EQDSK to JOREK (eqdsk2jorek.f90)

Equilibrium data reconstructed by EFIT and saved in EQDSK format can be converted into JOREK input data using eqdsk2jorek.f90.

Compiling

To compile eqdsk2jorek, you first need to install the Dierckx library. It is used to interpolate the poloidal flux function from the EQDSK rectangular $(R,Z)$ grid onto the JOREK boundary.

  • Download the Dierckx library in your home directory (GitHub distribution from Daan Van Vugt):

    cd $HOME
git clone https://github.com/Exteris/libdierckx.git

  • Compile the Dierckx library:

    cd libdierckx
make

  • Go to your JOREK main directory and add the path to the Dierckx library in Makefile.inc. For example:

    # --- DIERCKX Library
LIBDIERCKX = /marconi/home/userexternal/dbonfigl/libdierckx/libdierckx.a

  • Compile eqdsk2jorek:

    make eqdsk2jorek

Running

Pipe your EQDSK file to eqdsk2jorek:

./eqdsk2jorek < filename.eqdsk

Input files

This program reads standard EQDSK files. In some cases, however, EQDSK numeric formatting (number of digits per value) differs. In that case, some read statements in eqdsk2jorek.f90 may need to be adapted.

A namelist file named eqdsk2jorek.nml can be used to change the default behavior of eqdsk2jorek without recompiling. The eqdsk2jorek_params namelist must be defined inside eqdsk2jorek.nml.

Parameters in eqdsk2jorek_params:

  • tokamak_name: defines the hard-coded plasma boundary parameter family
    • Available tokamak-specific families: ITER (default), JET, DIII-D
    • User-defined plasma boundary parameters from namelist: USER_DEFINED

  • boundary_type: defines plasma boundary parameters for a specific tokamak. Parameters are magnetic-axis major radius and vertical position (R_axis, Z_axis), minor radius (r_minor), ellipticity ($\kappa$), upper/lower triangularity ($\delta_u$, $\delta_l$), and upper/lower quadrangularity ($\zeta_u$, $\zeta_l$).

    Omitting upper/lower identifiers, the plasma boundary is computed as:

    $R = R_{axis} + r_{minor}\cos(\theta + \delta\sin(\theta) + \zeta\sin(2\theta))$

    $Z = Z_{axis} + r_{minor}\kappa\sin(\theta)$

    Available values:

    • ITER
      • CLOSE_WALL_FIT: $\kappa$: 2, $\delta_u$: 0.55, $\delta_l$: 0.65, $\zeta_u$: -0.1, $\zeta_l$: 0.15, R_axis: 6.2, Z_axis: 0.1, r_minor: 2.25
      • OUTSIDE_WALL (default): $\kappa$: 2.1, $\delta_u$: 0.58, $\delta_l$: 0.65, $\zeta_u$: -0.12, $\zeta_l$: -0.0, R_axis: 6.2, Z_axis: -0.05, r_minor: 2.34
    • JET
      • OUTSIDE_WALL: $\kappa$: 1.85, $\delta_u$: 0.4, $\delta_l$: 0.4, $\zeta_u$: -0.2, $\zeta_l$: -0.2, R_axis: 2.9, Z_axis: 0.1, r_minor: 1.08
      • OUTSIDE_WALL_SHORT_LEG (default): $\kappa$: 1.7, $\delta_u$: 0.4, $\delta_l$: 0.4, $\zeta_u$: -0.4, $\zeta_l$: -0.2, R_axis: 2.85, Z_axis: 0.15, r_minor: 1.1
      • LIMITER: $\kappa$: 1.7264, $\delta_u$: 0.276, $\delta_l$: 0.2497, $\zeta_u$: -0.07, $\zeta_l$: 0.1274, R_axis: 2.875, Z_axis: 0.2213, r_minor: 1.026
      • INSIDE_LIMITER: $\kappa$: 1.785, $\delta_u$: 0.26, $\delta_l$: 0.2497, $\zeta_u$: -0.03, $\zeta_l$: 0.29, R_axis: 2.865, Z_axis: 0.19, r_minor: 0.999
      • CIRCULAR: $\kappa$: 1, $\delta_u$: 0, $\delta_l$: 0, $\zeta_u$: 0, $\zeta_l$: 0, R_axis: read in EQDSK, Z_axis: read in EQDSK, r_minor: read in EQDSK
    • DIII-D
      • OUTSIDE_WALL: $\kappa$: 1.85, $\delta_u$: 0.4, $\delta_l$: 0.4, $\zeta_u$: -0.2, $\zeta_l$: -0.2, R_axis: 1.7, Z_axis: 0, r_minor: 0.7
      • NIMROD_M3DC1: $\kappa$: 1.35/0.7, $\delta_u$: 0.3, $\delta_l$: 0.3, $\zeta_u$: 0, $\zeta_l$: 0, R_axis: 1.7, Z_axis: 0, r_minor: 0.7

For predefined machine families, n_tht_in is typically set to 257. Note that R_axis, Z_axis, and r_minor can be rescaled by setting R_scale different from 1. Examples of JET OUTSIDE_WALL and OUTSIDE_WALL_SHORT_LEG are shown in the Tips and Tricks section below.

  • ellip_in: user-defined ellipticity (default: 1)
  • tria_up_in: user-defined upper triangularity (default: 0)
  • tria_low_in: user-defined lower triangularity (default: 0)
  • quad_up_in: user-defined upper quadrangularity (default: 0)
  • quad_low_in: user-defined lower quadrangularity (default: 0)
  • n_tht_in: number of poloidal angles used to discretize the plasma boundary (default: 259)
  • r0_in: major radius of magnetic axis (default: 3)
  • z0_in: vertical position of magnetic axis (default: 0)
  • a0_in: plasma minor radius (default: 1)
  • B_scale: magnetic-field scaling factor (default: 1)
  • I_scale: plasma-current scaling factor (default: 1)
  • R_scale: spatial scaling factor (default: 1)
  • smth: smoothing parameter of plasma profile interpolator (default: 1.d-6, see Tips and Tricks below)
  • eqdsk_string_r_min: substring used to find plasma minor radius in EQDSK file (default: MINOR RADIUS -> A [m]). Currently used only for JET + CIRCULAR.

Extension of the pressure profile to the SOL

EQDSK files include pressure (and FFprime) only up to the separatrix. For most JOREK runs you will need a profile defined further outside the separatrix. In recent versions, pressure is extended into the SOL by matching a linear function and a tanh function with the same value and radial derivative at the separatrix. The far-SOL value of the extended pressure profile is set to 1\% of pressure at the separatrix.

You can modify this behavior in eqdsk2jorek.f90 by searching for p_bnd. This is used together with a predefined density profile to produce jorek_temperature.

Pressure extension to SOL

Note: this may misbehave if p(sep) > p(sep-1).

Output files

The program produces multiple files:

  • jorek_namelist
  • jorek_ffprime
  • jorek_pressure
  • jorek_temperature
  • jorek_density
  • profiles_eqdsk
  • limiter.dat
  • boundary.dat
  • psiRZ_eqdsk
  • eqdsk.vtk
  • eqdsk.ps

The original profiles from EQDSK are written to profiles_eqdsk against normalized poloidal flux:

psi_norm   F   pres   FdF/dpsi   dp/dpsi   q

psiRZ_eqdsk is an ASCII file containing the $\Psi(R,Z)$ map.

eqdsk.ps can be used to assess whether the produced data is usable for JOREK (mainly for experienced users).

Tips and Tricks

The OUTSIDE_WALL (blue line) and OUTSIDE_WALL_SHORT_LEG (red line) boundaries of the JET family are shown below. OUTSIDE_WALL_SHORT_LEG is used to avoid very long divertor legs. LIMITER has limiter shape without legs, while INSIDE_LIMITER is inside the limiter and includes part of a limiter leg (useful for STARWALL extensions when the first wall is used as the resistive wall, since response matrices are computed between the JOREK boundary and first wall and should not intersect).

JET wall contours

JET first-wall contours

The smoothing parameter smth can strongly affect interpolation and should always be checked (for example, with jorek2.ps produced by running JOREK) to ensure the interpolation along the JOREK boundary is smooth enough. The original choice smth = 1.d-6 may create non-smooth interpolation near the X-point, causing artifacts in JOREK's flux-aligned mesh. The value smth = 3.d-3 has been found to be a good trade-off both at and away from the X-point (compared with IDL cubic interpolation as reference) for JET pulse 89800, as shown below.

Dierckx smoothing example