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the energy balance equation becomes


          ldF la         3dT](.8
          i  FL3K     - (T)rT' + S = 0             (8.48)


Expanding the derivative term, equation (8.48) becomes


d2T   1dT -      dK    3 dT 2     3KR
    d        Fu 1              +  --   S = 0       (8.49)
dr2   r dr   LKR dT              16T3

The solution to the non-linear second order equation (8.49) represents the radial temperature distribution in the plasma core reactor having an opacity with arbitrary temperature dependence. Three boundary conditions are used with equation (8.49). The first two conditions are obtained by specifying the centerline temperature and by requiring that the radial temperature distribution be symmetric about r = 0. The third condition results from the constraint that the temperature at the inside face of the graphite chamber must not exceed the melting point of graphite. These three boundary conditions are expressed as T(O) T=


                      T (0) = 0


                      T(R)   TR                    (8.50)


where TR is the maximum allowable graphite temperature.