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Model with width based on magnetic and flow shear stabilization

  This model is given by Eq. (13) in Ref. [5]. It was assumed in this model that the pressure gradient within the pedestal region is constant and limited by the first stability of the ballooning mode. Then, the total pressure at the top of the pedestal (tex2html_wrap_inline404) is
where tex2html_wrap_inline396 and tex2html_wrap_inline408 are the density and temperature at the top of the pedestal, k is the Boltzmann's constant, tex2html_wrap_inline412 is the pedestal width and tex2html_wrap_inline414 is the critical pressure gradient of ballooning mode. Rewriting Eq. (gif), one can obtain the value of tex2html_wrap_inline408,
given the value of the pressure gradient and the width of the pedestal region.

In this model, the width of the pedestal, tex2html_wrap_inline412, is assumed to be determined by a combination of magnetic and flow shear stabilization of drift modes [4],
where s is the magnetic shear, tex2html_wrap_inline422 is the ion gyro-radius at the inner edge of the steep gradient region of the pedestal and CW is a constant of proportionality chosen to optimize the agreement with experimental data. The first stability ballooning mode limit is approximated by
where the magnetic q and shear s are evaluated one pedestal width away from the separatrix, R is the major radius, BT is the vacuum toroidal magnetic field evaluated at major radius R, tex2html_wrap_inline436 is the elongation at the 95% magnetic surface (tex2html_wrap_inline438, where tex2html_wrap_inline440 is the elongation at the separatrix) and tex2html_wrap_inline442 is the triangulrity at the 95% magnetic surface (tex2html_wrap_inline444, where tex2html_wrap_inline446 is the triangularity at the separatrix).

After combining Eqs. gifgif and gif with some algebra, the following expression can be obtained for the pedestal temperature [5]:
where tex2html_wrap_inline408 is the pedestal temperature in the unit of keV, AH is the average hydrogenic ion mass in the unit of AMU and tex2html_wrap_inline396 is the electron density at the top of the pedestal in units of m3.

The magnetic q has a logarithmic singularity at the separatrix. At one pedestal width away from the separatrix, the magnetic q is approximated by
where tex2html_wrap_inline460 is the position of the top of the pedestal and I is the plasma current. The magnetic shear, tex2html_wrap_inline464, which is computed using the magnetic q from Eq. (gif), is then reduced by the effect of the bootstrap current, as described in Ref. [5]. Since the pedestal width is needed to compute the magnetic q , the magnetic shear, s , and the normalized pressure gradient tex2html_wrap_inline472, and since the pedestal width is a function of the pedestal temperature, the right hand side of Eq. (gif) for the pedestal temperature depends nonlinearly on the pedestal temperature. Consequently, a non-linear equation solver is required to solve Eq. (gif) to determine tex2html_wrap_inline408.

The coefficient CW in the expressions for the pedestal width [Eq. (gif)] and the pedestal temperature [Eq. (gif)] 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. [5]. Ion temperature measurements were used for the pedestal temperature whenever they were available. However, this pedestal temperature model does not distinguish between electron and ion temperature. It is found that the value CW = 2.42 yields a minimum logarithmic RMS deviation of about 32.0% for this data.

next up previous
Next: Model with width based Up: H-mode temperature model Previous: H-mode temperature model

Wed Apr 2 12:00:26 EST 2003