The IFS/PPPL Transport Models

**implemented by Aaron J. Redd Lehigh University**

The 1995 IFS/PPPL model[] is an anomalous thermal transport model
based directly upon the predictions of nonlinear gyrofluid (GF) turbulence
simulations, in flux-tube geometry[].
The turbulent thermal diffusivities from this nonlinear GF code
were compared with
the predictions of a gyrokinetic (GK) linear stability code[].
It was found that the ratio of the nonlinear to a
mixing-length estimate from the linear code
() was a
slowly varying function.
This observation encouraged Kotschenreuther, *et al*, to map out the
plasma parameter space utilizing the linear GK code.
Each linear result could then be multiplied by the nearly-constant ratio
, giving a value for that would be a good
estimate of the nonlinear code result.

This technique represents a significant savings in human effort and computational time, as the linear GK code can be run much faster than the nonlinear GF code.

Once this method was established, ``many hundreds'' of linear GK runs were conducted, mapping out the parametric dependence of the drift instability. Then, interpolation formulas were devised, giving and as functions of various plasma parameters. The resulting turbulence model was published in 1995 as the IFS/PPPL model.

It is important to note, however, that the nonlinear GF runs that produced the 1995 IFS/PPPL model utilized certain simplifying assumptions:

- Only carbon impurities
- the effects of low-Z impurities, like helium, are ``not well-described'' by this model
- it was found that high-Z impurities will have little (or no) effect upon the mode

- constant in space (all density gradients equal)
- Simplified geometry: ``shifted circle'', low , high aspect ratio
- No finite- effects
- Only the usual ITG branch of the drift instability is important; that is, trapped-electron modes, ``ubiquitous modes''[], long-wavelength ITG modes (trapped-ion modes) and finite- ballooning modes are all neglected.

This coding of the 1995 IFS/PPPL model also includes a plasma elongation stabilization factor, as suggested at the 1996 Varenna Meeting[], a preliminary model of rotational stabilization[], and several corrections and refinements to the model that was reported in the 1995 paper. These modifications were suggested by Bill Dorland[].

Currently, the GF turbulence code, called `Gryffin`, is maintained and
operated by Mike Beer (PPPL).
The linear GK stability code is maintained by Mike Kotschenreuther (IFS),
and has been benchmarked against an eigenvalue kinetic stability code
(the FULL code[, , ], written and maintained
by Gregory Rewoldt of PPPL) for a series of simple cases[].

Wed Jul 8 11:54:05 EDT 1998