DIV3D

DIV3D field line followning and intersection code.
Jeremy D. Lore (2010 - 2024)

Description

This code was developed to assess divertor and baffle loads and design a new high heat flux component, the "scraper element" for the W7-X stellarator.

The code should be referenced with the following citiations:

[1] J.D. Lore, et al., "Design and Analysis of Divertor Scraper Elements for the W7-X Stellarator", IEEE Trans. Plasma Sci. 42 (2014), 539-544. DOI: 10.1109/TPS.2014.2303649

[2] J.D. Lore, et al., "Modeling and Preparation for Experimental Testing of Heat Fluxes on W7-X Divertor Scraper Elements", IEEE Trans. Plasma Sci. 46 (2017), 1387-1392. DOI: 10.1109/TPS.2017.2780624(https://doi.org/10.1109/TPS.2017.2780624)

Comparison to experimental data is given in:

[3] J.D. Lore, et al., "Measurement and modeling of magnetic configurations to mimic overload scenarios in the W7-X stellarator", Nuclear Fusion 59 (2019), 066041. DOI: 10.1088/1741-4326/ab18d1(https://doi.org/10.1088/1741-4326/ab18d1)

Compilation

To build:

1. Add MACHINE_ID to build/setup_cmake.sh. Set correct location of fortran mpi compiler.
2. from ./build run setup_cmake.sh
   • If hdf5 (or lapack) is not detected by cmake check default path (/usr/lib/x86_64-linux-gnu/hdf5/openmpi)

Running the code

Call the executable with mpirun or equivalent. At least two processes are required. The controller process distributes the work and loops over the worker processes which follow field lines and check for intersections.

mpirun -np 5 /path/to/div3d.exe

Code Description and Logic

run_settings and bfield_nml namelists are read from run_settings.nml

1. Magnetic field is initialized
2. Intersection components are read from part files and triangular facets are defined.
3. Controller node traces a field line from the input point. Assumed to be a closed flux surface.
4. Points are initialized randomly along the field line defining the closed surface.
5. Worker processes follow fieldlines with diffusion from start points, then check for intersections.
   • Fieldlines are integrated in toroidal angle. To get a full representation, diffusion should be performed in both toroidal directions.
   • If no part intersection is found then intersections with the vessel are checked.
   • Vessel intersections currently only consider nearest toroidal slice.
   • The intersection data is output, including optionally segments of the local (diffused) field line.

I/O Description

Input files

1) run_settings.nml

This file contains namelists for the magnetic field description (bfield_nml namelist) and DIV3D run settings (run_settings namelist)

• bfield namelist

  • rmp_type = specifies format of magnetic field info
  • bgrid_fname = bgrid path + file name (if rmp_type=bgrid)
  • vmec_coils_file = path + file name of VMEC coils file (if rmp_type=vmec_coils)
  • vmec_extcur_set = external current scaling(if rmp_type=vmec_coils)
  • gfile_name = path + file name of equdsk file (if rmp_type=g)

• run_settings namelist

  • fname_plist = parts.list file name

  • fname_ves = vessel.part file name

  • fname_surf = surface line output file name

  • fname_launch = launch points output file name

  • fname_parts = all parts output file name

  • fname_hit = fieldline trace prior to strikepoint output file name

  • fname_intpts = intersection points output file name

  • fname_nhit = number of hits output file name

  • fname_ptri = part triangular groups output file name

  • fname_ptri_mid = triangular mid-points output file name

  • nfp = number of field periods

  • Rstart, Zstart, Phistart = location of LCFS trace start point

  • dphi_line_surf_deg = step size in field line tracing (degrees), used for LCFS surface without diffusion

  • ntran_surf = number of toroidal transits for LCFS field line tracing

  • npts_start = number of points randomly distributed along the LCFS surface line

  • dmag = diffusion coefficient in m^2 / m

  • dphi_line_diff_deg = step size in field line tracing (degrees), used for field line tracing with diffusion

  • ntran_diff = number of toroidal transits to trace each field line with diffusion

  • trace_surface_opt = whether to trace out surface, false means skip tracing surface and read in launch_points (from previous run)

  • myseed = random number generator seed

  • hit_length = length of end of fieldline recorded. This is an estimate computed as floor(hit_length/Rstart/abs(dphi_line_diff))

  • lsfi_tol = tolerance in computing intersection of line segment with facets, when int point is along edge

  • calc_lc = logical variable controlling whether connection length is computed. (default true)

  • calc_theta = logical variable controlling whether angle between field line and plane of facet is calculated. (default false)

  • quiet_bfield = logical variable controlling whether warnings from bfield routines are printed to screen. (default true)

2) parts.list

This file contains the description of the components to be checked for intersection.

Example:

2
"/path/to/component.part"
"/path/to/component.jpart"

The format of the part is specified by the file extension.

• .part files have the following format:

Label 
ntor npol nfp rshift zshift
Do itor = 1,ntor
  phi(itor)
  Do ipol = 1,npol
     R(itor,ipol), Z(itor,ipol)

The .part files are defined as a fixed number of poloidal points (npol) at a number of toroidal planes (ntor). Parts are structured in the sense that the poloidal resolution is fixed, this is used to define the triangular facets. All parts are shifted to the first field period. Parts should be defined fully within a field period to avoid issues where the remapped part can overlap the domain. Stellarator symmetry is NOT assumed, so even up/down symmetric parts should be included across the domain [0,2*pi/nfp]. Units are cm, degrees. Internal to the code these are converted to meters, radians. Label : Descripitive part label. Character(len=100) ntor : Number of toroidal planes. Integer npol : Number of poloidal points. Integer nfp : Field period symmetry of the component. Integer Rshift, Zshift : The part can be uniformly shifted from the given (R,Z) points using these inputs. Real, [cm]. phi : Toroidal coordinate of each slice. Real, [deg]. R,Z : Radial and vertical coordinate of each point. Real, [cm].

• .jpart files have the following format:

Label 
ntor npol nfp rshift zshift
Do itor = 1,ntor
  Do ipol = 1,npol
     R(itor,ipol), Z(itor,ipol), phi(itor,ipol)

The .jpart files are very similar to the .part format, with the generalization that the toroidal coordinate of each point is also defined. This is useful for components that are not aligned with toroidal planes. Other than the 2D array nature of phi, all other variables have the same meaning and units.

3) vessel part

This file contains the description of the vessel

The vessel is defined using the same format and units as the .part files above. The vessel is not triangulated. Instead, after checking for intersection with the components in the parts list, the field line is checked for an excursion from the vessel. This is done by finding the the first point that leaves the vessel polygon at the nearest vessel slice of the local field line coordinate.

4) Magnetic Field Grid

Magnetic field options:

• vmec_coils – coils file from VMEC, may be slow
• vmec_coils_to_fil – turns the VMEC coilset into a series of current filaments
• Xdr – format used by W7X, basically just RZ cartesian slices with the RZ grid shifting with the axis toroidally
• Bgrid – a RZ cartesian grid at some toroidal resolution (most general, fast)

Output files

The names of these files can be set in the run_settings namelist

1) surface_line.out

This file contains one fieldline trace followed from (rstart, zstart, phistart) without diffusion to make a LCFS surface approximation.

Row 1: period:toroidal angle of a field period (radians), nip0:number of points at each toroidal angle, ip_step:stride to stay at constant toroidal angle
Row 2: nline: total number of points along field line
Do i = 1:nline
  R(i)  : meters
  Z(i)  : meters
  phi(i) :radians
end

A Poincare plot can be made from this data from an index I using stride ip_step
e.g., R(1:ip_step:end),Z(1:ip_step,end)

2) allparts.out

This file contains all the data from the parts-list parts reformatted

3) hitline.out

This file contains locations of the last section of the fieldline at and before strikepoint

Line-by-line information about diffused fieldlines that intersect the parts and vessel.
Controlled by input hit_length, if negative this file is not written to. If set to a positive value
then approximately the last hit_length distance along the field line is output.

Format:
For each line:
npts (int)
r(npts)   (m)
z(npts)   (m)
phi(npts) (radians)

4) int_pts.out

This file contains the points of intersection between each fieldline and vessel / divertor surfaces

Row by row information of points that hit "parts".

R (m) | Z (m) | Phi (rad) | ihit | ipart | itri | i | Lc | theta
R,Z,Phi -> Int point in mapped periodic section  
ihit    -> (1) hit a "part", (2) hit the vessel, (0) no intersection.  
itri    -> Index of intersected triangle  
i       -> Index along field line
Lc      -> one-directional distance along diffused fieldline from start point to intersection point
theta   -> signed angle (radians) between field line and plane of facet.

6) hitcount.out (fname_nhit)

This file contains the number of points that hit a divertor / vessel surface vs not hitting anything

7) part_triangles.out (fname_ptri)

This file contains part triangles defined by three (x,y,z) corner locations

8) part_triangle_mids.out (fname_ptri_mid)

This file contains the mid-points of the triangles from parts file

9) launch_pts.out (fname_launch)

This file contains the launch (starting) location points of the fieldlines that are traced

All launch points are defined in the first field period (positive phi).

Row by row information of points where fieldlines are initiated. 
number of points
R,Z,Phi (m, radians)

Screen output

Regular "part" hit: [i,ipart,P] -> P is the intersection point in X,Y,Z (m)
Vessel hit: [i,P] -> P is the intersection point in X,Y,Z (m)

Bfield namelist example

! Several options are available, see bfield_module.F90
! Coils defined in filaments
! B components on grid
rmp_type = 'bgrid'
bgrid_fname = 'path/to/bgrid'
! VMEC coils with extcur
! xdr grid format
! gfile example
/

run_settings namelist example

fname_plist    = 'parts.list'
fname_ves      = 'path/to/vessel.part'
fname_surf     = 'surface_line.out'
fname_launch   = 'launch_pts.out'
fname_parts    = 'allparts.out'
fname_hit      = 'hitline.out'
fname_intpts   = 'int_pts.out'
fname_nhit     = 'hitcount.out'
fname_ptri     = 'part_triangles.out'
fname_ptri_mid = 'part_triangle_mids.out'

nfp = 3

Rstart   = 4.d0 
Zstart   = 0.d0
Phistart = 0.d0
dphi_line_surf_deg = 0.1d0
ntran_surf = 20

npts_start = 10
dmag = 3.155d-4
dphi_line_diff_deg = 0.5d0
ntran_diff = 1000

trace_surface_opt=.true.
myseed = 110115

!hit_length = 1.0d0
hit_length = -1.0d0

lsfi_tol = 1.d-12