解cosmic-ray调制问题的解析迭代法
An analytically iterative method for solving problems of cosmic-ray modulation
摘要：
提出了一种求解宇宙线调制稳态和非稳态问题的解析迭代方法。迭代获得的解决方案构造的CR传播方程的球对称形式。所考虑的问题的主要解决方案包括零阶的解决方案，这是在初始迭代和修正，可以通过后续迭代获得。零阶解的发现是基于在空间中传播期间的CR各向同性，而各向异性在发现下一修正时被考虑在内。首先，该方法被用来解决CR调制的问题，其中扩散系数$κ$和太阳风速度$u$是常数与本地星际光谱（LIS）的频谱。用两次迭代得到的解与解析解和数值解进行了比较。最后，对用$u = constant$进行CR调制的两个问题和同样形式的LIS谱进行了一次迭代求解，并与数值解进行了比较。对于第一个问题，$κ$与粒子$p$的动量成正比，因此它具有$κ=k_0η$的形式，其中$η=\frac{p}{m_0c}$。对于第二个问题，扩散系数以$κ=k_0βη$的形式给出，其中$β=\frac{v}{c}$是相对于光速的粒子速度。有一个很好的匹配所获得的解决方案与数值解以及与解析解的问题，其中$κ= constant$。
英文摘要：
The development of an analytically iterative method for solving steady-state as well as unsteady-state problems of cosmic-ray (CR) modulation is proposed. Iterations for obtaining the solutions are constructed for the spherically symmetric form of the CR propagation equation. The main solution of the considered problem consists of the zero-order solution that is obtained during the initial iteration and amendments that may be obtained by subsequent iterations. The finding of the zero-order solution is based on the CR isotropy during propagation in the space, whereas the anisotropy is taken into account when finding the next amendments. To begin with, the method is applied to solve the problem of CR modulation where the diffusion coefficient $κ$ and the solar wind speed $u$ are constants with an Local Interstellar Spectra (LIS) spectrum. The solution obtained with two iterations was compared with an analytical solution and with numerical solutions. Finally, solutions that have only one iteration for two problems of CR modulation with $u = constant$ and the same form of LIS spectrum were obtained and tested against numerical solutions. For the first problem, $κ$ is proportional to the momentum of the particle $p$, so it has the form $κ=k_0η$, where $η=\frac{p}{m_0c}$. For the second problem, the diffusion coefficient is given in the form $κ=k_0βη$, where $β=\frac{v}{c}$ is the particle speed relative to the speed of light. There was a good matching of the obtained solutions with the numerical solutions as well as with the analytical solution for the problem where $κ= constant$.
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