Abstract The motion of cosmic rays and energetic particles in general is described via transport equations. If a pitch-angle dependent description is desired, a Fokker-Planck equation provides the basis for exploring the particle motion. To date, no exact and pure analytical solution to the two-dimensional cosmic ray Fokker-Planck equation has been found. Previous attempts are either solutions of the pitch-angle averaged equation or the space integrated equation. Of course, numerical calculations can easily be performed but those are not very useful in astrophysical applications. In the current paper we employ perturbation theory in order to solve the cosmic ray Fokker-Planck equation. Corrections up to fourth-order to the eigenvalues and second-order eigenfunctions are computed. Our results are compared with previous solutions. Furthermore, we discuss applications such as estimating higher order correlations occurring in analytical treatments of perpendicular transport.


    Access

    Check access

    Check availability in my library

    Order at Subito €


    Export, share and cite



    Title :

    Perturbation theory based solution of the pitch-angle dependent cosmic ray diffusion equation


    Contributors:
    Shalchi, A. (author) / Gammon, M. (author)

    Published in:

    Advances in Space Research ; 63 , 1 ; 653-664


    Publication date :

    2018-09-21


    Size :

    12 pages




    Type of media :

    Article (Journal)


    Type of material :

    Electronic Resource


    Language :

    English




    Pitch Angle Diffusion as Seen by CRRES

    Albert, J.M. | Online Contents | 2000


    Pitch Angle Diffusion as Seen by CRRES

    Albert, J. M. / International Council of Scientific Unions | British Library Conference Proceedings | 2000



    Trajectory Analysis of a Zero-Pitch-Angle E-Sail with Homotopy Perturbation Technique

    Niccolai, Lorenzo / Quarta, Alessandro A. / Mengali, Giovanni et al. | AIAA | 2022


    PITCH ANGLE CONTROL SYSTEM, PITCH ANGLE CONTROL METHOD, AND VEHICLE

    MIKI MASAYUKI | European Patent Office | 2015

    Free access