托卡马克等离子体粒子输运方程的半解析研究

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

SEMI-ANALYTIC MODELLING OF TOKAMAK PARTICLE TRANSPORT

Assuming that the transport operator is linear, the tokamak particle transport equations are systematically analyzed. The particle transport consists of outward diffusion and inward convection. A Green function expression and an equivalent generalized Fourier expansion with corresponding Sturm-Liouville eigenfunctions and eigenvalues are given. For an edge-localized particle source (shallow fuelling), using the complementarity relation of the solution, wellbehaved generalized Fourier expansion of the solution can be obtained. From this expression, it is clearly seen that for very low wall recycling of particles, some rather peaked profile described by the first eigen function can he realized. For a transient internal point source, using the comple mentarity relation, the evolution of particle density can also be described by the well-behaved generalized Fourier expansion.