在输运算子为线性算子的条件下 ,对托卡马克等离子体粒子输运方程的求解进行了系统的分析。粒子输运由向外扩散和向内对流构成。给出了用格林函数表示的普遍解和相应的 Sturm-Liouville本征函数及本征值。对粒子源处在边界附近 (浅加料 )的情形 ,通过解的互补性关系 ,可以获得品质好的广义傅里叶展开。从解的一般性质看出 ,在器壁再循环很小时 ,由第一个本征函数描述的粒子密度剖面对应于较高的峰化因子。对于瞬间内部点源产生的密度剖面演化 ,通过解的互补性也可得到品质好的广义傅里叶展开表示 Under the condition that the transport operator is a linear operator, the solution of tokamak particle transport equation is systematically analyzed. Particle transport consists of outward diffusion and inward convection. The general solution and the corresponding Sturm-Liouville eigenfunctions and eigenvalues, which are expressed by Green’s function, are given. In the case that the particle source is near the boundary (shallow charge), a good generalized Fourier expansion can be obtained by the complementarity of solutions. From the general nature of the solution, it can be seen that the particle density profile described by the first eigenfunction corresponds to a higher peaking factor when wall recirculation is small. For the evolution of the density profile generated by an instantaneous internal point source, a good generalized Fourier representation can also be obtained by complementarity