Assuming that all ions have the same temperature Ti and the same
thermal diffusivity , SNAP's power balance for the ion
where As is the area of the flux surface, is the RF power density to ions including both direct heating and heating from a minority tail, qcx is the net power density lost to charge-exchange, qion-i is the power density lost by thermal ions in ionizing neutrals, represents heating due to viscous dissipation, is the flux of the jth ion species, nj is the density of the jth ion species, Cv is the convective multiplier, specified by the user, and the other terms have their usual meanings.
When the routine for solving the ion power balance is called, SNAP\ has either calculations or measurements for all variables appearing in Eq.10 except . It can therefore solve the equation for . If, instead, the user has specified a model for , then Eq. 10 can be solved to yield a new estimate of the local , given a previous estimate of the Ti(r) profile (which is necessary to determine the qei and other terms appearing on the left hand side). By iterating, a Ti(r) profile consistent with the chosen model for is obtained.
The corresponding equation for electrons is
As for the ions, all terms in this equation are known to SNAP\ except the electron thermal diffusivity , which it proceeds to solve for.