Probing Heliospheric Turbulence with Cosmic Rays: Theory - de Koning, Curt A; Bieber, John W (The Astrophysical journal, 2004)
Cosmic rays impacting a spacecraft have already passed through and interacted with the turbulent solar wind surrounding the spacecraft; therefore, they carry information on the three-dimensional structure of the turbulence. In particular, the simple, unlagged correlation between the magnetic fluctuations and fluctuations of the cosmic-ray flux can potentially provide unique information on the detailed nature of interplanetary magnetic turbulence. Starting with the Vlasov equation, subject to the usual quasi-linear approximations, we derive the leading-order approximation of the particle-field correlation for generalized axisymmetric turbulence geometry in a plasma flowing in an arbitrary direction with respect to the average magnetic field. This work presents the theoretical basis for interpreting future measurements of the particle-field correlation in the real solar wind. As an example, we apply the theory to mirror-symmetric magnetostatic slab turbulence and clearly show the effect of the fluctuating convection electric field.