delayed fall of the middle energy ion fluxes at the end of events are often evident in high time resolution data. The energy spectra at the onset and the decay of this kind of events show a characteristic hump at middle (50–120 keV) energies and the angular distributions display either anisotropic or broad forms. The time scale of energy dispersion in the ion events examined was found to range from several seconds to ∼1 h depending on the ion energies compared and on the rate of variation of the Interplanetary Magnetic Field (IMF) direction. Several canditate processes are discussed to explain the observations and it is suggested that a rigidity dependent transport process of magnetospheric particles within the magnetosheath is most probably responsible for the detection of this new type of near bow shock magnetospheric ion events. The new class of ion events was observed within both the magnetosheath and the upstream region.
Dominant Acceleration Processes of Energetic Protons at the Earth's Bow Shock
We examined magnetic field and energetic (E ≥ 30 keV) proton and (E ≥ 220 keV) electron observations obtained by the spacecraft IMP-6, 7, and 8 in the vicinity of both the (quasi-) parallel and (quasi-) perpendicular bow shock of the Earth. The observations analysed show that: (a) for a quasi-perpendicular (45 ≤ θBn 50 keV ion events is not a continuous phenomenon, but is strongly correlated with the substorm activity of the magnetosphere. The above observations along with other previously published observations are discussed in the context of the Shock Drift Acceleration (SDA) and the Diffusive (1st order Fermi) acceleration theories. We infer that: (a) a seed population of superthermal (energetic) protons are accelerated to higher energies at the oblique (quasi-perpendicular) bow shock via the SDA process, and (b) there is no convincing evidence for acceleration of either the solar wind or ambient energetic ions to energies 30–50 keV via the Fermi acceleration process.
The parallel waveform relaxation stochastic Runge–Kutta method for stochastic differential equations
For large-scale non-autonomous Stratonovich stochastic differential equations, we study a very general parallel waveform relaxation process which is on the basis of stochastic Runge–Kutta (SRK) method of mean-square order 1.0 in this literature. The convergence of the whole parallel numerical iterative scheme can be guaranteed and the scheme provides better properties in terms of decreasing the load of the computation and operating speed. At the same time, the related limit method is also introduced as the continuous approximation derived from the iterative scheme. In the approximation interval, it is worth noting that the mean-square order of the parallel numerical iterative scheme can be kept consistent with the previous SRK method at any arbitrary time point, not just at discrete points. Some numerical simulations are presented to elaborate the computing efficiency of the parallel numerical iterative scheme.