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.
The Quasi-Perpendicular Bow Shock as a Temporal Trapping Barrier and Accelerator of Magnetospheric Particles
The bow shock has been studied so far, mostly as a boundary that influences the particles that are incident from the upstream region (of solar origin). In this paper, we provide, for the first time, observational evidence from the energetic-particle-experiment and the charged-particle-measurement-experiment instruments onboard the IMP-8 spacecraft, showing that ions leaking from the magnetosphere, during storms or substorms, are affected by the quasi-perpendicular (Q-P) bow shock and can be temporally trapped just downstream from the shock in a magnetic configuration opposite to the magnetic mirror. The observations from three representative event periods examined in this paper suggest that magnetospheric energetic ( keV) ions show general flows along the field lines in the direction from the magnetosheath toward the interplanetary space, in both sides of the shock (up- and downstream), and characteristic cross-field anisotropic distributions just downstream from the shock, consistent with a ldquotrapped population.rdquo In a series of successive bow-shock crossings within several hours, the IMP-8 spacecraft observed intensity gradients toward the magnetosheath, which strongly suggest a spatial modulation of magnetospheric ion fluxes at the Q-P bow shock. Highest peaks of ion intensities and a very hard spectrum in the energy range between 100 and 400 keV were observed just at the shock front, which suggest acceleration of magnetospheric particles during their temporal trapping at the bow shock. The observations near the Earth's bow shock examined in this paper are well explained in terms of the shock drift acceleration (SDA) theory for magnetospheric particles reaching the bow shock. The phenomenon discussed here, an apparent temporal trapping-and acceleration-of escaped magnetospheric ions at the Earth's bow shock, appears to be an important mechanism that influences the particle distributions near the Earth's bow shock and may have important applications to other shocks in our solar system (planetary, heliospheric, interplanetary, and corotating shock waves) and the interstellar medium (supernova shocks).
NUMBER OF TRIANGULATIONS OF A MÖBIUS STRIP
Consider a Möbius strip with n chosen points on its edge. A triangulation is a maximal collection of arcs among these points and cuts the strip into triangles. In this paper, we proved the number of all triangulations that one can obtain from a Möbius strip with n chosen points on its edge is given by 4n−1 + (2n−2 n−1 ) , then we made the connection with the number of clusters in the quasi-cluster algebra arising from the Möbius strip.