Thresholdless OHE Model

The OHE model derivation begins with the assumption that the ion thermal diffusivity will be given by a quasilinear form, related to the radial correlation length and correlation time for ITG-driven turbulence:

The correlation length is estimated from the large-scale poloidal cutoff () of the turbulent spectrum:

where , the ion inertial gyroradius, is defined by

and where L_Ti, the local ion temperature gradient scale length, is defined by

Note that the correlation length is inversely proportional to the ion temperature scale length; hence, is directly proportional to the normalized ion temperature gradient. However, in the case of a very small or reversed gradient, it is obviously nonsense to have a vanishing or negative correlation length. In the coding of the model, the correlation length is bounded underneath by multiplied by zbound. Wendell Horton (IFS) recommends that zbound = 1.0. In the work of Ref.[2], we used zbound = 0.0. This difference is not large, in the test cases we have considered so far, but could be significant when attempting to replicate the results in Ref. [2].

In order to give the correct scaling with plasma current (essentially, the correct scaling of the transport with q), the correlation time is chosen to be:

where v_i is the ion thermal velocity.

Putting these estimates together, we find that the ion thermal diffusivity is (in MKS units):

where C_i is a constant to be calibrated (see below).

With regards to the electron thermal diffusivity , Ottaviani, et al [1] simplify the situation considerably by assuming that the electron heat energy will be conducted only by the trapped electrons. Then, simplify further by assuming that will be equal to multiplied by the trapped particle fraction (, where is the inverse aspect ratio r/R):

where C_e is a constant. These expressions were calibrated against the medium power L-mode JET discharge #19649. The optimum fit between the JETTO runs and the experimental data were achieved when: