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 LTi, 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., 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. .
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 vi is the ion thermal velocity.
Putting these estimates together, we find that the ion thermal diffusivity
is (in MKS units):
where Ci is a constant to be calibrated (see below).
With regards to the electron thermal diffusivity ,
Ottaviani, et al  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 Ce 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: