TJ-II Eirene geometry
J. Guasp, A.Salas
Contents
1. TJ-II New geometry.
2. Cell interception,
3.Vacuum Vessel interception .
4. Examples of trajectories.
5. Present code structure.
6. Future work.
7. Conclusions
Ciemat. 27 April 2006
1. TJ-II New geometry
An alternative geometry module for the application of Eirene to TJ-II has been built
that avoids the problems of cell intersection, re-entry and holes that appear in
other TJ-II models and simplifies at maximum the cell location and the
intersection with the cell walls and other intercepting surfaces (Vacuum Vessel,
limiters, etc.) that is the main time consuming task in the code.
In this new model all the cells are hexahedra (6 plane faces, 8 vertex), two of the
faces lie on toroidal planes and are square (but are not parallel), the two lateral
faces are rectangles whose arists are horizontal or vertical while the upper and
lower faces are quadrilateral (trapezoids) lying on an horizontal plane.
The plasma is divided in toroidal layers (usually 38 by semiperiod, one octant,
DF=1.2º) and in each layer an uniform cartesian grid, centered at the local
magnetic axis position for the middle toroidal plane of the layer, is drawn. The
grid extends both sides of the magnetic axis (the center) until the last node lies
more than 5 cells outside the plasma. Usually there are, at maximum, 35 cells
along the horizontal and vertical directions (DR , DZ~2 cm)
The geometry is built only once for each magnetic configuration, outside Eirene,
and is kept permanently as a binary file (44 Gby, ~5 min., program grideir).
1. TJ-II New geometry
FDF
FDF
.
F
FDF
FDF
.
axis
axis
Y
Z
X
.
R
Z
The cells are built starting from the middle toroidal plane and launching horizontal lines
normal to that plane until they intercept the near and rear toroidal planes. These
intersections determine the cell vertex. By construction the cell walls are contiguous
without neither holes nor overlapping.
1. TJ-II New geometry
Drawing
not very correct !!!
.
.
o
.
o
x
Z
R
The cells are built starting from the middle toroidal plane and launching horizontal lines
normal to that plane until they intercept the near and rear toroidal planes. These
intersections determine the cell vertex.
Central cells
1. TJ-II New geometry
100_44_64
Red: Plasma
Blue:
Completelly
insi
de the VV
Orange:Some corner
outside, Center inside
Black crosses: Some
corner outside. Center
outside.
Black Asterisk:
All the cell outside
the VV
Vacuum cells
Black X: Some corner
inside. Center outside
Blue X. Fully outside
Cell distribution at F = 0.6º (RA1) for the TJ-II geometry.
View at the center of the 1st toroidal layer. Toroidal projection
(R-R0, Z). 35x35 cells, at maximum, in each cross section (1.9
cm), 38 layers by semiperiod (1.2º). 91 poloidal vertex in VV
(4º). Ports of VV eliminated farther than 50 cm from coil center.
1. H detection chords
Chord
dz(cm)
smin
1
0.64
0.89
2
1.95
0.76
3
3.27
0.69
4
4.59
0.57
5
5.91
0.48
6
7.23
0.39
7
8.55
0.27
8
9.86
0.18
9
11.2
0.11
10
12.5
0.08
11
13.8
0.0
__________________________
12
----0.0
13
----0.14
Toroidal cut at F = -155º showing the plasma cross section, the 2nd limiter and the
projection of the 1st chord, the closest point to the magnetic axis has s = 0.90 and is
very near the limiter position.
There are in total 11 chords, sharing a common origin, that are on the same vertical
plane. The closest plasma radius reached by these chords appears in the table above
and goes from 0.9 (1st) up to the axis (11th).
1. TJ-II New geometry
Physical input variables (densities, temperatures, magnetic field, average plasma
radius, etc.) are assigned to the cell centers.
In addition a short series of codified labels are also associated to the cells, indicating
the position of corners and center with respect to the Vacuum Vessel (VV), if
they correspond either to the inside of the plasma, the border or the Scrape-off
Layer (SOL), etc.
Each of these cells (called central cells, cf. §3) has an associated number and also a
label that says in which toroidal layer as well as horizontal and vertical cell is
placed.
Even if the geometry file is limited to a single octant, the Eirene calculations can be
done (if so wished) for the full TJ-II 4 periods in order to deal with aperiodic
scenarios. The real geometry seen by Eirene is the multiplication of the
contained in the file after applying the Stellarator symmetry. For this reason
each cell has a double identification: the one corresponding to the full 4 period
geometry and the equivalent cell of the 1st octant.
1. TJ-II New geometry
100_44_64
Central cells
Red: Plasma
Blue:
Completelly
insid
e the VV
Orange:Some corner
outside, Center inside
Black crosses: Some
corner outside. Center
outside.
Black Asterix:
All the cell outside
the VV
Vacuum cells
Cell distribution for the TJ-II geometry. Vertical projection
(X, Y), ortogonal view from top. 35x35 cells, at
maximum, in each cross section (2.0 cm). 38 layers by
semiperiod (1.2º). 91 poloidal vertex in VV (4º). Ports
eliminated farther than 50 cm from center.
Black X: Some corner
inside. Center outside
Blue X. Fully outside
1. TJ-II New geometry
100_44_64
Central cells
Red: Plasma
Blue:
Completelly
insid
e the VV
Orange:Some corner
outside, Center inside
Black crosses: Some
corner outside. Center
outside.
Black Asterix:
All the cell outside
the VV
Vacuum cells
Cell distribution for the TJ-II geometry. Lateral projection
(F, Z), ortogonal view from outside. 35x35 cells, at
maximum, in each cross section (2.0 cm). 38 layers by
semiperiod (1.2º), 91 poloidal vertex in VV (4º). Ports
eliminated farther than 50 cm from center.
Black X: Some corner
inside. Center outside
Blue X. Fully outside
2. Cell interception
As the cell grid is uniform in all coordinates, it is very easy given a point in space to
know to which cell corresponds, even in the full 4 period case.
The interception with the cell walls is also very easy and quick, it is enough to
calculate the distance from a point inside the cell to the planes that limit it and
are ahead in the velocity direction. As all the planes are either horizontal,
vertical or toroidal the normal vectors to these faces are trivial and a very
simple analytical formula can be applied.
As, in addition, all the cells are concave from the inside there is certainty the the
first intersection correponds to the minimum calculated distance, without need
to do any residual or area sum checking.
2. Cell interception
Pv
n
d = ([PV - P0] . n) / (n . v)
Pf = P0 + d .v
Pf
v
P0
Example of intersection with the call walls. As the cells are concave from the
inside, there is certainty the the first intersection correponds to the minimum
calculated distance, without need to do any residual or area sum checking.
3. Vacuum Vessel interception
The Vacuum Vessel (VV) of TJ-II has not been modelled in our geometry by
volume cells, but as a mosaic of triangular plane plates. It forms always integral
part of the geometry file.
The starting point for this element was a VV CAD model (as with the plasma a
single octant is enough) that later has been divided in uniform toroidal sections
(just the same number as before: 39, DF = 1.2º), and each toroidal section in 90
pieces along the poloidal direction (DQ=4º). These rectangular, non planar,
(sometimes extremely non planar) pieces were afterwards, divided consistently
in 2 contiguous triangles. The triangle vertex list, as well as the normal vector
of each triangle, are written into the geometry file.
The origin (0º) of the poloidal direction is chosen starting from the helix described
by the toroidal coil centers and along a radial horizontal line going to the inside
of the torus. The poloidal angle goes in counter clock wise direction.
In order to discard unnecessary complexity and useless space, before that depiecing,
the VV was stripped of part of the ports. Anything lying farther than 50 cm
from the coil center was ignored.
3. Vacuum Vessel interception
In order to be able to determine when a trajectory intersects the VV a supplementary
set of cells (called, perhaps not very properly, Vacuum cells) has been added to
the geometry.
It consists, for each toroidal layer, in a ring of 8 wide rectangular cells that
surrounds completely the central cells. The inner walls of these new cells are in
contact with the outer central layer. The more external walls are chosen so as
they are fully outside the VV. So every point of the VV lies with certainty either
inside these Vacuum cells or (i.e. the Hard Core points) somewhere in the
central region.
Further than these Vacuum cells there is only the Outside Darkness, any point lying
there corresponds to an illegal cell, and when checked (i.e. by function
LEAUSR) gives a negative cell number.
This helps to determine if the intersection has happened: if a trayectory coming
from a cell inside the VV goes either to a cell (central or not) where all the
corners are outside the VV or it falls in the Darkness, it is a clear indication
that, somewhere along the path, the VV has been hit, and this puts limits to the
region where it is to be found.
3. Vacuum Vessel interception
This finding is done in the following way.
The more extreme coordinates of the intersecting trajectory are calculated, and for
security measurements they are increased, along every direction, by a finite
quantity (usually 10 times the size of a central cell).
Inside this region all the VV triangles are checked, first calculating the distance to
the initial point but, as the VV can be as well concave as convex from the
inside (and sometimes extremely convex), we can not, anymore, take the
nearest triangle, as was done for the central cells. Instead, this time, we must be
sure that the point of intersection with the plane of the triangle is really inside
that triangle.
This check is done by an sum of areas algorithm, that is the equivalent of the
residual theorem in complex variable, when applied to a triangular contour. If
the point is inside, then the sum of the areas subtended by the point and each
couple of vertex must be just equal to the triangle area. In the contrary the point
is outside. Of course allowance must be given for the finite accuracy of the
computer.
3. Vacuum Vessel interception
P1
Incorrect
drawing !!
Pv n
Q
v
P0
F
d = ([PV - P0] . n) / (n . v)
Pf = P0 + d .v
Example of intersection with the VV: For every one of the triangles placed
inside the extreme limits of the detection zone (increased by some security
margins), a sum of areas algorithm must be performed, and only if the check
is affirmative the point retained as the exit one.
3. Vacuum Vessel interception
3
1
.
3
.
P
P
1
2
3
2
¡¡¡ Plane Geometry!!!
1
P
.
2
In the Sum of Areas algorithm, if point P is inside the triangle (123) then:
AP12 + AP23 + AP31 = A123
Otherwise if P is outside:
AP12 + AP23 + AP31 > A123
And it is enough than anyone of the partial areas AP12, etc. be > A123 to be sure
that the point is outside the triangle.
4 Examples of trajectories
In this way the neutral trajectories can be followed
The next figures show two different examples of trajectories, both correspond to a
He case, where the neutrals are born at the vacuum vessel surface and, usually,
are absorbed at the plasma and reflected many times at the VV.
Each point corresponds to either a cell interception of a VV reflexion
The first couple correspond to an unusually short trajectory, and therefore can be
visualised much better, under a vertical and a lateral view.
The second couple is a more usual one, 261 points, this is the usual number of
interceptions and reflections before the particle is absorbed.
4 Examples of trajectories
A very very short trajectory for an He atom. Vertical projection (X, Y). It starts in the
green square an finish, by ionisation, near the plasma center (red losange).
4 Examples of trajectories
A very very short trajectory for an He atom. Lateral projection (F, Z). It starts in the
green square an finish, by ionisation, near the plasma center (red losange).
4 Examples of trajectories
A more usual trajectory for an He atom (261 points). Vertical projection (X, Y).
It starts in the green square (first cuadrant near the wall) an finish, by ionisation,
near the plasma center (red losange, lower 4th cuadrant).
4 Examples of trajectories
261
A more usual trajectory for an He atom (261 points). Vertical projection (F, Z)
It starts in the green square (right middle) an finish, by ionisation, near the plasma
center (red losange, left middle).
5. Present code structure
The 2004 version of Eirene has been installed in the two parallel computers of
Ciemat and is running properly:
jen50: SGI Origin-3800 with a f90 MIPSpro compiler version 7.41, and 124
processors
fénix: SGI Altix-3700 with the f90 INTEL compiler version 8.0, and 96 PE's
In both computers the code has been compiled with optimisation -O2/3 and
runs in parallel under MPI.
The code itself runs after a preparatory program preproc, serial, very fast that makes
many things: reads and checks the geometry, reads the files containing the
plasma input profiles, or alternatively extracts them for the TJ-II discharge Data
Base, reads data for the diagnostic chords and generates the corresponding
cartesian coordinates expected by Eirene and, mainly, modifies and prepare the
input file.
In the same way, after Eirene exits, a second serial program postproc is executed, it
reads several files created by Eirene (i. e. the detailed tallies results from
PRTTAL that have been diverted, at Ciemat, to files, etc.) and prints several
kind of results or generates files for graphic representation.
5. Present code structure
Preproc
Geometry
Preliminay input file for Eirene
Namelist (modalities, chords, etc.)
Radial plasma profiles
Eirene
Initialisation
Trajectory
calculation
Gathering of data
and results
Postproc
Graphic files
Main results:
(neutral distribution in plasma,
ibid. along chords, etc.)
5. Present code structure
The TJ-II helical geometry has been adapted to Eirene using the options:
LEVGEO = 6 (general geometry), INDPRO = 12*5 (calls to PROUSR for the
input plasma profiles) and SORLIM < 0. (calls to SAMUSR for the source
distribution).
In the present version for TJ-II there are up to 19 non standard surfaces:
1. The Vacuum Vessel. Reflecting.
2. The limbo. Absorbing. Used to finish pathological trajectories (~ 10-5)
3. The plasma border. Transparent
4.- 5. Two limiters. Reflecting.
6.- 7. Two gas puffing valves. Transparent. Included to allow these sources.
8.- 19. 4 NBI injectors. Included as sources. And 4 Pump valves.
Usually there are up to 13 sources. (7 in jen50 due to some unfathomable errors)
1. The VV wall.
2.- 3. The two limiters
4.- 5. The two gas puffing valves.
6.- 13. The 4 NBI injectors and 4 Pumps.
In reason of a parallelisation problem we can use now only a single stratum for all
the sources distributed in up to 12(7) substrata. Although a palliative has been
found.
5. Present code structure
Execution times at fenix computer (with diagnostic chords):
Case He: 9.5x106 trajectories, total time = 12 min. (24 PEs, Batch)
Case H: 2.4x106 trajectories, total time = 8 min. (24 PEs, Batch)
These execution times are approx. double at Jen50 computer.
5. Present code structure
Many of the results that previously did appear on the output file have been diverted
to files that can be read by other programs (i.e. postproc, vertray, verflux, etc.).
The main results that can be obtained now are the following:
Resulting electron density radial profiles
Distribution of neutral particles in the plasma, averaged over magnetic surfaces.
Distribution of neutral particles along selected TJ-II and diagnostic chords
CX Energy spectra along selected TJ-II chords.
Halpha emissivity along selected TJ-II chords.
All those results allow the possibility for plotting
Plots for trajectories ( < 15000, < 1000 points by trajectory). Program vertray.
Also included:
Emissivity of 4 He lines (similar to sigha.f and halpha.f) along chords.
Distribution of impacts on the VV and the plasma surface (too much disk
space consuming … …). Program verflux.
Driver to allow parameter scans.
Driver to allow parameter fits to experimental data.
5. Present code structure
Neutral density
Helium
enl (10
1,5 10
1 10
7 10
tp = 13 ms
6 10
cm )
10
-3
10
10
13
2 10
13
-3
cm )
2,5 10
10
enl (10
3 10
enl13=0.95
10
5 10
Fit
5 10
4 10
3 10
2 10
9
enl13=0.65
enl13=1.00
enl13=1.80
Neutral density
Hydrogen
tp = 13, 13, 17 ms
9
9
9
9
9
9
1 10
0
9
0
0
0,2
0,4
r/a
0,6
0,8
1
0
0,2
0,4
r/a
0,6
0,8
1
Radial profiles of the neutral density in the plasma, averaged over magnetic surfaces.
Near the plasma border the exponential fitting separates visibly from the calculations.
The absolute values of these densities are inversely proportional to the supposed particle
confinement time (tp).
5. Present code structure
Neutral density (cm
Helium
3,5 10
3 10
2,5 10
2 10
1,5 10
1 10
5 10
-3
)
Neutral density (cm
Helium
10
5 10
10
SA1Top
4 10
tp = 13 ms
10
10
3 10
10
2 10
s = 0.41
10
1 10
9
0
-3
)
10
SD1T ang( Co)
10
tp = 13 ms
10
10
s = 0.12
10
0
20
30
40
50
dist (cm)
60
70
80
100
120 140
Longitudinal profile of neutral density along two chords of TJ-II.
160 180
dist (cm)
200 220
6. Supplementary work
Already done:
Emissivity of 4 He lines (similar to sigha.f and halpha.f) along chords.
Distribution of impacts on the VV and the plasma surface (too much disk
space consuming … …). Program verflux.
Driver to allow parameter scans.
Driver to allow parameter fits to experimental data.
Comparison of Eirene results with the experimental emissivity of He spectral
lines.
Partially done:
Determination of the neutral distribution near the limiters by means of H signals.
In preparation:
Determination of the neutral distribution inside the plasma by means of CX signals.
Explore the possibility to use the H signals present in the Scattering Thomson
measurements.
Etc., etc.
7. Conclusions
An alternative geometry module for the application of Eirene to TJ-II has been built
that avoids the problems of cell intersection, re-entry and holes, and simplifies
at maximum the cell location ant the intersection with the cell walls and other
intercepting surfaces (Vacuum Vessel, limiters, etc.) that is the main time
consuming task in the code.
Efficient algorithms for the interception of the trajectories with cell walls and the
TJ-II Vacuum Vessel have been incorporated.
The geometry has been adapted to the 2004 Eirene version and is now working
satisfactorily in the two parallel computers of Ciemat.
Comparison with experimental data of He spectral line emission and H has been
adressed also.