A Numerical Study Of The Anisotropy Of The Galactic Cosmic Ray Positron Induced By Solar Modulation

alactic cosmic rays are high-energy charged particles from the Milky Way,widely present in the heliosphere,with a minimum energy of about 10^-3 eV and a maximum energy of 10¹¹ eV.Cosmic rays with energies below 30 eV are affected by solar wind plasma and the heliospheric magnetic field frozen therein,resulting in changes in their flux in space and time,this process is called cosmic rays modulation.The modulation process of cosmic rays in the heliosphere is described by Parker’s transport equation,which includes all the solar modulation mechanisms such as solar wind convection,diffusion caused by the heliospheric magnetic field,drift caused by the heliospheric magnetic turbulence,and changes in adiabatic energy.Cosmic rays exhibit isotropic properties when they reach the top of the heliosphere due to the deflection of the Milky Way’s magnetic field during transport.However,considering the influence of solar modulation on cosmic rays during propagation within the heliosphere,the flux of cosmic rays may vary in different directions,resulting in slight but significant anisotropy.The transport of positrons in the heliosphere is mainly described by diffusion tensors.In order to establish their contribution to the three-dimensional anisotropic vector and its components,we are examined the elements in the diffusion tensors.The main research contents are as follows:First,the alternating direction implicit method（ADI）in finite difference is used to numerically solve the flux of cosmic ray positrons in Parker’s transmission equation by taking the local interstellar spectrum at 120AU as the boundary condition.By comparing with the observed values,we found a more suitable diffusion and drift coefficient model for cosmic ray positrons,reproducing the flux of cosmic ray positrons observed earth by the PAMELA detector during the solar minimum periods of2006 and 2009.Then,the high-order difference approximation method is used to solve the radial and polar gradients of cosmic ray positrons in two solar polar periods.Finally,the expression for the anisotropy of cosmic ray intensity derived from the expression of cosmic ray flow is used to obtain the radial and polar anisotropy of positrons with different energies in two solar polar periods.Research has found that:Firstly,when the energy of positrons is below 0.2 eV,the slope of the positron modulation spectrum is the same as that of the local interstellar spectrum.This is because positrons below 0.2 eV are only affected by diffusion,and the diffusion coefficient is constant at this energy.Secondly,the intensity gradient of low energy positrons is inversely correlated with the diffusion coefficient.As the radial diffusion coefficient increases,the radial gradient of positrons decreases;The larger the polar diffusion coefficient,the smaller the gradient of positron polarity.The distribution of the intensity gradient of positrons affected by drift in the entire heliosphere during two solar polarity cycles is related to the path of positrons entering the heliosphere.Finally,in terms of radial anisotropy,the radial anisotropy of low energy positrons that are not affected by drift is only determined by diffusion anisotropy and Compton etting anisotropy,while the radial anisotropy of high energy positrons is determined by a combination of diffusion anisotropy,drift anisotropy,and Compton etting anisotropy.In addition,the polar region and equator are two relatively special positions,Due to the large diffusion and drift coefficients near the polar region,there is a significant radial anisotropy here.Due to the polar gradient near the equator being 0,the radial anisotropy here is only determined by diffusion and Compton-etting anisotropy;In terms of polar anisotropy,the polar anisotropy of low energy positrons that are not affected by drift is only determined by diffusion anisotropy.Therefore,its polar anisotropy at the equatorial position is 0,and the absolute values of polar anisotropy in the north and south hemispheres are equal.Higher energy positrons are jointly affected by drift and diffusion,and the absolute values of polar anisotropy are not equal in the north and south hemispheres.