Pedestal Module

In predictive simulations TRANSP uses boundary conditions at a radial location set by the variable XIBOUND (for electron and ion temperature) and at XNBOUND (for the electron density)

These boundary conditions are overwritten with the pedestal location when the following switches are selected:

MODEEDG=5

to use boundary conditions for the electron temperature profile set by the pedestal module

MODIEDG=5

to use boundary conditions for the ion temperature profile set by the pedestal module

MODNEDG=5

to use boundary conditions for the electron density profile set by the pedestal module

NOTE: it is possible to use pedestal boundary conditions separately for the ion, electron and density profile. However, TRANSP enforces the boundary conditions for T$$_e and T$$_i to be the same. This means that, if MODEEDG=5 and MODIEDG=4, the boundary condition for T$$_e will be enforced to be at XIBOUND.

Users can impose the values of the pedestal width and height from the namelist or use a predictive model.

User-defined pedestal width

To impose the pedestal width from the namelist: NMODEL_PED_WIDTH = 0

TEPEDW

Electron temperature pedestal width. Positive value for physical units of cm, negative value for sqrt(ϕ/ϕ$$_B)

TIPEDW

Ion temperature pedestal width. Positive value for physical units of cm, negative value for sqrt(ϕ/ϕ$$_B)

XNEPEDW

Electron density pedestal width. Positive value for physical units of cm, negative value for sqrt(ϕ/ϕ$$_B)

User-defined pedestal height

To impose the pedestal height from the namelist: NMODEL_PED_HEIGHT = 0

TIPED

Ion temperature at the pedestal top [eV]. The default value is 100.0 eV

TEPED

Electron temperature at the pedestal top [eV]. The default value is 100.0 eV

XNEPED

Electron density at the pedestal top [cm$-3$]. The default value is 10$12cm-3$

Predictive models for the pedestal pressure and width

To use a predictive model for the pedestal pressure: NMODEL_PED_HEIGHT = 1

To use a predictive model for the pedestal width: NMODEL_PED_WIDTH = 1

NOTE: the two models are not independent, since some models predict both pressure and width and results will be over-written. It is recommended to set both flags equal to 1.

When the pedestal height is predicted, the calculated density and temperature can be rescaled using the following namelist variables:

SCALE_TEPED

Scale factor for the electron temperature pedestal height

SCALE_TIPED

Scale factor for the ion temperature pedestal height

SCALE_NEPED

Scale factor for the electron density pedestal height

It should be noted that all pedestal models calculate the pedestal pressure, thus the pedestal temperature is derived for a given pedestal density, as (p$$_ped/2k_Bn_ped). The resulting pedestal temperature depends on how the pedestal density is calculated.

Options to calculate the pedestal density

LPED(2)=1

n$$_ped= 0.71 n$$_lin, where n$$_lin is the line averaged density. This is the original NTCC module assumption.

LPED(2)=2

pedestal density and width set from a fit over the density profile, according to the following parametrization:

where:

r$$₁ is the ratio of the density at the pedestal to the central value, n$$_e,ped = r$$₁ n$$_e,0

r$$₂ is the ratio of the density at the separatrix to the central value, n$$_e,sep = r$$₂ n$$_e,0

The fit returns the width of the pedestal in normalized poloidal flux coordinates and the value of the density at the pedestal location.

The mid-pedestal location is taken at a pedestal half-width to the right of the pedestal. The pedestal top is defined as a pedestal half-width to the left of the pedestal location.

LPED(2)=3

n$$_ped= C n$$_sep, where C is set with the namelist variable CPED(4).

LPED(2)=4

pedestal density and width set at the location of the maximum profile gradient.

Important: the output values NEPED and NEPEDW represent the values at the pedestal top, which is used in TRANSP as a boundary conditions for the core transport predictions.

Options to calculate the pedestal pressure

Original NTCC model options:

The description of the NTCC PEDESTAL module can be found here and the standalone code can be downloaded from the NTCC directory.

The models included in the NTCC module are described in the paper by T. Onjun et al, Phys. Plasmas 9 (2011) 5018

LPED(3)=1

Pedestal model using the pedestal width based on magnetic and flow shear stabilization (see section 3.1 in this pdf document for detailed information).

LPED(3)=2

Pedestal model using the pedestal widhth based on flow shear stabilization (see section 3.2 in this pdf document for detailed information)

LPED(3)=3

Pedestal temperature model using the pedestal width based on normalized pressure (see section 3.3 in this pdf document for detailed information)

LPED(3)=11

Pedestal temperature model based on thermal conduction model I (see section 3.4 in this pdf document for detailed information)

LPED(3)=12

Pedestal temperature model based on thermal conduction model II (see section 3.5 in this pdf document for detailed information)

Models based on MHD stability calculations

These options are based on the work by P. Maget et al, NF 53 (2013) 093011:

LPED(3)=21

This model needs the pedestal width in cm as an input, using CPED(3). Alternatively, the pedestal width can be taken from a fit over the pedestal density, when the density profile is prescribed with UFILE. In this case set CPED(3)=0.0 and LPED(2)=2

NOTE: this parametrization has been derived for ITER, do not use otherwise.

LPED(3)=22

This model needs the pedestal width in cm as an input, using CPED(3). Alternatively, the pedestal width can be taken from a fit over the pedestal density, when the density profile is prescribed with UFILE. In this case set CPED(3)=0.0 and LPED(2)=2

NOTE: this parametrization has been derived for ITER, do not use otherwise.

LPED(3)=24

Pedestal that combines the calculation of the width from the NTCC model #3 (density proportional to sqrt of poloidal beta at pedestal with the parametrization by Sugihara (PPCF 45)

LPED(3)=25

This model sets the pedestal width $w_{\rm ped}$, pedestal pressure $p_{\rm ped}$, and pedestal electron temperature $Te_{\rm ped}$ from a few machine-dependent constants and a normalized plasma current. It is intended for spherical tokamaks with built-in defaults for MAST and NSTX/NSTX-U. For other machines, four pedestal coefficients cped(9:12) need to be set explicitly.
In this model, the pedestal width and pressure are $$ w_{\text{ped}} = \dfrac{cped_9}{\,z_{in}^{\,cped_{11}}}\,, \qquad p_{\text{ped}} = cped_{10} \cdot \; z_{in}^{\,cped_{12}} \; \dfrac{B_t^{2}}{1+\kappa^{2}}. $$

Here, $ z_{in} = {I_p}/{(a\,B_t)} $, $I_p$ is the plasma current, $a$ is the minor radius, $B_t$ is the toroidal field on axis, $\kappa$ is the elongation, $n_{\rm e,ped}$ is electron density at the pedestal top, $k_B$ is the Boltzmann’s constant, $cped_{9}$, $cped_{10}$, $cped_{11}$, and $cped_{12}$ are the machine-specific pedestal coefficients.

The electron temperature at the pedestal top (in eV) is computed using the density pedestal values: $T_{e,\text{ped}} = \dfrac{p_{\text{ped}}}{2\,n_{e,\text{ped}}\,k_B\,}. $

Built-in defaults (applied by machine)

If any of the following are unset, the code fills them using the table below. “Unset” is detected as cbound(9)<0, cbound(10)<0, or cbound(11)/cbound(12) equal to the sentinel value 99.

LPED(3)=213

This model combines the option LPED(3)=3 for the calculation of the pedestal width and LPED(3)=21 for the calculation of the height. In this case, even when LPED(2)=2 is selected, the pedestal width is calculated from the NTCC model. There is no need for specifying the value of CPED(3) with this option.

NOTE: this model uses a parametrization that has been derived for ITER, do not use otherwise.

LPED(3)=223

This model combines the option LPED(3)=3 for the calculation of the pedestal width and LPED(3)=21 for the calculation of the height. In this case, even when LPED(2)=2 is selected, the pedestal width is calculated from the NTCC model. There is no need for specifying the value of CPED(3) with this option.

NOTE: this model uses a parametrization that has been derived for ITER, do not use otherwise.

Models based on EPED1

LPED(3)=23

LPED(3)=100

This model uses a multi-dimension interpolation over the space of parameters that are input to the EPED1 calculations [P. Snyder et al, Nucl. Fusion 51 (2011) 103016]. The lookup table consists of over 6000 EPED1 calculations that cover the operational parameter space of ITER and that are described here.

NOTE: this lookup table has been derived for ITER, do not use otherwise.

LPED(3)=111

Neural network based on EPED1 calculations, trained over calculations for ITER, DIII-D, C-Mod, JET and KSTAR [O. Meneghini et al, Nucl. Fusion 57 (2017) 086034].

Tanh fit reconstruction of the pedestal

LPED(9)=1

An option has been implemented to reconstruct a pedestal shape from a tanh function (see equation above for the density profile). This option is activated by setting LPED(9)=1. For backward compatibility this option is not available for the NTCC module, which uses a linear profile between the pedestal and the plasma boundary.

Top: Analytic density profile; the inset shows the position of the pedestal and the pedestal top. Bottom: predicted temperature profile, with (black) and w/o (red) a hyperbolic tangent parametrization for the pedestal region (default setting in the NTCC pedestal module).