DIMENSIONAL METHOD TO SOLVE THE DIFFUSION CONVECTION EQUATION OF SOLAR COSMIC RAYS

  • Physical processes of the propagation of the solar cosmic rays in the interplanetary space include the diffusion in interplanetary disordered magnetic fields and the convection in solar winds. Dimensional method can be applied to solve those equations convertible into Bessel equation, the results obtained are identical with those solved by the commonly used separate variable method. In order to derive an analytic solution to the diffusion convection equation in an unbounded, uniform medium, two dimensionless parameters reflecting the diffusion and convection characteristics of the particles are introduced. In the diffusion dominated case, the solution is similar in form to the diffusion of a source moving with the convection velocity and is modified by another convection term, which can be expanded into a power series of the convection parameter with coefficients composed of the generalized hypergeometric function series of the diffusion parameter. This solution has a clear physical meaning, and can suitably be used in the discussion of the rise phase characteristics of the solar cosmic rays from medium to high energies (Ep≥101 MeV).
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  • [1] 章公亮,太阳宇宙线传播方程的解法,(内部报告,1974).[2] 爱尔台里主编,《高级超越函数》,(科学技术出版社,1958).[3] L. F. Burlaga, J. Geophys. Res., V. 72(1967), 4449.[4] L. A. Fisk, W. I. Axford, J. Geophys. Res., V. 73(1968), 4396.[5] J. Feit, J. Geopys. Res., V. 74(1969), 5579.[6] M. A. Forman, J. Geophys. Res., V. 76(1971), 759.[7] J. R. Jokipii, Rev. Geophys. Space Phys., V. 9(1971), 27.[8] S.M.Krimigis, J. Geophys. Res., V. 70(1965), 2943.[9] Y. L. Luke, Special Functions anal Their Approximations, V.1, V.2, (1969).[10] Y. L. Luke, Integrals of Bessel Functions, (1962).[11] J. E. Lupton, E. C. Stone, J. Geophys. Res,V. 78(1973), 1007.[12] L. J. Stater, Confluent Hypergeometric Functions, (1960).[13] G. N. Watson, A Treatise on The Theory of Bessel Functions, (1952).
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CHANG KONG-LIANG. DIMENSIONAL METHOD TO SOLVE THE DIFFUSION CONVECTION EQUATION OF SOLAR COSMIC RAYS[J]. Chinese Physics C, 1978, 2(3): 200-210.
CHANG KONG-LIANG. DIMENSIONAL METHOD TO SOLVE THE DIFFUSION CONVECTION EQUATION OF SOLAR COSMIC RAYS[J]. Chinese Physics C, 1978, 2(3): 200-210. shu
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Received: 1977-08-16
Revised: 1900-01-01
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DIMENSIONAL METHOD TO SOLVE THE DIFFUSION CONVECTION EQUATION OF SOLAR COSMIC RAYS

  • Institute of Space Physics, Sian

Abstract: Physical processes of the propagation of the solar cosmic rays in the interplanetary space include the diffusion in interplanetary disordered magnetic fields and the convection in solar winds. Dimensional method can be applied to solve those equations convertible into Bessel equation, the results obtained are identical with those solved by the commonly used separate variable method. In order to derive an analytic solution to the diffusion convection equation in an unbounded, uniform medium, two dimensionless parameters reflecting the diffusion and convection characteristics of the particles are introduced. In the diffusion dominated case, the solution is similar in form to the diffusion of a source moving with the convection velocity and is modified by another convection term, which can be expanded into a power series of the convection parameter with coefficients composed of the generalized hypergeometric function series of the diffusion parameter. This solution has a clear physical meaning, and can suitably be used in the discussion of the rise phase characteristics of the solar cosmic rays from medium to high energies (Ep≥101 MeV).

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