This pedestal temperature model, which is given by Eq. (29) in Ref. , employs similar approach with the model in section , but uses different scaling of the pedestal width. The width of the temperature pedestal, , is taken from the width scaling that fits to DIII-D database ,
where is the poloidal normalized pressure, R is the major radius and CW is a constant of proportionality chosen to optimize the agreement with experimental data. In the steep gradient region of the pedestal, the pressure gradient is assumed to be constant and to be limited by the ideal, short-wavelength, ideal MHD ballooning limit, which is described in Eq. above.
After combining Eqs. , and with some algebra, the following expression can be obtained for the pedestal temperature in the unit of keV:
where is the electron density at the top of the pedestal in units of m3, q95 is the safety factor at 95% flux surface and gs is the shaping factor, which is defined as
Note that Eq. is a non linear equation as explained in section . The coefficient CW in the expressions for the pedestal width [Eq. ()] and the pedestal temperature [Eq. ()] is determined by calibrating the model for the pedestal temperature against 533 data points for type I ELMy H-mode plasmas obtained from the International Pedestal Database version 3.1, using discharges from ASDEX-U, DIII-D, JET, and JT-60U tokamaks, as described in Ref. . It is found that the value CW = 0.021 yields a minimum logarithmic RMS deviation of about 32.9% for this data .