4.19. Calculation of connection lengths for ELM cases

4.19.1. Introduction

The given input to ELM loss model that calculates the heat flux profile, as described in , are the connection lengths as a function of distance from the first separatrix (or LCFS - last closed flux surface). To calculate connection lengths in SMITER, one must prepare an appropriate mesh, starting from the point where the first separatrix is piercing through the midplane (this could be from on outer or the inner side). In this section, the calculation of connection lengths for ITER_IDM_DML5YK is presented, where the field lines are starting at outer midplane on the cross section with LCFS.

The point at which the field line calculation starts is calculated with GEOQ code and can be obtained in geoq_geoq.out file. The values for R and Z coordinates are given as zcen and rbdry. See Fig. 4.61.

../../_images/icrh_antenna_dml5yk_lcon_start_point.png

The mesh should then extend from this point on the midplane towards the target. See Fig. 4.62.

../../_images/icrh_antenna_dml5yk_lcon_start_mesh.png

The general approach here is to generate as much of those meshes in toroidal direction on the midplane as possible, calculate fieldlines for each of them and then average the connection lengths on triangles, that have the same radial distance from the separatrix. In case of ITER_IDM_DML5YK study, the shadow is axisymmetric around the z-axis, so one can take into an account only the 20-degree segment. Thus we can generate 40 such meshes in toroidal direction inside the 20-degree segment. See Fig. 4.63.

../../_images/icrh_antenna_dml5yk_lcon_start_40meshes.png

After that, one can calculate the connection lengths on this mesh, setting it as a target.

4.19.2. Generate mesh for connection length (baseline scenario)

To create an appropriate mesh with several segments inside SMITER, move to SMITER->case->get connection length mesh SMITER ‣ Case ‣ Create connection length mesh, as shown in Fig. 4.64.

../../_images/icrh_antenna_dml5yk_lcon_get_mesh_path.png

The following appears on screen Fig. 4.65.

../../_images/icrh_antenna_dml5yk_lcon_get_mesh_dialog.png

In the box Mesh data the following parameters need to be adjusted:

  • Mesh name = ‘lcon_mesh’: Name of mesh to be displayed in Mesh module)
  • Toroidal sector = ‘20’: Toroidal sector in degrees starting from phi=0. If the shadow is axisymmetric on every 20 degrees, then 20 degrees should be the input number.)
  • Number of segments = ‘40’: Number of segments in the specified toroidal sector. The segments are equally spaced in toroidal direction. The step between two neighbouring segments is ‘toroidal sector’/’number of segments’, i.e. 20/40=0.5 deg)
  • Number of points per segment = 250*: Number of points per one segment)
  • Length of segment = ‘99’: Length of segment, starting from LCFS)

In the box GEOQ values the following parameters need to be adjusted:

  • Selected SMITER case = ‘case’: To specify this value, select a SMITER case from the object browser to get the position of starting point for the meshes)
  • Rm [m] = ‘0.0’: Radial distance to outer midplane - LCFS cross section, calculated by GEOQ, updated when selecting a SMITER case in the Object Browser)
  • Zcen [m] = ‘0.0’: Position of outer midplane, calculated by GEOQ, updated when selecting a SMITER case in the Object Browser)

Click on Apply to generate the mesh. The mesh with specified name will appear in Object Browser in Mesh module.

To better grasp the definition of the parameters in Mesh data, consider the setup of the Mesh data as shown in Fig. 4.65. The resulting mesh is displayed in Fig. 4.66.

../../_images/icrh_antenna_dml5yk_lcon_mesh_values.png

4.19.3. Creating the SMITER cases

For calculation of the connection lengths one should refer to smiter/study/icrh_antenna/ and open ITER_IDM_DML5YK_connection_length.hdf.

Inside, there are 10 cases:

  • shift_10_connection_length_to_inner: 10 cm shift of baseline equilibria towards the outer targets. The fieldlines are traced from outer midplane to inner targets.
  • shift_8_connection_length_to_inner:8 cm shift of baseline equilibria towards the outer targets. The fieldlines are traced from outer midplane to inner targets.
  • shift_6_connection_length_to_inner: 6 cm shift of baseline equilibria towards the outer targets. The fieldlines are traced from outer midplane to inner targets.
  • shift_4_connection_length_to_inner: 4 cm shift of baseline equilibria towards the outer targets. The fieldlines are traced from outer midplane to inner targets.
  • baseline_connection_length_to_inner: Baseline equilibrium. The fieldlines are traced from outer midplane to inner targets.
  • shift_10_connection_length_to_outer:10 cm shift of baseline equilibria towards the outer targets. The fieldlines are traced from outer midplane to outer targets.
  • shift_8_connection_length_to_outer: 8 cm shift of baseline equilibria towards the outer targets. The fieldlines are traced from outer midplane to outer targets.
  • shift_6_connection_length_to_outer: 6 cm shift of baseline equilibria towards the outer targets. The fieldlines are traced from outer midplane to outer targets.
  • shift_4_connection_length_to_outer: 4 cm shift of baseline equilibria towards the outer targets. The fieldlines are traced from outer midplane to outer targets.
  • baseline_connection_length_to_outer: Baseline equilibrium. The fieldlines are traced from outer midplane to outer targets.

The difference between tracing to inner or outer targets is defined with the orientation of normals on the target mesh. To change orientation of triangles in SMITER, go to Mesh module and then Modification ‣ Orientation.

Target mesh consists of 40 segments in the toroidal section of \(20^{\circ}\). The shadow repeats itself around the torus for every 20 degrees, so one can analyze just one sector of 20 degrees. One mesh segment has 498 points. Refer to Fig. 4.63.

4.19.3.1. Settings parameters for POWCAL

To increase the maximum length of the field line, one should tweak the odesparameters in POWCAL, mainly max_numsteps and max_zeta. For more detail and options one should refer to SMARDDA documentation.

Parameter Value Description
max_numsteps 200000 Maximum number of steps for one fieldline integration
max_zeta 60 Maximum allowed change of one field line segment in toroidal direction

4.19.3.2. Plotting the result

Once the computation is finished, one has to get the average connection length from all 40 segments as a distance from the first separatrix (or last closed flux surface). This can be achieved by going to Smiter ‣ Case ‣ Plot connection lengths. The dialog in Fig. 4.67 will appear on screen.

../../_images/icrh_antenna_dml5yk_lcon_plot_lcon_dialog.png

In the box Selected case and number of segments select one of the cases in the study and the Rm parameter will be updated automatically. For number of segments one should add 40, since this is the number of segments in the mesh.

  • Selected SMITER case = case: To specify this value, select a SMITER case from the object browser to get the position of starting point for the meshes.
  • Rm [m] = 0.0: Radial distance to outer midplane - LCFS cross section, calculated by GEOQ.
  • *Number of segments** = 0: Number of segments in the specified toroidal. User must fill this manually.

Button Plot will plot the average connection length for the selected case as a function of distance from the first separatrix.

In the box Save to file navigate to the folder and set the name of the file to save the connection lengths and the distance from the separatrix. Then click on button Save to save the data. The saved file contains two columns, separated by whitespace. First column contains distance values in \(mm\) and second column contains connection lengths in \(mm\).

The results for the connection lengths going to inner targets is shown in Fig. 4.68.

../../_images/icrh_antenna_dml5yk_lcon_plots.png

4.19.3.3. Specifying ELM power deposition profile to POWCAL

Connection lengths are the input to the Edge localized mode model proposed by Fundamenski (refer to A model of ELM filament energy evolution due to parallel losses [PP05]).

[PP05]W Fundamenski, R A Pitts and JET EFDA contributors, Plasma Physics and Controlled Fusion, Vol. 48, Num. 1 (2005) https://doi.org/10.1088/0741-3335/48/1/008

To specify the ELM profile in SMITER, move to Smiter ‣ Case ‣ Custom exponential profile. In Profile parameters select ELM loss option. Refer to Fig. 4.69.

../../_images/icrh_antenna_dml5yk_lcon_elm_profile_dialog.png

Input parameters are given as

  • v_elm = 500: Velocity of ELM. Default=500m/s
  • n0 = 0.375000: Initial average density (\(*10^20/m^3\))
  • Te0 = 2500.000000: Initial mean electron temperature (eV)
  • Ti0 = 2500.000000*: Initial mean ion temperature (eV)
  • Aion = 2.500000: Coefficient for deuterium plasma. Default=2.5
  • fELM = 40: Frequency of ELM filament [Hz]
  • WELM = 1: Energy lost per ELM [MJ]
  • nfil = 10: Number of ELM filaments
  • poloWidth = 0.600000: Poloidal cross section of the filament [m]
  • aveFac = 1.700000: “Averaging” factor for the ELM filament impact onto the first wall
  • Connection lengths = file: Connection lengths profile as a distance from the first separatrix. Refer to prevoius chapter Plotting the results to see format of the file.

Specify the range and plot the result. The select the corresponding case in Object browser and click Apply profile to powcal to save the normalised ELM profile to powcal.