NDEFINE=1

With this option the ion density profile for each species ig is calculated for given diffusivity and flow velocity, by solving for the flux:

where n is density of the ion species (to be predicted), v_c is the non-diffusive radial velocity (from UFILE) and D is the diffusivity (from UFILE).

Alternatively, a UFILE for the diffusive flow scale length can be given to TRANSP, which will then calculate the diffusivity from:

The density profile is then evolved from the continuity equation:

where the source S is the sum of the beam source/sink, the gasflow and recycling source.

The following provides a list of the input UFILES names for the density profiles of each thermal ion species:

• hydrogen:
• D: PREDFH,EXTDFH
• v_c: PREVCH,EXTVCH
• L_f: PRELFH,EXTLFH
• deuterium:
• D: PREDFD,EXTDFD
• v_c: PREVCD,EXTVCD
• L_f: PRELFD,EXTLFD
• tritium:
• D: PREDFT,EXTDFT
• v_c: PREVCT,EXTVCT
• L_f: PRELFT,EXTLFT
• helium-3:
• D: PREDF3,EXTDF3
• v_c: PREVC3,EXTVC3
• L_f: PRELF3,EXTLF3
• helium-4:
• D: PREDF4,EXTDF4
• v_c: PREVC4,EXTVC4
• L_f: PRELF4,EXTLF4
• lithium-6:
• D: PREDF6,EXTDF6
• v_c: PREVC6,EXTVC6
• L_f: PRELF6,EXTLF6

If only the UFILE for v_c is provided, then TRANSP assumes D=0.

If only the UFILE for D is provided, then TRANSP assumes v_c=0.

Either D and v_c, or L_f and v_c can be supplied together to solve for the flux and the continuity equation.

The diffusivity D is constrained to be between DFIMIN and DFIMAX

When NDEFINE(ig)=1 the ion outflux is pre-determined by the value of the input transport profile data at the plasma boundary (r=a). If no recycling input source data is provided, then the fraction of this ion outflux that is recycled is controlled by the namelist input RECYCH(ig). Simulations where the transport is set by the user are prone to fail unless reasonable assumptions are made. For example, if RECYCH(ig)=0, none of the ion outflux is recycled and the ion density will rapidly decrease. Conversely, if RECYCH(ig)=1.0, all the ion outflux is recycled and the ion density can never decrease. This would cause the ion density to grow above the electron density and the simulation will fail.

Alternatively, the user may specify a total recycling source as an input Ufile. However, this can result in large dn/dt terms that may be hard to predict. These dn/dt terms might be thought of by defining a recycling "coefficient" expressed as the ratio between the (ion source due to recycling neutral ionization) and the (total ion outflux).

If the total ion outflux is specified by the transport model AND the recycling source by input data, then the recycling coefficient is determined and may not satisfy expected constraints (e.g. it might be larger than unity, leading to dn/dt > 0 due to recycling alone).

With NDEFINE(ig)=1, the initial, relative concentration of the thermal ion species must be provided by setting FRAC(ig). This can be zero.

By default, the specie density profile BOUNDARY CONDITION is that the scale length match the scale length of the electron density profile. This has its hazards, because it assumes that the electron density has a reasonable non-zero outward sloping gradient at the boundary.

Alternatively, the user may set (for ndefine(ig)=1 specie) the namelist variable fbdy_nd2(ig)< 1.0, to constraint the density at the boundary as a fraction of the electron density

An alternate recycling source model is available. When using NRCYOPT=2, if separate recycling source data is not provided, the recycling source for the NDEFINE(ig)=1 species is simply RFRAC(ig)*[total ion recycling source]. and RECYCH(ig) is not used.