The containment properties of alpha particles during the slowing-down process in an axisymmetric tokamak reactor are studied by using Monte-Carlo calculations, in which the pitch-anglescattering effects are included. The loss of alpha particles during slowing-down is found to be safely negligible in a pure DT plasma, but increases proportionally to the effective charge number of the plasma and cannot be ignored in a highly contaminated plasma (Z e ff > 4), compared with the loss of 3.5-MeV particles.

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The approximate solutions of the 1, w p and a,, eigenvaluc problems of the group-diffusion equation for a multi-region reactor are obtained by expandivg neutron fluxes into finite numbers of eigenfunctions satisfying the Helmholtz equation and the boundary condition at the extrapolated boundary of the reactor. The original eigenvalue problem is reduced to that of an asymmetric real matrix for the vector whose components constitute the expansion coefficients. For the numerical calculation of the real matrix thus derived, to dctermine the higher 1, w p and w,, modes, the QR iteration method based on numerically stable unitary transformation, in comhination with inverse iteration is effective in saving computation time.The R, w p and od modes obtained by the above method are expressed by a linear combination of a comparatively small number of simple clementary functions, and are thus of high practical value in the numerical calriilotion of higher order perturbations and for exmniniug space-dependent reactor dynamics.

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