Analytic treatment of distributions of lithium neutrals and ions in linear devices

Neutral lithium (Li) has been used for the mitigation of heat flux to the plasma facing components and for the control of hydrogen of fusion plasmas. Radial and axial variations of densities of Li neutrals and ions are obtained analytically for a cylindrical chamber by assuming the classical diffusion with or without the magnetic field (B). Neutrals and ions without B can be expressed as a linear combination of the modified Bessel functions of order zero (I₀ and K₀), while ions with B are to be expressed as the square root of them. Analytical solutions of Li neutral densities with Dirichlet and Neumann boundary conditions are compared to those using Monte Carlo simulation and experimental values of the LIGHT-1 (Lithium Injection Gettering of Hydrogen and its Transport experiments) device. Proper combinations of the relaxation length and size of the source would produce well fitted profiles similar to those observed experimentally and those using Monte Carlo codes.