Mean free path of low‐energy protons upstream of selected interplanetary shocks

There are two fundamentally different approaches in calculating the mean free path of energetic charged particles. The first approach is concerned with the particle data. Here measured time intensity profiles are fitted to theoretical models and a best fit value for the mean free path is obtained. For undisturbed propagation of solar particles this theoretical model usually is a numerical solution of a Fokker-Planck equation. In the case of quasi-parallel interplanetary shocks the mean free path can be determined from the exponential increase of the particles intensity in the upstream region of the shock. The second approach starts with the magnetic field properties. One often-applied model assumes that the scattering of the particles is due to Alfven waves that propagate along the guiding field. Here the particles are scattered resonantly by the components of the field fluctuations perpendicular to the guiding field. A second model assumes that a different type of magnetohydrodynamic wave, the magnetosonic wave, in addition to Alfven waves plays an important role in particle scattering. The scattering by magnetosonic waves is a nonresonant interaction. We discuss the time intensity profiles of low-energy protons (35–1600 keV) associated with interplanetary shocks observed by ISEE 3 during the period August 1978 to December 1981. For five shock-associated particle intensity increases, we calculate the amount of scattering upstream of the shock by fitting the intensity increase as an exponential in time. The anisotropy in the solar wind frame is analyzed. We hereby test the validity of our diffusion model. We compare the mean free paths obtained from the particle data with mean free paths derived from magnetic field data. Here we first calculate the amount of resonance scattering from the power density spectrum of the magnetic field fluctuations and then include the effect of magnetosonic waves. The main difference between these two models lies in the predicted rigidity dependence of the mean free path. For all five events, pure resonance scattering predicts mean free paths that increase with particle rigidity; this disagrees with the observed particle behavior. Quite good agreement is obtained by the model of a mixture of Alfven waves and magnetosonic waves; here a more complicated rigidity dependence is possible. Therefore we conclude that magnetosonic waves together with Alfven waves are responsible for scattering of particles, at least in the upstream region of interplanetary shocks.