Contributions of MEdC Association to EFDA ITM – 2010
EFDA Task
Title of the MEdC contribution
MEdC
Coordinator
Page
WP10-ITM-AMNSACT2-T1-01/MEdC
Contribution of AMNS data - Supply atomic data
for collision strengths, cross sections and rates
for electron collision with atoms and ions. This
task will be done under joint collaboration with
ADAS and ISIP teams.
Viorica SANCALIE
2
WP10-ITM-AMNSACT3-T1-01/MEdC
Development and maintenance of AMNS
modules. - Development of modules to modules
delivering AMNS data in a standardized form to
ITM codes.
Viorica SANCALIE
6
WP10-ITM-IMP12ACT9-T1-01/MEdC
Resistive wall modes - Numerical model to
calculate the wall response (for a real 3D
geometry with holes, in the thin wall
approximation) to the external kink mode
perturbations of diverted tokamak configurations
(module complying with ITM specifications.).
Calin ATANASIU
9
WP10-ITM-IMP5-ACT4T1-01/MEdC
Development of an advanced 3D ion FokkerPlanck solver for ions
Gyorgy
STEINBRECHER
12
WP10-ITM-ISIP-ACT3T1-01/MEdC
Simulation catalogue querying tool
Vasile PAIS
23
WP10-ITM-ISIP-ACT10T1-01/MEdC
Administration of the collaborative software
Vasile PAIS
26
1
WP10-ITM-AMNS-ACT2-T1-01/MEdC
Contribution of AMNS data - Supply atomic data for collision strengths, cross sections and
rates for electron collision with atoms and ions. This task will be done under joint
collaboration with ADAS and ISIP teams.
Report for TA WP10-ITM-AMNS-ACT2
Reference:
Task Force: ITM
Area:
Task: WP10-ITM-AMNS-ACT1-T1
Document:
Contribution of AMNS data
Author(s):
Martin O'Mullane
BS
0.17
Vasili Kiptily
BS
0.10
MEdC
Viorica Stancalie
BS
1.00
ÖAW
Katharina Igenbergs
BS
0.50
ÖAW
Alexander Kendl
BS
0.10
Josef Seebacher
BS
0.10
Alan Keim
BS
0.20
CCFE
ÖAW
Start/End dates:
2010-01 / 2010-12
Distribution list:
Project Leader: D. Coster
Contributors:
Task Force Leader: G. Falchetto
MEdC Association (1.00 ppy BS )
CSU Responsible Officer: D.
Kalupin
Viorica Stancalie, MEdC Association (1.0 ppy BS)
Content:
Contribution of AMNS data
a. AMNS data are needed in several ITM modelling projects. The contribution
refers to Atomic data calculation in support of AMNS activity. The R-matrix
method and the Breit-Pauli R-matrix Method (BPRM) will be used to
2
Report for TA WP10-ITM-AMNS-ACT2
Reference:
Task Force: ITM
Area:
Task: WP10-ITM-AMNS-ACT1-T1
provide collision strengths, cross sections and rates for electron collision
with atoms and ions. This task will be done under joint collaboration with
ADAS and ISIP teams.
b. Deliverables/Milestones as given in Task Agreement (table 4.1, see below)
(1) R-matrix calculation of atomic data for C atoms and Fe-peak elements ;
(2) Electron impact excitation of C atoms and Fe –peak elements: collision
strengths, cross sections and rates.
c. Work description and outcome (results / particular highlights)
1. Collision strengths for the electron-impact excitation of forbidden
transitions between 136 terms arising from 3d6, 3d54s and 3d54p
configurations of Co3+ are calculated using the R-matrix method. The
accuracy of a series of models for the target terms is considered which
form the basis of R-matrix collision calculations. The importance of
including configuration interaction wave functions both in the target-state
expansion and in the (N + 1)-electron quadratically integrable function
expansion is discussed. Collision strengths are calculated for incident
electron energies up to 6 Ryd. These results are believed to be the first
such values for this system and are important for plasma modelling.
2. To assure a high level of consistency and integration of the data, as for
example the information on the lines and levels of an atom, benchmark
results for simulation of plasma population kinetics and emission spectra is
needed. Preliminary results from the Dirac Atomic R-matrix Calculation of
electron impact excitation with C, Ar and B atoms and their ions have been
obtained. Critical numerical comparison of perturbative (Breit-Pauli) and
non-perturbative (MCDF –EAL) predictions of fine structure splitting is
considered.
d. Achievement of objectives / deliverables
The objectives/deliverables proposed for 2010 have been achieved. Atomic
data and collision data for a series of atoms and ions have been obtained.
Results for Co IV ion have been submitted and accepted for publication in
3
Report for TA WP10-ITM-AMNS-ACT2
Reference:
Task Force: ITM
Area:
Task: WP10-ITM-AMNS-ACT1-T1
refereed journal.
e. Outstanding issues (could be empty only if task is closed!)
In collaboration with ADAS, IAEA and ITM groups, the work will continue in
order to secure the precision of level energy, radiative transition probabilities,
and collisional data. Methods and codes exist.
f.
Summary paragraph (to be copied to main project report section as the
task summary!)
Atomic data for Fe, Ni and Co and their ions are important in hot plasmas with low
electron density since the collisional rate of de-excitation for metastable levels may
be lower than the decay rate by magnetic dipole or electric quadrupole transitions,
which become observable. These ‘forbidden’ lines are the only transitions of the
multicharged ions in the visible or near ultraviolet spectral regions in which ion
temperatures can be derived from line profile measurements. Transition
probabilities of the iron group elements are of great importance in the calculation
of non-local thermodynamic equilibrium (LTE) line formation. We have carried out
the first detailed calculations of electron-impact excitation of forbidden transitions
amongst states with 3d6, 3d54s and 3d54p configurations in Co3+ (Stancalie V,
2011, Phys. Scr. in press). We explored the effect of including configuration
interaction wave functions both in the target states expansion and in the (N +1)electron quadratically integrable functions expansion. The target states have been
represented by elaborate configuration interactions in an attempt to account for
electron correlation effects where it is essential to include the 3p2  3d2 core
excitation in both the target and scattering wave functions. We found that this give
rise to very distinctive two-particle one hole resonances at higher energies.
g. Publications
Stancalie V., 2011 in press, Phys.Scr. 82, Forbidden transitions in excitation by
electron impact in Co3+: an R-matrix approach’
h. List of code camps attended in 2010
Revision No 1:
Changes:
4
Report for TA WP10-ITM-AMNS-ACT2
Reference:
Task Force: ITM
Area:
Task: WP10-ITM-AMNS-ACT1-T1
Date:
2011-01-04
Association
Written by:
Revised by:
Approved by:
MEdC
Viorica Stancalie
Ion MORJAN
Florin Spineanu
General Director, INFLPR
HRU – MEdC Association
5
WP10-ITM-AMNS-ACT3-T1
Development and maintenance of AMNS modules. - Development of modules to modules
delivering AMNS data in a standardized form to ITM codes.
Report for TA WP10-ITM-AMNS-ACT3
Reference:
Task Force: ITM
Area:
Task: WP10-ITM-AMNS-ACT3-T1
Document:
Author(s):
Development and maintenance of AMNS modules
MEdC
Viorica Stancalie
PS
0.30
ÖAW
David Tskhakaya
BS
0.30
David Tskhakaya
PS
0.30
Start/End dates:
2010-01 / 2010-12
Distribution list:
Project Leader: D. Coster
Contributors:
Task Force Leader: G. Falchetto
Association MEdC (0.3 ppy / PS actually committed
to task)
CSU Responsible Officer: D.
Kalupin
Content:
i.
V Stancalie, MEdC (0.3 ppy /PS actually committed)
Task description as given in Task Agreement
Development and maintenance of AMNS modules
A FORTRAN module will be developed to provide atomic data (cross sections,
collision strengths, energy levels, radiative transition probabilities) to ITM-TF
codes.
j.
Deliverables/Milestones as given in Task
Module in F90 for delivering AMNS data using ITM data structures to retrieve
data from the ITM database. Implementation of a module callable from a c
program for delivering AMNS data using ITM data structures to retrieve data
from the ITM database. Report documenting the Fortran and C modules
mentioned above.
k. Work description and outcome (results / particular highlights)
A crucial aspect for the ITM-TF is to provide AMSN data in a standardized form
6
Report for TA WP10-ITM-AMNS-ACT3
Reference:
Task Force: ITM
Area:
Task: WP10-ITM-AMNS-ACT3-T1
to different codes. The interface modules for AMSN data should be available as
libraries to be included in the link stage of an ITM-TF module. This means that one
has to consider different versions that can communicate with codes in different
languages supported by the ITM-TF infrastructure. A procedure needed to be
worked out to assure that the most relevant data is transferred to the ITM
database, and for notification that updates of data is recommended.
l.
Achievement of objectives / deliverables
A first version of the wrapper interface to call functions in AMNS module. C from
F90.
m. Outstanding issues (could be empty only if task is closed!)
To extend the work including: development of the existing wrapper interfaces,
testing the existing module taking more elements from the ADAS database and
write them to the ITM AMNS database (via the data structure), and to provide
documentation of data transfer to the ITM-TF
n. Summary paragraph (to be copied to main project report section as the
task summary!)
The strategy proposed at the end of 2009 for delivery of AMNS data to ITM-TF
codes has been implemented in order to decide on the appropriate
technologies for software development (version management tools and
collaborative tools). The main task was to decide on how the ADAS database
could be used by the ITM-TF. A first version of the wrapper to call functions in
AMNS module has been provided.
o. Publications
1. Pais V.F. et al., "Enabling remote access to projects in a large collaborative
environment", Fusion Engineering and Design 85,2010, 633.
2. Pais V., "Web Services Usage in Distributed File Systems", Fusion
Engineering and Design 85, 2010, 419.
3. Guillerminet B, Iannone F, Imbeaux F, Manduchi G, Maslennikov A, Pais V,
Strand P, “Gateway: New high performance computing facility for EFDA
task force on integrated Tokamak modelling”, Fusion Engineering and
7
Report for TA WP10-ITM-AMNS-ACT3
Reference:
Task Force: ITM
Area:
Task: WP10-ITM-AMNS-ACT3-T1
Design 85, pp. 410-414, 2010
p. List of code camps attended in 2010
Revision No 1:
Changes:
Date:
2011-01-04
Association
Written by:
Revised
by:
Approved by:
MEdC
Viorica Stancalie
Viorica
Stancalie
Ion MORJAN
8
General Director, INFLPR
WP10-ITM-IMP12-ACT9-T1-01/MEdC
Resistive wall modes - Numerical model to calculate the wall response (for a real 3D
geometry with holes, in the thin wall approximation) to the external kink mode perturbations
of diverted tokamak configurations (module complying with ITM specifications.).
EFDA ITM Task Force
Deliverable under Base- Line Support
Reference:
Task Force: ITM
Area: Equilibrium, MHD and disruptions
Task: WP10-ITM-10-IMP12-ACT9-T1-01/MEdC
Document:
Task Title: Application of our numerical model to calculate the wall response (for
a real 3D geometry with holes) to the external kink mode perturbations in a
diverted tokamak configurations.
Author(s):
Name and Association(s) of the Author(s) :
Calin Vlad Atanasiu, Augustin Moraru, Association EURATOM – MEdC Romania
Date:
31, December, 2010
Distribution list:
Project Leader: Maurizio Ottaviani
Gloria Falchetto (Task Force Leader)
Denis Kalupin (CSU Responsible Officer)
9
EFDA ITM Task Force
Deliverable under Base- Line Support
Reference:
Task Force: ITM
Area: Equilibrium, MHD and disruptions
Task: WP10-ITM-10-IMP12-ACT9-T1-01/MEdC
Content:
In order to calculate the wall response (for a real 3D geometry with holes) to the
external kink mode perturbations, the following tasks have been achieved:
1.
The vacuum field due to a helical perturbation of an External Kink
Mode (EKM) in a diverted tokamak configuration has been determined by using our
single layer potential model [C.V. Atanasiu et al. P.OP, 11, 2004].
2. To calculate the wall response to the EKM, the following intermediate steps
have been followed:
2.1. First, a time domain formulation for a fixed plasma has been considered;
2.2 For the more complex case of rotating plasma, a frequency domain
formulation has been deduced. All considered values are complex now;
2.3 To check our equations, the moving wall and fixed plasma case has been
considered, by using Minkowski’ formulation for the Maxwell equations and
Ohm’s law,
3. Due to the big error around re-entry corners existing practically in all walls,
and knowing that conformal transforms can not be used for Poisson type
equations, nor for non-Cartesian coordinates, we have developed a special
methodology to remove the re-entry corner singularity (the relative error due to
this singularity is of ~ 10% around the corner. After removing it, we succeeded to
decrease it to 0.24%)
4. First, tests of our programme on Gateway, after changing NAG and IMSL
routines with free of licence routines, have been performed.
Revision No: 1
Changes:
Written by:
Revised by:
Approved by:
Calin.V. Atanasiu
Ion MORJAN
Florin Spineanu
General Director,
INFLPR
HRU – MEdC
Association
10
Objectives
Elaboration of a numerical model to calculate the wall response (for a real 3D geometry with holes, in
the thin wall approximation) to the EKM perturbations of diverted tokamak configurations (module
complying with ITM specifications.).
Achievements
The wall response (with holes and in the thin wall approximation) has been calculated in a very effective
manner. For example, on a test 2D problem, for 151 x 151 grid points the classical approach needs 690s
CPU time, while with our new method 14s are necessary only. First runs on Gateway, without ITM
standard input-output, have been performed.
Shortcomings
In 2011, the input-output forms will be adapted to the ITM standards.
Conclusions and General perspectives
A very efficient numerical model to calculate the wall response (for a real 3D geometry with holes, in the
thin wall approximation) to the external kink mode perturbations of diverted tokamak configurations
has been finalised. First runs on Gateway, with appropriate mathematical libraries, have been
performed. Software modules will be compiled with ITM specifications.
References (to Conference paper/poster, Meeting, Publication)
1. C.V. Atanasiu, A. Moraru, L.E. Zakharov, “Influence of a nonuniform resistive wall on the External
Kink Mode in a tokamak”, ITM General Meeting, Lisbon, Spain,13-17 September, 2010.
11
WP10-ITM-IMP5-ACT4-T1-01/MEdC
Development of an advanced 3D ion Fokker-Planck solver for ions
Report for TA WP10-ITM-IMP5-ACT4
Reference:
Task Force: ITM
Area:
Task: WP10-ITM-IMP5-ACT4-T1-01/MEdC
Document:
Author(s):
Development of an advanced 3D ion Fokker-Planck solver for ions.
Gyorgy Steinbrecher (EURATOM-MEdC), ...
Start/End dates:
1.1.2010 - 1.12.2010
Distribution list:
Project Leader: D. Farina
Contributors: Gyorgy Steinbrecher
Task Force Leader: G. Falchetto
Association: EURATOM-MEdC
CSU Responsible Officer: D.
Kalupin
(0.5 ppy/PS)
Content:
A. Task description
A comparative study of the statistical errors by using different, exact or
approximate, Gaussian random number generators and new stochastic RungeKutta methods. The stochastic Runge-Kutta methods will be specially
adapted and optimised according to the explicit choice of the phase space
coordinates
B. Deliverables/Milestones as given in Task Agreement
B1. A document defining the agenda for a Working Session on the
Task, which also sets out the options to be discussed.
B2. Progress report on the developments within the task.
B1. Agenda for Working Session
S1. Study of the possibility of obtaining by analytical or numerical
methods information on the first and second order derivatives of the
diffusion coefficients with respect to the invariants, especially the
magnetic momentum.
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Report for TA WP10-ITM-IMP5-ACT4
Reference:
Task Force: ITM
Area:
Task: WP10-ITM-IMP5-ACT4-T1-01/MEdC
S2. The possibility to obtain (by analytic or numerical methods) and
asymptotic form of the diffusion coefficient near zero-value (or other
singularity points) of the magnetic momentum, together with clear error
bound. For instance, the possibility to find the linearity coefficient in the
formula
D(  )  c  O(  2 );   0
S3. If S1, and especially S2 are achieved, then the Fokker-Planck as well
as the backward Kolmogorov equation has exact solution, that can be
expressed by inverse Laplace transform of Bessel functions. Thus the,
numerically problematic, effect of the singularity of the diffusion
coefficient, for   0 are solved, at the expense to perform inverse
Laplace transform at each time step. Discussion how to implement
numerically this result.
S4. Mathematical study and elaboration of new class of robust numerical
methods for the solution of the category of stochastic differential
equations used in the Monte-Carlo solution of the Fokker-Planck
equation.
S5. Study of the approximations necessary to treat the effect of
singularities of the coefficients of stochastic differential equations
S6. Numerical tests of the corresponding FORTRAN 90 codes on
Gateway.
C. Work description and outcome (results / particular highlights)
C1. The problems studied
The stochastic differential equation (SDE) used for Monte-Carlo (MC)
solution of the Fokker-Planck equation that models the RF interaction in an
ideal axial symmetric tokamak configuration be reduced to the particular
form
dx   ( x) ' ( x)dt   ( x)dw(t )
where
13
(1)
Report for TA WP10-ITM-IMP5-ACT4
Reference:
Task Force: ITM
Area:
Task: WP10-ITM-IMP5-ACT4-T1-01/MEdC
 ( x) 2 / 2  D( x)  diff .coefficien t
(2)
, up to a constant x(t) is the magnetic momentum and
dw(t ) is a standard
Brownian motion.
The first, main problems are related to the singularity of the derivative of
 (x) , near x=0, that reduces the speed of convergence of the standard
stochastic integration methods. Due this singularity the stationary probability
density function is also singular [2]. This phenomenon is related to the heavy
tail effects studied in the works [3,4] and models of the singularity in the
probability distribution function studied in [5].
The second question is the possibility to elaborate a special class stochastic
Runge-Kutta method that solves the Eq. (1) without computing numerically
the derivative.
The third question is related to the phenomena observed in the work [3]: in
singular problems even for computing mean values we must use exact
Gaussian generators for integrating SDE.
C2. General results
Mathematical aspects on the instabilities in the numerical methods for the
solution of the Fokker-Planck equation, induced by parametric noises, due to
parametric noises of numerical methods associated to the solution of the SDE
were studied in [6].
Numerical tests on SDE with singularities, different form those studied in
[3,4] were performed. The conclusion is: stochastic integrators that use exact
Gaussian random number generators are more robust.
C3. New numerical methods
Method 1. Adaptive time step
When the function  (x) is locally approximated by linear function:
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Task Force: ITM
Area:
Task: WP10-ITM-IMP5-ACT4-T1-01/MEdC
 ( x)  Ax  B ,
x(t )  [ x(t 0 ) 
then Eq.(1) is exactly solvable:
B
] exp( Aw (t  t 0 )  (t  t 0 ) A2 / 2)
A
B not.
  F (t  t 0 , x(t 0 ), B / A)
A
(3)
In the case of spatial discretization, the convergence problems were studied
In ref [7]. We used time discretization.
t
The algorithm is the following: Let
  x(t )
1. Compute:  2
2. Compute  1
the time step and denote
  ( )
  (   2 t );  3   (   2 t )
3. Compute the best linear fit
y  Ax  B
for 3 points
( yi , xi );1  i  3 , with
yi   i ; x1     2 t ; x2   ; x3     2 t
and compute the relative error,

of the best linear fit . Observe that the
approximation error in generic case is
4 Decrease the time step
t
until
Monte-Carlo relative error (order

O(t )
is less then the estimated
O ( N 1 / 2 sam ple) )
5. With the adapted time step compute, by using Eq. (3)
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Area:
Task: WP10-ITM-IMP5-ACT4-T1-01/MEdC
x(t  t )  F (t , x(t ), B / A)
This method has strong order ½ , when
 (x) has second order derivative
bounded and we have a strict relative error control.
Method 2. Adaptive time step
Steps 1. and 2. are the same as in method 1. At step 3 the error of the
best linear fit is computed, but instead of linear approximation, the
function  (x) is approximated as  ( x )
 mx 2  nx  p .
Step
4 is the same, but now the approximation error in the generic case is
O ( t 3 / 2 ) The update x(t  t )  x(t  t )
is performed by
using stochastic Taylor expansion described in
: P.E. Kloeden, E. Platten, "Numerical solution of stochastic differential
equations", page 351, eq. 4.1. In our case the strong order is 1.5, we have a
strict estimation of relative error of the order 1 term. Using
MATHEMATICA 5.1 generated the terms of the stochastic Taylor
expansion.
The weak convergence of these approximations follows from general
approximation theorems used in the numerical solution of the linear parabolic
equation.
Method 3
From Ito calculus results that by the updates
x(t  t )  x(t )   [ x(t )  x]dw(t ); where
x   [ x(t )]dw(t )
we obtain a strong order ½ method [6].
Discussion of the methods
The convergence of all of these methods can be proved only in the case when
 (x) has bounded second order derivative. Problems appears near x  0 , when
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Reference:
Task Force: ITM
Area:
Task: WP10-ITM-IMP5-ACT4-T1-01/MEdC
we have [2]
d '2
D( x) 
x  O( x 2 )
2
 ( x)  d ' x
(4)
Consequently it is non differentiable and near x=0 new methods must be used. The
applicability of the methods 1-3 is restricted to the domain
is a cut-off parameter, such that for
x  xmin , where xmin
0  x  xmin we can assume that Eq. (4)
holds.
In the test of the methods 1,2 we introduced explicitly this parameter (see remarks
on coding).
The following approximation is used in methods 1 and 2:
When we have
x(t  t )  xmin  x(t ) then we perform the reflection:
x(t  t )  2 xmin  x(t  t )
Method 4
In The Eq. (1), in the particular case (4) valid in the domain
0  x  xmin
perform the change of variable:
x  d '2 exp( 2 y ) , and we obtain the SDE in variable y(t)
17
we
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1
dy(t )  exp( y (t ))dw(t )
2
Eq. (5) is valid in the domain
(5)
y  ymin  log( d '2 / xmin ) / 2 .
From numerical point of view it is possible to treat this equation in a limited
domain, so a new cut-off parameter,
and reflection on the point
y max must be used, with ymin  y  ymax
y max
In this domain it is possible to use the same stochastic Taylor expansion, described
in method 2.
On the other hand, the Laplace transform (in time variable) of the Fokker-Planck
equation associated to Eq. (5) can be expressed by Bessel functions. This possibility
will be explored after having approximations for
d ' , xmin .
C4. FORTRAN 90 programs on the Gateway
The following new codes were tested, including on the Gateway and uploaded
to GFORGE
1. Random number generators.
The file RFOF_random_numbers_SG2.f90 contains the module
RFOF_random_numbers_SG2. The following subprograms are there.
The subroutine init_RANDOM_NUMBER, respectively the subroutine init_RM48
for generating random seed for the intrinsic uniform random number generator
RANDOM_NUMBER and the for the portable generator RM48 by using the
subroutine system_clock(,).
The subroutine gaussian_random_vectorRM48) that generate a pair of independent
N(0,1) by polar method. The algorithm is from: P.E. Kloeden, E. Platten,
"Numerical solution of stochastic differential equations p.13". The uniform random
number generator is RM48. In the subroutine gaussian_random_vector, we use the
same method, with intrinsic uniform random number generator.
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Also versions of single N (0,1) generator of Marsaglia and Bray (1964),
(Luc Devroye, page 390, chapter IX) was implemented
The subroutine Marsaglia_Bray_RM48 produces a single normal random numbers,
by using RM48 uniform generators. In the subroutine MarsagliaBray we use
intrinsic generator random_number().
The subroutine Correlated_Gauss_Gen, produces a pair of correlated Gaussian
random number, used in higher order stochastic integrators.
The file contains also subroutines for the test (speed and accuracy) of these
Gaussian generators.
In test subroutines can be called from the main programme given in the file
RFOF_random_test_main.f90
Methods 1, 2 and 4
These methods were tested by using an explicit form of the diffusion coefficient
[subroutine diffusion_coefficient], given in the file RFOF_testdiffusion_coef.f90.
The same file contains a subroutine that returns the derivative of the diffusion
coefficient [subroutine D_diffusion_coefficient], used only on test.
The methods 1,2,4 are implemented in the file RFOF_SpecialSolver.f90. This file
contains the following subprograms.
The function aprox_equal (x,y), that returns true when the numbers x and y are close
within given numerical precision.
The subroutine RFOF_sigma, that give the function defined above by Eq. (2). The
subroutines linear_aprox_minmax and linear_aprox_minmax2 for linear fit
of  (x) with 3 points. The subroutine quadratic_interpolation returns the
coefficient of second order polynomial approximation of  (x) .
The subroutine RFOF_exact_solution implements Eq. (3). The subroutine reflects is
used at the end points of the allowed domain. In the Fokker-Planck equation this
corresponds to Neumann boundary conditions (impenetrable wall). These last two
subprograms are used in the central subroutine RFOF_one_step_generalcase, that
implements the methods 1, and 2, by setting the variable “method” to values 1 or 2.
19
Report for TA WP10-ITM-IMP5-ACT4
Reference:
Task Force: ITM
Area:
Task: WP10-ITM-IMP5-ACT4-T1-01/MEdC
When method=2, then the subroutine RFOF_SDE_integrator_correction is called,
that contains higher order terms of a strong 1.5 order integrator.
We emphasize that this subroutine perform an adaptive reduction of the time step
size. In order to call methods 1, 2 we must call subroutine
RFOF_multi_step_generalcase, which perform the integration on a given finite
interval. It also produces adaptive increase of the step size.
Method 4 is implemented in the subroutine RFOF_one_step_boundarycase and in
the subroutine RFOF_multi_step_boundarycase.
Remains to write a subroutine that supervise the transition of the marker from the
regime when methods 1 or 2 are used, to the regime where method 4 is more
suitable.
At this point method 1 is the most viable and can be used alone, with more
effectiveness if the cut-off value
xmin
is given. Higher speed and precision can be
obtained if method 4 is used in combination with method 1.
The file contains also subroutines for accuracy and speed test. Integrating the same
SDE by the simplest Euler method performs the test. At test case the Euler method
can be used because we have an analytic form of derivative of diffusion coefficient.
The test programs can be called from the files RFOF_specialSolvertest3.f90
(methods 1 and 2) and RFOF_specialSolvertest1.f90 (method 4).
Method 3 is tested in the file RFOF_fixed_time_step_integrator.f90.
The general strategy of the entire test was the following. In all of the numerical
tests the mean values of some suitable observable are computed by the tested
method and with the simple Euler method. The Euler method was also verified
(despite it is too simple, difficult to miss), by computing the mean values on
stationary states, for models that allows exact solution. Then the tests of the new
subroutines were performed for finite time.
D. Achievements of the objectives.
The objectives were achieved. The methods 1 and 2 are robust integrators they
exploits the special choice of the parameterisation of the phase space, typical for
Fokker –Planck modelling of RF heating. These integrators can be coupled with the
20
Report for TA WP10-ITM-IMP5-ACT4
Reference:
Task Force: ITM
Area:
Task: WP10-ITM-IMP5-ACT4-T1-01/MEdC
rest of RFOF subroutines.
E. Outstanding issues
1. Connection of the subroutine RFOF_multi_step_generalcase that implements the
most efficient adaptive methods 1 and 2, in an efficient way to the existing modules.
2. Estimation of the cut of the parameter
xmin , the range of the validity of the linear
approximation.
3. Estimation of the parameter
d ' from Eq. (4)
4. Asymptotic estimation of the effect of the cut-off
xmin
on the errors in the
computation of the mean values
F. Summary
Four numerical integration methods of the stochastic differential equations used in
the accelerated orbit following Monte-Carlo method were elaborated. The
integration method is specially designed for the modelling of the RF heating in ideal
axial symmetric tokamak. These algorithms were implemented as a FORTRAN 90
codes, were tested on the Gateway and uploaded to GFORGE. Two of the methods
were robust, because exploits the possibility of low order polynomial interpolation
of the diffusion coefficient far away the singularity and uses exact solution or high
order stochastic Taylor expansion. The integrators have very efficient error control
and adaptive step-size.
G.
Publications
[1]. L-.G. Ericsson, M. Schneider, “Monte-Carlo operators for ions interacting
with radio frequency waves”. Physics of Plasmas 12, 072524, (2005).
[2]. Q. Muhtar, T. Hellsten, T. Johnson, “On solving Singular Diffusion Equation
by Monte-Carlo Method”, IEEE Transactions on Plasma Science 38, 2185-2189
(2010), doi: 10.1109/TPS.2010.2057259.
21
Report for TA WP10-ITM-IMP5-ACT4
Reference:
Task Force: ITM
Area:
Task: WP10-ITM-IMP5-ACT4-T1-01/MEdC
[3] Steinbrecher G., Weyssow B., “Generalized Randomly Amplified Linear
System Driven by Gaussian Noise. Extreme Heavy Tail and Algebraic Correlation
Decay in Plasma Turbulence”, Physical Review Letters 92, 125003 (2004).
[4]. G. Steinbrecher, X. Garbet, B. Weyssow, “Large time behaviour in random
multiplicative processes”, arXiv:1007.0952v1 [math.PR], (2010)
[5]. X. Garbet, G. Steinbrecher, “On-off intermittency. Exact results”. Presented
at the “Solvay Workshop <A Tribute to Radu Balescu>”, Brussels, 6-8 March
2008.
[6] G. Steinbrecher, R. J. Dumont “Numerical Instabilities in the Accelerated
Orbit Following Monte-Carlo Method”, ITM General Meeting 2010, Lisbon
[7] Omid S. Fard, “New Numerical Scheme for Solving Nonlinear Stochastic
Differential Equations ”, International Journal of Computational and Applied
Mathematics, 2, 101-113 (2007).
Revision No:
Changes:
Date:
14/01/2011
Association
Written by:
Revised by:
Approved by:
EURATOM-MEdC
Gyorgy Steinbrecher
Name
Florin Spineanu
HRU – MEdC Association
22
WP10-ITM-ISIP-ACT3-T1-01/MEdC
Simulation catalogue querying tool
Integrated Tokamak Modeling Task Force
Deliverable under Priority Support
Reference:
Task Force: ITM
Area: ISIP
Task: WP10-ITM-ISIP-ACT3-T1-01
Document:
Task Title :
Simulation Catalogue Querying Tool
Task Coordinator F.Imbeaux
Author(s):
Name and Association(s) of the Author(s)
V.F. Pais, Association EURATOM-MEdC Romania
Date:
31, December, 2010
Distribution list:
F. Imbeaux (Task Co-Ordinator)
G. Falchetto (Task Force Leader)
(CSU Responsible Officer)
(CSU Group Leader)
23
Integrated Tokamak Modeling Task Force
Deliverable under Priority Support
Reference:
Task Force: ITM
Area: ISIP
Task: WP10-ITM-ISIP-ACT3-T1-01
Content:
Work on the ITM Simulation Catalogue started last year and led to the creation of a
database structure that is going to hold simulation related data. In order to make
this data accessible to both users and applications a catalogue interface was
required.
A new tool, called “Catalogue Querying Tool”, was developed and installed on the
Portal machine in order to give web access to the Catalogue Database.
Because the tool is supposed to run inside a web portal environment it was decided
to use PHP as the programming language. Furthermore, since the tool must be
integrated with other applications, it is made out of two parts.
First, a data access web service creates a programmable interface allowing easy
access to the mysql database holding the simulation data. This web service offers
access to both “raw” data, as stored in the database, and to some “pre-processed”
data, in order to facilitate the integration in other applications.
The second layer of the application is a “presentation” layer, offering the actual
human interface to the tool. This consists of a web interface that takes queries
from users and accesses the underlying web service in order to resolve the queries
and display the requested information.
The web interface allows for searching through the database tables and to paginate
results. Details will be available for each data entry. In order to allow easy
integration of this tool with other, more complex tools, a web service interface was
used for actually accessing the data.
A set of tests were performed on the Query Tool in order to test its functionalities.
This was achieved using test data present in the Catalogue Database.
Further development of the application may be needed in the future in order to
add new functions or to refine the existing ones. The need for any of this will
become apparent only when the volume of data stored will become large enough.
Revision No 1
Changes:
24
Integrated Tokamak Modeling Task Force
Deliverable under Priority Support
Reference:
Task Force: ITM
Area: ISIP
Task: WP10-ITM-ISIP-ACT3-T1-01
Written by:
Revised by:
Approved by:
Vasile PAIS
Ion MORJAN
Florin SPINEANU
General Director,
INFLPR
HRU – MEdC
Association
Objectives
The objective was to create an interface to the Simulations Catalogue Database, which can be used
directly by the users and integrated in other applications.
Achievements
An application was developed, comprising two parts:
-
A data access web service, interfacing with the actual database
-
A web interface allowing queries to be performed on the database, using the web service
Shortcomings - None
Conclusions and General perspectives
The “Catalogue Querying Tool” application was developed and installed on the ITM Portal machine.
References (to Conference paper/poster, Meeting, Publication)
- No paper has been published yet.
25
WP10-ITM-ISIP-ACT10-T1-01/MEdC
Administration of the collaborative software
Integrated Tokamak Modeling Task Force
Deliverable under Priority Support
Reference:
Task Force: ITM
Area: ISIP
Task: WP10-ITM-ISIP-ACT10-T1-01
Document:
Task Title :
Administration of the collaborative software
Task Coordinator F.Imbeaux
Author(s):
Name and Association(s) of the Author(s)
V.F. Pais, Association EURATOM-MEdC Romania
Date:
31, December, 2010
Distribution list:
F. Imbeaux (Task Co-Ordinator)
G. Falchetto (Task Force Leader)
(CSU Responsible Officer)
(CSU Group Leader)
26
Integrated Tokamak Modeling Task Force
Deliverable under Priority Support
Reference:
Task Force: ITM
Area: ISIP
Task: WP10-ITM-ISIP-ACT10-T1-01
Content:
During the previous years, the ITM Portal application was created and made
available to ITM users. This collaborative platform is comprised of various tools, like
Shibboleth single sign-on, JBoss portal, GForge, wiki, forums, subversion versioning
mechanism, online editors.
Some of the software packages were updated this year in order to solve potential
security issues and to add new functionality. This includes: GForge editor, wiki, part
of JBoss portal for connection to LDAP. Furthermore, new packages were installed,
like the equation editor integrated with GForge global editor, allowing for easier
equation writing inside wikis and comments.
The overall usage of the ITM Portal has increased significantly since its first release.
This means there are now more users and more files stored in its storage facilities.
In order to accommodate this increase a new machine was created and the Joomla
content management system was deployed and integrated in the existing
infrastructure.
The catalogue querying tool, developed for the WP10-ITM-ISIP-ACT3-T1 task, was
also integrated inside the ITM Portal infrastructure, in order to make it available
only to authorized users.
Some of the ITM software had already existing versioning repositories and in order
to facilitate the transition towards the ITM infrastructure, a subversion
synchronization procedure was put in place, thus allowing for master-slave
repository configuration.
Revision No 1
Changes:
Written by:
Revised by:
Approved by:
Vasile PAIS
Ion MORJAN
Florin SPINEANU
General Director,
INFLPR
HRU – MEdC
Association
Objectives
27
The objective was to maintain and update the existing ITM collaborative infrastructure, namely ITM
Portal and GForge.
Achievements
Maintenance tasks where performed on the existing components.
A new component, the Joomla content management system, was deployed inside ITM Portal in order to
take care of the increasingly large number of files published.
Subversion mirroring and synchronization tools where installed in order to facilitate the transition of
existing software repositories towards ITM.
Shortcomings - None
Conclusions and General perspectives
The usage of the ITM infrastructure has increased continuously during the last years, thus making it
necessary to update existing components and to install new ones in order to offer a better user
experience.
References (to Conference paper/poster, Meeting, Publication)
- No paper has been published yet.
28