errata for "Quantitative Predictions of Tokamak Energy Confinement from First-Principles Simulations with Kinetic Effects", Kotschenreuther, Dorland, Beer, and Hammett, Phys Plasmas 2, 2381 (1995) (last updated 11 June 1999):

On p. 2381, in the definition of the collisionality parameter $\nu$, 4 lines before Eq. 2, the factor of 2.1 should be replaced by 2.5.

On p. 2381, in the definition of R/L_n^* in the 3rd line after Eq. 2, R/L_n^* is defined as max(6,R/Ln). It should be defined as min(6,R/Ln).

Both of these are typos in the paper only. These corrections bring the paper into agreement with the subroutine that has been used to evaluate and test the model. The IFS-PPPL parameterization in this paper is fairly complicated, and there are many opportunities for typos if you try to code this up from scratch. Contact us and we will send you a copy of the fortran subroutine used to evaluate the formulas.


In calculating D_ML = D_mixing = max(gamma/k_perp^2) as described on the bottom of p. 2382, for practicality the range of k_theta*rho scanned was typically from approximately 0.1 to 0.8.

Though it is only used for intermediate calculations and not for the final
form of chi, we define here the "W_NL" function used on page 2382.  This
definition is taken from two emails (the second one corrects a factor of
6.6 to be 13) from:

Date: Tue, 13 May 1997 00:25:29
From: Bill Dorland
To: Multiple recipients of list


The precise relationship between chi and D_ML in the IFS-PPPL model is the

chi_i = W * D_ML


D_ML == max(gamma/k_perp**2)

where the maximum is taken over all k_theta, and k_perp**2 is defined in
our PoP paper, Vol. 2, page 2382, 1995, and where 

W == 13 * (1 + s_hat**2.5)/(1 + s_hat) / G(R/LT - R/LTcrit)

where G(x) = 1 for x < 1, and sqrt(x) for x > 1.  

Here, s_hat is the usual magnetic shear parameter.  

The strong increase of W with s_hat is not representative of the dependence
of chi on s_hat, since D ~ 1/(1+s_hat**2.5), according to our calculations.

The final expression for chi_i that constitutes the IFS/PPPL is constructed
from this W and a parameterization of the D_ML from Kotschenreuther's GK

Thus, the differences between the observed nonlinear chi from the GF ITG
simulations and the mixing length estimate was parameterized by three

a) a factor of 13
b) weaker magnetic shear dependence
c) weaker dependence on R/LT far from marginal stability.