Ultra low Frequency Waves and Energetic Particles Upstream of Earth's Quasi-Parallel Bow Shock: Cluster Observations

Upstream of Earth's quasi-parallel bow shock ultra low frequency waves and energetic particles are intrinsically connected: bow shock accelerated particles streaming away from the shock constitute a free energy source for beam instabilities and the resulting ULF waves scatter the particles back to the shock, thus leading to diffuse shock acceleration. We have investigated the dependence of the power in the low frequency magnetic field fluctuations parallel and perpendicular to the average magnetic field in the quasi-parallel bow shock region as a function of distance from the shock along the magnetic field line between spacecraft and intersection with the shock. During one particular upstream event the distance dependence has been investigated over about 7 Earth radii. The power has been evaluated at the resonant frequency of energetic particles of various energies. The power at the resonant frequency of field aligned beams (FAB) is constant as a function of distance indicating that these waves are convected by the solar wind from the region close to the foreshock boundary into the quasi-parallel region of the shock. The power of compressional fluctuations which are resonant with higher energy diffuse ions increases exponentially with decreasing distance from the shock, while the transverse wave energy density is independent of distance from the shock. The energetic particle energy density increases exponentially with decreasing distance from the shock. The importance of these results concerning diffusive shock acceleration theories will be discussed.