Perturbation of the solar wind in a model terrestrial foreshock

Abstract

We analyze the perturbation of the solar wind in the earth's foreshock. The foreshock is modeled as a planar magnetic flux tube having a 15 RE half width. Within the flux tube the upstream energetic particle pressure is assumed to fall monotonically to zero at the flux tube boundary and decline in the upstream direction with a scale length of 8 RE. The incident solar wind is assumed to flow uniformly with a velocity of 400 km s−1, a density of 8 cm−3, a pressure of 50 eV cm−3, and a magnetic field of 4γ directed parallel to the flow. The solar wind density, velocity, and magnetic field within the foreshock are described by the steady state ideal MHD equations. We find that (1) the vector solar wind velocity perturbation rotates from the sunward to the transverse direction with increasing distance from the axis of the flux tube, (2) the peak solar wind deflection is located ∼3 RE within the flux tube boundary, (3) a central upstream pressure of 200 eV cm−3 produces a maximum deceleration of 6 km s−1 and a maximum deflection of 1.3°, (4) a central upstream pressure of 600 eV cm−3 produces a maximum deceleration of 19 km s−1 and a maximum deflection of 3.6°, and (5) the deflection and deceleration are accompanied by perturbations of the solar wind density and magnetic field. These perturbations are largest near the flux tube boundary where both form spikes having a width of ∼2 RE. For a 600 eV cm−3 central pressure those spikes have amplitudes of 2 cm−3 and 1γ, respectively. We have analyzed the linearized flow problem analytically and reduced the solutions to quadrature. These solutions are found to be good approximations to the numerical nonlinear solutions for moderate values of the upstream particle pressure.