About

NMODEL

The NMODEL control applies only to species with NDEFINE(ig)=0. If only one thermal species is present, then NMODEL has no effect, even with NDEFINE=0. The following options can be selected:

NMODEL=1

Species independent density profile shape model.

A profile for the thermal ion density is calculated by solving the equations for Z_eff and quasi-neutrality. The individual thermal ion species are assumed to have a shape that is proportional to the total ion density. The fraction attributed to each species depends on gas flow, recycling and neutral beam fueling and calculated from the global particle balance equation.

NMODEL=2

Species independent radial velocity model.

As with NMODEL=1 the total (i.e. Z weighted summed) ion density profile is calculated. However, now the Z weighted summed PARTICLE BALANCE (CONTINUITY) equation is solved:

Using summed beam and recycling sources [sum Zi*Si], and dne/dt and dZeff/dt and fast ion density data to get d/dt[sum Zi*ni], this equation is solved for the summed flux. The resulting flux profile implies an "average" radial ion velocity profile. In NMODEL=2, this radial velocity profile is assumed to apply individually to all species; i.e. the assumption is that all species move radially with the same velocity. Then the continuity equation is solved individually for each specie, to advance the mix. Note (dmc Sept 2004): NMODEL=2 is now the same as NMODEL=4 but with a small, constant diffusivity, set equal to DFIMIN. DFIMIN=0 is the default.

NMODEL=4

Mixed model.

Similar to with NMODEL=2, the Z weighted summed continuity equation is solved to yield a Z weighted summed flux constraint. However, with this model each ion species evolves independently, using species radial flux modeled as the sum of two terms:
Γ = D ∇(n)+nv
where the diffusivity D is an input and the non-diffusive term v is calculated to satisfy the global flux constraint. With NMODEL=4, the input diffusivity model must be specified with NDIFFI (see below).

Selecting the model for the ion diffusivity

When NMODEL=4, the model for the ion diffusivity must be specified, using the namelist variable NDIFFI.

NDIFFI=1

Use this value to set a time and space independent input diffusivity DIFFUS in the namelist, with units of cm²/s.

NDIFFI=2

Ue this value to prescribe a diffusivity Ufile PREDE2/EXTDE2. Note that the diffusivity defined this way (units of cm²/s) is input through the electron diffusivity channel of TRDAT.

NDIFFI=3

Use this value to use the net electron diffusivity fluxe/∇(n_e) from the electron particle balance calculated at the previous timestep, as the input diffusivity for the ions.

NDIFFI=4

Use this value to use the electron diffusivity (as in NDIFFI=3) with a correction for the neoclassical Ware pinch.

NDIFFI=5

Use this value to set D₀=χ_i, where χ_i is derived from the ion power balance calculation

NDIFFI=6

Use this value to set D₀=χ_e, where χ_e is derived from the electron power balance calculation

The local time rate of change of D₀ is bounded by the namelist parameter DLTKIE, which constrains the factor by which D₀ can change, per millisecond of model time. DLTKIE is also used to constrain the rate of change of χ_i and χ_e when these are being used predictively.

The diffusivity D₀ is applied to individual species as follows. Set:

DFIMIN = minimum allowed diffusivity (units of cm2/s)
DFIMAX = maximum allowed diffusivity (units of cm2/s)
DIFAC(ig) = species dependent diffusivity anomaly factor

To obtain the diffusivity for each ion species ig:
D = min[ DFIMAX, max( DFIMIN, DIFAC(ig) * D₀ )]
where D₀ is selected by NDIFFI.

The parameter DIFAC can be used to make one species to diffuse more rapidly than another, if an isotope dependent effect is desired.
Solution of the particle balance using available data puts a constraint on the radial flux; this is in general not met by a diffusion model alone. Therefore a non-diffusive velocity must be computed for each species, so that the sum of species fluxes satisfies a global constraint. However, this still leaves NG-1 degrees of freedom (where NG=# of species); one may make one species more "mobile" than another, to carry a larger fraction of the flux needed to meet the global constraint. Set
VIFAC(ig) = non-diffusive flow velocity factor for species ig.
(caution: VIFAC(ig) .gt. 0.0 required, and VIFAC(IG1)/VIFAC(IG2) .ge. 0.1 required for all IG1,IG2)
Only the ratios VIFAC(ig)/VIFAC(1) are important, not their absolute value. This means that the two definitions below are equivalent:
VIFAC=1.0,2.0
VIFAC=0.5,1.0

Example 1: to make species 1 "three times as mobile" as species 2 in the non-diffusive flow term, set VIFAC=3.0,1.0.
Example 2: if the input diffusivity is set to 0.0 and VIFAC=1.0,1.0 is specified, then NMODEL=4 and NMODEL=2 are equivalent.

Defaults values: NDIFFI=1, DIFFUS=0.0, DFIMIN=0.0, DFIMAX=10⁵, DIFAC(ig)=VIFAC(ig)=1.0 for all ig.
These controls have effect only when NMODEL=4 is in use.