Interplanetary Plasma Scattering Diagnostics from Anisotropy-time Profiles of Solar Energetic Particles

The anisotropy-time profile of solar particle events provides a powerful diagnostics tool to the interplanetary plasma scattering parameters of energetic charged particles. In the weak focusing limit of the transport of solar particles in axisymmetric MHD turbulence, the particle anisotropy consists of two contributions, the streaming and the ComptonGetting contribution, resulting from the parallel spatial gradient and the momentum gradient of the isotropic part of the particles’ phase space density, respectively. These gradients can be calculated from the appropriate solution to the timedependent focused transport equation of solar particles. For the illustrative case of the solution of the one-dimensional time-dependent focused transport equation with a constant focusing length and a point-like instantaneous injection of particles the streaming and Compton-Getting contributions to the anisotropy-time profile are analytically calculated in MHD turbulence consisting of isospectral undamped slab Alfven waves for equal magnetic helicity. The Compton-Getting contribution scales proportional to the ratio of interplanetary Alfven speed to solar particle speed, and therefore is much smaller than the streaming contribution for the observed mildly relativistic solar particles. After vanishing anisotropy values at times t < tM the streaming anisotropy suddenly attains its maximum value AS,max = 3 2 + (p) 2L at tM = t0 + (z z0)/v. At later times the streaming anisotropy decreases (t t0) 1 approaching the asymptotic finite value ( (p)/2L) for t t0 , positive or negative, depending on the sign of the focusing length L. The new analytical form of the streaming anisotropy provides an excellent fit to the observed anisotropy profiles from the easter solar particle event of 2001 April 15 for 1.3 GeV protons, but does not well reproduce the anisotropies of 510 keV electrons.