.. |newcase_icon| image:: ../../../resources/new_case.png .. _hnb_study: SMITER-PFCFLUX benchmark 'HNB FW study' Test case ------------------------------------------------- Introduction ^^^^^^^^^^^^ The purpose of the :abbr:`HNB (Heating Neutral Beam)` FW study was to measure the worst case heat loads on FW panels ``14NE`` and ``15NE``, located around the :abbr:`HNB (Heating Neutral Beam)`-:abbr:`DNB (Diagnostic Neutral Beam)` ports. The scenario is an outer limiter configuration, operated at half-field (2.65T) and I_p=5MA with an assumed P_sol=5MW with the longest possible decay length of 29 millimeters. The EQDSK file is ``glimOWL175cm5p0MA2p65T_t10s_RDMR.txt``. This report examined the ``14NE`` and ``15NE`` panels and evaluate the worst case heat loads in the case of a outer limiter configuration. The misalignment of the shadow panels is also considered and the results mainly focus on results of the case with the highest resolution target mesh and the misaligned shadow mesh. To further see how vertical shifts affect the panels, the EQDSK is vertically shifted from 500 mm to -500 mm with 100 mm increments. Since the software is still in development along the version release number the GIT hash string is also provided. The version of SMITER used: * ``SMITER release/1.6: 9dba7d9aa03e7f1498cc48a5b7615b4656550040`` The field line ray trace program SMARDDA version: * ``smardda_lib: 7cef21bff13f1ff8ae10ebbfcd871a0af4319202`` * ``smardda_pfc: 3db912ffb0425ee9614f5a4738f188703ccd8dfe`` Input data ^^^^^^^^^^ Meshes """""" Target mesh consists of panels 14NE and 15NE. There are three variants of the mesh: * Low resolution variant with maximum 10 mm triangle edge length * Higher resolution variant with maximum 5 mm triangle edge length * Same as second but with refined panel edges that contain triangles with maximum 1 mm triangle edge length .. note:: The low and higher resolution both have holes, while the refined mesh is without holes .. figure:: images/hnb_target_mesh_10mm.png Mesh 14NE15NE with maximum triangle edge length 10 mm .. figure:: images/hnb_target_mesh_5mm.png Mesh 14NE15NE with maximum triangle edge length 5 mm .. figure:: images/hnb_target_mesh_5mm_refined1mm_edge.png Mesh 14NE15NE with maximum triangle edge length 5 mm with refined panel edges that contain triangles with maximum triangle edge length 1 mm Differences between the meshes: .. figure:: images/hnb_target_mesh_comparison.png Comparison of panel edges for **5 mm** and **5 mm + refined 1 mm** For shadowing the following list of meshes were used. All were meshed with maximum triangle edge length 25 mm: * 13A_S2_VVS01 * 13A_S3_VVS02 * 13A_C4_VVS02 * 14A_S2_VVS01 * 13AD_C3_VVS02 * 14NC_C5_VVS03 * 14ND_S3_VVS02 * 14ND_S4_VVS02 * 15A_S2_VVS01 * 15NC_C5_VVS03 * 16A_S4_VVS02 * 16A_C5_VVS03 * 16A_C4_VVS02 .. figure:: images/hnb_shadow_mesh_full.png .. note:: Shadowing meshes are translated to allow for worst case misalignments between neighboring panels. Translations are done parallel to the insertion/installation axis of each shadow FW panels. The following table shows the translation vector for each shadow panel. Namely, the translation is done by 5 mm in the direction of insertion/installation of each panel respectively. All values are in millimeters and values are rounded to the second digit. +--------------+--------+--------+-------+ | Panel | dx | dy | dz | +==============+========+========+=======+ |13A_S2_VVS01 | 3.44 | 2.9 | 2.1 | +--------------+--------+--------+-------+ |13A_S3_VVS02 | 2.25 | 3.9 | 2.1 | +--------------+--------+--------+-------+ |13A_C4_VVS02 | 1.55 | 4.25 | 2.1 | +--------------+--------+--------+-------+ |14A_S2_VVS01 | 3.8 | 3.2 | 0.6 | +--------------+--------+--------+-------+ |13AD_C3_VVS02 | 2.9 | 3.44 | 2.1 | +--------------+--------+--------+-------+ |14NC_C5_VVS03 | 0.0 | 4.95 | 0.6 | +--------------+--------+--------+-------+ |14ND_S3_VVS02 | 0.85 | 4.9 | 0.6 | +--------------+--------+--------+-------+ |14ND_S4_VVS02 | 0.85 | 4.9 | 0.6 | +--------------+--------+--------+-------+ |15A_S2_VVS01 | 3.2 | 3.2 | -0.4 | +--------------+--------+--------+-------+ |15NC_C5_VVS03 | 0.0 | 4.95 | 0.6 | +--------------+--------+--------+-------+ |16A_S4_VVS02 | 0.8 | 4.5 | -2.0 | +--------------+--------+--------+-------+ |16A_C5_VVS03 | 0.8 | 4.5 | -2.0 | +--------------+--------+--------+-------+ |16A_C4_VVS02 | 1.55 | 4.3 | -2.0 | +--------------+--------+--------+-------+ The translated shadow meshes in the HNB.hdf carry the name of the mesh and the suffix ``_translated``. The change is not visible from a plane, but it impacts the results significantly since the wetted on the shadowed or target mesh depends on the surrounding meshes. .. figure:: images/hnb_shadow_mesh_translation.png Display of the translation on mesh of panel ``13A_C4_VVS02`` Equilibrium """"""""""" The equilibrium used is EQDSK-G **glimOWL175cm5p0MA2p65T_t10s_RDMR.txt**. .. figure:: images/hnb_equilibrium_limiter_and_plasma.png Written limiter and plasma (LCFS) geometry in the EQDSK-G file Display of meshes and EQDSK """"""""""""""""""""""""""" The following picture shows the shadowed, shadowing, LCFS and plasma geometry all together. The LCFS and plasma geometry were rotated by 70 degrees around the z axis. .. figure:: images/hnb_meshes_with_eqdsk_geometry.png And a closed up image to the target NE14NE15 mesh. .. figure:: images/hnb_target_eqdsk_closeup.png Setting up the SMITER case ^^^^^^^^^^^^^^^^^^^^^^^^^^ The study ``HNB.hdf`` already contains the meshes of the target panels and shadow panels. Together the meshes of shadow panels are joined into a single mesh called ``Shadow``. Similarly the grouped mesh for translated shadows are called ``Shadow_translated``. Since self-shadowing is also important, the final version of the shadow meshes are: * Shadow_with_tri_10mm * Shadow_with_tri_10mm_translated .. image:: images/hnb_list_of_meshes_in_browser.png Creating the SMITER case """""""""""""""""""""""" When in SMITER, activate the SMITER module. Then click on the |newcase_icon| to open up the dialog. Set the ``Case name`` to ``HNB_10mm_translated``. For this configuration the ``decay length`` is 0.029 meters or 29 millimeters. The power loss defined is to 5 MW. Leave the optional wall mesh empty and set the ``target mesh`` to ``mesh_tri_10mm_14NE15NE`` and shadow mesh to ``Shadow_with_tri_10mm_translated``. For the ``EQDSK file`` click on the file browser, set the ``Files of type`` to ``All files (*)``, go to ``smiter/study/hnb`` and select **glimOWL175cm5p0MA2p65T_t10s_RDMR.txt**. Click :guilabel:`Ok`. .. image:: images/hnb_prepare_case.png Settings parameters for GEOQ """""""""""""""""""""""""""" In the Salome Object browser right click on the target GEOQ, which has the same name as the target mesh. Select :guilabel:`Edit CTL`. Under ``beqparameters`` change the parameters to the following values: +--------------+-------------+-------------------------------------------------+ | Parameter | Value | Description | +==============+=============+=================================================+ | beq_bdryopt | 9 | Plasma flux value at boundary is given as input | +--------------+-------------+-------------------------------------------------+ | beq_cenopt | 4 | Read the center values of R and Z from eqdsk | | | | file | +--------------+-------------+-------------------------------------------------+ | beq_fldspec | 3 | Use Cartesian coordinate system | +--------------+-------------+-------------------------------------------------+ | beq_nzetap | 1 | Fieldlines might go around torus! | +--------------+-------------+-------------------------------------------------+ | beq_psiref | -13.6917 | Specify flux value at LCFS | +--------------+-------------+-------------------------------------------------+ .. note:: The current ``beq_psiref`` is user specified, but the one written in the EQDSK G file is ``-13.653458``. The LCFS flux value depends on the geometry of the target mesh. Do the same for the shadow mesh. .. note:: SMARDDA can evaluate the LCFS flux value with setting the ``beq_bdryopt`` to 3. But since it depends of type of interpolation (smardda uses a bivariate spline) users might specify their own calculated value. Setting parameters for HDSGEN """"""""""""""""""""""""""""" Right click on ``Hdsgen`` and select :guilabel:`Edit CTL`. Set the following value under ``positionparameters``. +---------------------+-------------+--------------------------------+ | Parameter | Value | Description | +=====================+=============+================================+ | position_transform | 1 | Scale in Cartesian coordinates | +---------------------+-------------+--------------------------------+ Under ``btreeparameter`` set the following values. +------------+-------------+-------------------------------------+ | Parameter | Value | Description | +============+=============+=====================================+ | tree_nxny | 1,2,2 | Multi-octree no. of children | +------------+-------------+-------------------------------------+ | tree_ttalg | 2 | Use nxyz, set split at top directly | +------------+-------------+-------------------------------------+ | tree_type | 3 | Type of tree is multi-octree | +------------+-------------+-------------------------------------+ Under ``hdsgenparameters`` set the following values. +--------------------+-------------+---------------------------------------------+ | Parameter | Value | Description | +====================+=============+=============================================+ | geometrical_type | 2 | Element type is triangles | +--------------------+-------------+---------------------------------------------+ | limit_geobj_in_bin | 200 | Max number of geometrical objects per bin | +--------------------+-------------+---------------------------------------------+ | margin_type | 2 | Expand global bounding box bin | +--------------------+-------------+---------------------------------------------+ Setting parameters for POWCAL """"""""""""""""""""""""""""" Right click on ``Powcal`` and select :guilabel:`Edit CTL`. Set the following values under ``powcalparameters``. +--------------------+-------------+---------------------------------------------------------------+ | Parameter | Value | Description | +====================+=============+===============================================================+ | calculation_type | global | 'global' shadowing by fieldlines which may wrap around torus | +--------------------+-------------+---------------------------------------------------------------+ | shadow_control | 1 | Enable shadowing | +--------------------+-------------+---------------------------------------------------------------+ Prepared the rest of the cases in almost exact manner, except the meshes are different. The other cases can be prepared by duplicating the first one, changing the case name and replacing the meshes: - Case with 10 mm target mesh and misalignment is not applied to shadow mesh - Case with 5 mm target mesh and misaligned shadow mesh - Case with 5 mm + refined edges target mesh and misaligned mesh .. image:: images/hnb_prepared_cases_in_study.png Run case """""""" Now right click on the ``HNB_10mm`` and select :guilabel:`Compute case`. Next step is running with shifted EQDSK data in ``Z-axis``. The reason behind is to see how the wetted area and heat load deposition changes in regards of the shift. The following values are applied in such steps: +-----------------+-----------------+-------------------+ | Plasma position | beq_zmove (mm) | beq_psiref (LCFS) | +=================+=================+===================+ | 500 | 500 | -13.871 | +-----------------+-----------------+-------------------+ | 400 | 400 | -13.823 | +-----------------+-----------------+-------------------+ | 300 | 300 | -13.775 | +-----------------+-----------------+-------------------+ | 200 | 200 | -13.726 | +-----------------+-----------------+-------------------+ | 100 | 100 | -13.679 | +-----------------+-----------------+-------------------+ | 0 | 0 | -13.6917 | +-----------------+-----------------+-------------------+ | -100 | -100 | -13.725 | +-----------------+-----------------+-------------------+ | -200 | -200 | -13.76 | +-----------------+-----------------+-------------------+ | -300 | -300 | -13.794 | +-----------------+-----------------+-------------------+ | -400 | -400 | -13.828 | +-----------------+-----------------+-------------------+ | -500 | -500 | -13.862 | +-----------------+-----------------+-------------------+ We could duplicate each case for such shift, but that will result in larger .hdf file, too much data used on the filesystem when running the cases. Instead we can use the provided dialog under :menuselection:`&Smiter --> &Case --> Rerun SMITER case with different parameters`. When activated we select a SMITER case from the SALOME object browser, select which parameter we would like to change, in this case ``beq_zmove`` and provide a space separated list of values for the parameter (``beq_zmove``) we wish to change and a space separated list of of values for the ``Psiref``. Both lists must contain the same number of values to run.:: # beq_zmove values 500 400 300 200 100 0 -100 -200 -300 -400 -500 # beq_psiref values -13.871 -13.823 -13.775 -13.726 -13.679 -13.6917 -13.725 -13.76 -13.794 -13.828 -13.862 .. figure:: images/hnb_example_of_rerun_cases_dialog.png Then click :guilabel:`Ok` and the selected SMITER case will be rerun fully for all those values. This way we minimize the number of SMITER cases and therefore we minimize the risk of making small mistakes. The output powcal_powx.vtk VTK file generated by ``POWCAL`` is saved as ``__.vtk``. Therefore when the dialog finishes all the runs, activate ``ParaVis`` module, and open the results as a ParaView **group**. This way instead of having multiple pipeline objects in the VTK pipeline browser, you will have a grouped object that has slide like functionality. Results ^^^^^^^ Effect of misalignment on wetted area """"""""""""""""""""""""""""""""""""" The following images shows the importance of regarding misalignments on the shadow meshes. The images are for the case where no shift is applied to the EQDSK. It depends on what we focus, but for the base example, where no shift is added to the EQDSK, the wetted area changes on the center faces of the target. .. figure:: images/hnb_misalignment_comparison.* Importance of taking panel misalignment into account when it comes to shadowing effect POWCAL results on HNB 5mm + refined edges meshes + misaligned shadow """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" The following images show the results of case with misaligned (or translated) shadow mesh and the 5mm + refined edges target mesh. The value shown of the images is the heat load Q :math:`[\frac{MW}{m^2}]`. The corresponding SMITER case in the ``HNB.hdf`` study is ``HNB_5mm_refine1mm_edges_translated``. For each case only the **beqparameter** ``beq_zmove`` and ``beq_psiref`` is different. The results were obtained by using the dialog to rerun cases at a different beq parameter and beq_psiref. .. figure:: images/hnb_10mm_up_shift.* Heat load profile for EQDSK shift > 0 along the z-axis .. figure:: images/HNB_5mm_refined_edges_0.png :scale: 50% :align: center EQDSK not shifted (beq_zmove=0, beq_psiref=-13.6917). .. figure:: images/hnb_10mm_down_shift.* Heat load profile for EQDSK shift > 0 along the z-axis Edge results comparison ^^^^^^^^^^^^^^^^^^^^^^^ As in the reference study, the values will be shown for each edge and compared to the values in the study in the SMITER/PFCFLUX value. The tables show heat deposition values and penetration length in dependence of EQDSK shift along the z-axis. The values were taken inside ``ParaVis`` module. For :math:`q_{edge-Be}` the maximum value was taken right at the edge on the outer side. While for :math:`q_{edge-Steel}` the maximum value was taken at penetration length 20 millimeters. The way the penetration length was taken was to measure the maximum achieved depth at each edge. If the specified value is ``Full`` or ``Full edge`` then the wetted are is along the whole edge. Edge indexing """"""""""""" The following picture shows the numerical indexing of edges. .. figure:: images/hnb_edge_indexing.png Edge #1 """"""" +------------------+-------------------------------------+------------------------------------------+--------------------------+ | beq_psiref (mm) | :math:`q_{edge-Be} [\frac{MW}{m^2}]`| :math:`q_{edge-Steel} [\frac{MW}{m^2}]` | penetration length (mm) | +==================+=====================================+==========================================+==========================+ | 500 | / | / | / | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | 400 | / | / | / | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | 300 | / | / | / | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | 200 | / | / | / | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | 100 | 0.39 / 0.33 | 0.24 / 0.2 | Full edge / Full edge | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | 0 | 0.58 / 0.5 | 0.25 / 0.29 | Full edge / Full edge | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | -100 | 0.58 / 0.5 | 0.24 / 0.23 | Full edge / Full edge | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | -200 | 0.58 / 0.5 | 0.24 / 0.23 | 30 mm / 30 mm | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | -300 | / | / | / | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | -400 | / | / | / | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | -500 | / | / | / | +------------------+-------------------------------------+------------------------------------------+--------------------------+ Edge #2 """"""" +------------------+-------------------------------------+------------------------------------------+--------------------------+ | beq_psiref (mm) | :math:`q_{edge-Be} [\frac{MW}{m^2}]`| :math:`q_{edge-Steel} [\frac{MW}{m^2}]` | penetration length (mm) | +==================+=====================================+==========================================+==========================+ | 500 | / | / | / | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | 400 | / | / | / | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | 300 | / | / | / | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | 200 | / | / | / | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | 100 | / | / | / | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | 0 | 0.6 / 0.6 | 0.3 / 0.33 | 35 / 30 | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | -100 | 0.6 / 0.6 | 0.3 / 0.33 | Full / Full | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | -200 | 0.6 / 0.6 | 0.3 / 0.33 | Full / Full | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | -300 | 0.6 / 0.6 | 0.3 / 0.33 | Full / Full | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | -400 | 0.61 / 0.6 | 0.29 / 0.33 | Full / Full | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | -500 | 0.61 / 0.6 | 0.31 / 0.33 | Full / Full | +------------------+-------------------------------------+------------------------------------------+--------------------------+ Edge #3 """"""" +------------------+-------------------------------------+------------------------------------------+--------------------------+ | beq_psiref (mm) | :math:`q_{edge-Be} [\frac{MW}{m^2}]`| :math:`q_{edge-Steel} [\frac{MW}{m^2}]` | penetration length (mm) | +==================+=====================================+==========================================+==========================+ | 500 | / | / | / | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | 400 | / | / | / | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | 300 | / | / | / | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | 200 | / | / | / | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | 100 | / | / | / | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | 0 | / | / | / | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | -100 | 1.38 / 1.3 | / | ~2 / 2 | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | -200 | 0.9 / 1.0 | / | 10 / 10 | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | -300 | 0.55 / 0.55 | / | 13 / 10-15 | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | -400 | 0.29 / 0.35 | 0.2 / 0.19 | 20 / 20 | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | -500 | 0.125 / 0.15 | 0.08 / 0.07 | 25 / 25 | +------------------+-------------------------------------+------------------------------------------+--------------------------+ Edge #4 """"""" +------------------+-------------------------------------+------------------------------------------+--------------------------+ | beq_psiref (mm) | :math:`q_{edge-Be} [\frac{MW}{m^2}]`| :math:`q_{edge-Steel} [\frac{MW}{m^2}]` | penetration length (mm) | +==================+=====================================+==========================================+==========================+ | 500 | / | / | / | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | 400 | / | / | / | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | 300 | 0.15 / 0.15 | 0.09 / 0.09 | Full / Full | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | 200 | 0.3 / 0.3 | 0.2 / 0.2 | 35 / 35 | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | 100 | 0.6 / 0.6 | / | 15 / 15 | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | 0 | / | / | / | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | -100 | / | / | / | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | -200 | / | / | / | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | -300 | / | / | / | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | -400 | / | / | / | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | -500 | / | / | / | +------------------+-------------------------------------+------------------------------------------+--------------------------+ Edge #5 """"""" +------------------+-------------------------------------+------------------------------------------+--------------------------+ | beq_psiref (mm) | :math:`q_{edge-Be} [\frac{MW}{m^2}]`| :math:`q_{edge-Steel} [\frac{MW}{m^2}]` | penetration length (mm) | +==================+=====================================+==========================================+==========================+ | 500 | / | / | / | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | 400 | / | / | / | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | 300 | / | / | / | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | 200 | / | / | / | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | 100 | / | / | / | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | 0 | 0.87 / 0.95 | / | 5 / 5 | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | -100 | 0.5 / 0.55 | / 0.27 | 18 / 20 | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | -200 | 0.2 / 0.27 | 0.1 / 0.13 | 27 / 25 | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | -300 | 0.09 / 0.1 | < 0.04 / 0.05 | 37 / 30 | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | -400 | / | / | / | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | -500 | / | / | / | +------------------+-------------------------------------+------------------------------------------+--------------------------+ Edge #5 bis """"""""""" +------------------+-------------------------------------+------------------------------------------+--------------------------+ | beq_psiref (mm) | :math:`q_{edge-Be} [\frac{MW}{m^2}]`| :math:`q_{edge-Steel} [\frac{MW}{m^2}]` | penetration length (mm) | +==================+=====================================+==========================================+==========================+ | 500 | / | / | / | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | 400 | 0.15 / 0.16 | 0.055 / 0.05 | > 50 / >>40 | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | 300 | 0.36 / 0.4 | 0.11 / 0.11 | > 50 / >>40 | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | 200 | 0.71 / 0.8 | 0.23 / 0.23 | 50 / > 40 | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | 100 | 1.14 / 1.35 | 0.35 / 0.35 | 25 / 25 | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | 0 | 0.9 / 0.9 | / | 10 / 10 | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | -100 | / | / | / | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | -200 | / | / | / | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | -300 | / | / | / | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | -400 | / | / | / | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | -500 | / | / | / | +------------------+-------------------------------------+------------------------------------------+--------------------------+ Edge #6 """"""" +------------------+-------------------------------------+------------------------------------------+--------------------------+ | beq_psiref (mm) | :math:`q_{edge-Be} [\frac{MW}{m^2}]`| :math:`q_{edge-Steel} [\frac{MW}{m^2}]` | penetration length (mm) | +==================+=====================================+==========================================+==========================+ | 500 | 0.3 / 0.4 | 0.18 / 0.17 | Full / Full | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | 400 | 0.55 / 0.5 | 0.35 / 0.35 | Full / Full | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | 300 | 0.9 / 1 | 0.5 / 0.5 | 35 / 40 | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | 200 | 1.04 / 1.15 | / | 11 / 10 | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | 100 | / | / | / | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | 0 | / | / | / | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | -100 | / | / | / | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | -200 | / | / | / | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | -300 | / | / | / | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | -400 | / | / | / | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | -500 | / | / | / | +------------------+-------------------------------------+------------------------------------------+--------------------------+ Edge #7 """"""" +------------------+-------------------------------------+------------------------------------------+--------------------------+ | beq_psiref (mm) | :math:`q_{edge-Be} [\frac{MW}{m^2}]`| :math:`q_{edge-Steel} [\frac{MW}{m^2}]` | penetration length (mm) | +==================+=====================================+==========================================+==========================+ | 500 | 0.3 / 0.3 | 0.15 / 0.2 | Full / Full | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | 400 | 0.55 / 0.6 | 0.35 / 0.4 | Full / Full | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | 300 | 0.85 / 0.8 | 0.45 / 0.4 | 65 / 65 | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | 200 | 1 / 1 | 0.6 / 0.65 | 35 / 30 | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | 100 | 1.1 / 1.1 | / | 9 / 7 | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | 0 | / | / | / | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | -100 | / | / | / | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | -200 | / | / | / | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | -300 | / | / | / | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | -400 | / | / | / | +------------------+-------------------------------------+------------------------------------------+--------------------------+ | -500 | / | / | / | +------------------+-------------------------------------+------------------------------------------+--------------------------+ .. |beginfigref| raw:: latex \begin{minipage}{\textwidth} .. |endfigref| raw:: latex \end{minipage}