an r-matrix approach for plasma modelling and the interpretation of astrophysical observation
DESCRIPTION
Talk presented by C. Ballance at the 27th ICPEAC, Queen's University Belfast, 27/07-02/08 2011.TRANSCRIPT
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An R-matrix approach for plasma modelling and the interpretation of
astrophysical plasmas
July 27th , Queen's University, ICPEAC 2011
Connor Ballance
Auburn University
Collaborators : T G Lee, S D Loch, M S Pindzola (AU) : N R Badnell ( Strathclyde ) : B M McLaughlin (QUB) : M A Bautista (WMU)
Supported by : US DoE Fusion Energy Sciences
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Overview
● Introduction : Comprehensive approach to plasma modelling, our current capabilities and future directions.
● Electron-impact ionisation : high n shell ionisation
● Electron-impact excitation : scripted R-matrix calculations : parallel DARC code : Fe-Peak elements and beyond
● Photo-ionisation of Mid-Z elements : parallel dipole (DARC) codes
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Introduction
● In recent years, EIE R-matrix calculations, have moved beyond the isolated, one-off serial calculations to parallel calculations along entire iso-nuclear/iso-electronic sequences
Witthoeft et al 2007 (J. Phys. B Vol 40) Liang and Badnell 2010 (Astron. Astrophys. Vol 518 A64)
Perl-scripted calculations, automatically calculate tabulated every effective collision strength for all transitions from user given structure.
● This data is stored in a well-prescribed format that includes the atomic configurations, the energy levels, the A-Values for all E1,E2,M1,M2 transitions, Maxwellian averaged collision strengths for a range of temperatures and the Born/Bethe infinite energy limit points. (why?).
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http://www-cfadc.phy.ornl.gov/home.html
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Introduction
● Modern computing archictectures have over 100,000 cpu cores
Kraken, NICS Oak Ridge, TN (Cray ) Hopper, NERSC, Berkley, CA (Cray)
and if utilised correctly, can support PetaFlop/sec calculations.
● The serial codes (1973-1999) could take a week(s) to calculate an ion stage. The first generation of parallelcodes (2-3 hundred levels, 1-2 thousand channels) a day
● Now we need adapt to (1-3 thousand level calculationswith 5-20 thousand channels) if we are to address open p-and-d shell systems.
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R-matrix/R-matrix with Pseudostates (RMPS) review
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The importance of excited state ionisation
●Effective ionisation rates include the contribution of excited state ionisation,which becomes computationally demanding for non-perturbative methods such the RMPS
Allain et al 2004Nucl. Fusion 44, 655 (2004)
How do we employ the RMPS method effectively, for high n shell ionisation ?
The calculation of ionisation from every term of a high n can be an order of magnitudemore computationally demandingthan the groundstate alone.
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There are many non-perturbative ionisation cross-sections from the
groundstate For example, consider the closed shell groundstate of neutral neon
Groundstate Excited terms
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However systems with several valence electrons soon become problematic
Consider the all LS coupling electron-impact ionisation (both ground and excited) state from a boron-like system such as B I / C II
This will require ionisation from : 1s^2 2s^2 nl (where n=2-4, l=0-3) : 1s^2 2s 2p^2 : 1s^2 2p^3 (for C II )
In addition to the above spectroscopic terms, we shall require minimum pseudostate expansions of the form:
1. 1s^2 2s^2 nl (where n=5,14,l=0-6)2. 1s^2 2s 2p nl (where n=5,14,l=0-6)3. 1s^2 2p^2 nl (where n=5,14,l=0-6)
If you want to calculate
a) Direct ionisation of the outer shell electronb) Direct ionisation of the 2s electron c) All the excitation-autoionisations from every term ie. e + 1s^2 2s^2 3s --> 1s^2 2s2p 3s
Well, 1444 terms , approximately 5000 close-coupled channels and 5 Tb of Hamiltonian matrices requiring diagonalisation poses an interesting challenge ...
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This represents the current work, that extends beyond naively splitting the serial problem over more processors, to one in which the parallel code adapts to a particular problem
Hamiltonian formation
1. Serial : Each partial wave is calculated consecutively ( 50-100 ) .... a month
2. Naive parallelism : each partial wave is carried out concurrently .... 3 days (remember a single partial wave > 200 Gbs) .... 100 procs
3. Adaptive parallelism : As well as each partial wave being carried out concurrently the target terms are grouped into their L S Pi groups (perhaps 20-40 unique groups) .... 2000-4000 procs … 4hrs
RESULT : Hamiltonian formation is reduced scattering from a set of target terms with the same L S Pi values.
Hamiltonian diagonalisation
1.Serial : Impossible ! Every eigenvalue of a 200 K by 200 K Hamiltonian 2. Naive parallelism : sequential parallel diagonalisation using Scalapack, possible, but regardless of diagonalisation time, you must read 5 Tb .... 4 days
3.Adaptive parallelism : Each Hamiltonian is concurrently diagonalised in parallel , with an n^3 scaling law controlling the distribution of processors … 5 hrs
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RESULT : Adaptive diagonalisation ---> 1 Hamiltonian read, 1 diagonalisation
Better load balancing as processing power is distributed to where it is needed
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Electron-impact ionisation of neutral Boron , n=3 shell
Notice: large excitation-autoionisation (EA) i.e. e + 1s^2 3l --> 1s^2 2s 2p 3l + e
Large EA destroys any n^4 scaling law (or rescaling of an empirical formula) needed to extrapolate to higher n shell ..... solution ?
3s
3p
3d
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If we can explicitly caculate to high enough n shell, that the direct ionisation completely dominates over EA , then we can scale simple ionisation expressions from the last explicitly calculated n shell shell of the RMPS
B
B
B
+
2+
n=4
n=4
n=5
Below , we have statistically averaged the term resolved RMPS results used to rescale an expression, such as the Burgess-Vriens for the higher n shells.
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Excited state ionisation from higher charged ions
Higher partial waves begin to dominate the cross section, for high n , multiply charged systems
Convergence is very slow
Comparisons with distorted wave are favourable, again
RMPS becomes computational Demanding, requiring 110-130 pseudo-orbitalsranging from n=6-16,18 and l=0-10to achieve convergence
Time : distorted wave (15 mins) RMPS (4 hrs)
Distorted wave (Younger Potential)Distorted Wave (Macek Potential) RMPS
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Electron-impact excitationand how we adapt to future challenges.
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Scripted Semi-relativistic ICFT (Intermediate Coupling Frame Transformation) R-matrix calculations
● A perl-script has been developed that automatically takes structure calculations for atomic ions Z < 36 , through to effective collision strengths for ALL ions along an iso-electronic sequence
● Intermediate Coupling Frame Transformation, developed by D C Griffin is an R-matrix approach primarily carried out in LS coupling but including mass-velocity and Darwin terms, that transforms term-resolved K-matrices into level-level K-matrices, and ultimately level resolved excitation rates. Provides comparable cross sections to the Breit-Pauli R-matrix codes.
Example Papers:
G. Y. Liang et al Astron. Astrophys. 528 A69(15) (2011). Li-like sequenceG. Y. Liang et al Astron. Astrophys. 518 A64(20) (2010). Neon sequenceG. Y. Liang et al J. Phys. B 42 225002(12) (2009). Na-like sequenceM. C. Witthoeft et al J. Phys. B 40 2969-93 (2007). Fl-like sequence
Typically 100-300 levels calculations, with 1000-1500 channels
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However, eventually as Z increases we must adopt the a parallel version of relativistic R-matrix codes.
DARC (Dirac Atomic R-matrix Code)● These codes have been modified in an analguous way to the non-relativistic codes - distribution of integral generation - multi-layered parallelism of the Hamiltonian formation - Concurrent adaptive diagonalisation of the Hamiltonian
0.6 billion Racah coefficients 0.6 billion Racah coefficients per symmetry per symmetry
Excitation/ionisation of Mo II
8000-10000 channelsstill a challenge
4d^5,4d^4 4f-5f
This is preparationcalculation for futureW ion stages.
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e.g. DARC calculations for Fe III
Target : 3d^6, 3d^54s, 3d^54p, 3p^43d^8, 3p^53d^7 (2-3 hundred level)ideally now we would add (3p^54d, 3p^43d^74s ,3p^43d^74p)
which if we keep to 0.0-0.5 Ryds, provides a satisfactory description of Fe III
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e.g. DARC calculations for Fe II
Before After
(Ith -Iobs)/Iobs
Collision strengths : Zhang 1992A-values : Nahar and Pradhan
Collision stengths : parallel DARC A-values : HFR (cowan)
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A typical collision strength within the groundstate complex of Fe III illustrates the need for a very fine energy mesh !
ICFT DARC
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However, if we want continued scaling to 5-12 thousand close-coupledchannels, reconsider electron-impact ionisation of B I * 1444 terms * 5000 channels ,* Hamiltionian Matrices close to 200,000 by 200, 000 in size* over 1 million possible transitions
But the formation of the R-matrix is crippling in both memory and the time required! .... cannot be left to a single processor
RRij =
k
W * Wik kj
E - Ek
=
w ik / E - E k
wkj
200 000 * 5000 * 8 * 2
= 16 Gb ! (takes mins )
5000*5000*8
0.2 Gb N slices
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928/61440 = 0.015 sec per R-matrix formation
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Test run : 4 partial wavesSe III (225 levels): 437,737,748,1017 channels
12,000 pts. CPU TIME= 1.380 MIN -- processors=: 250 sub world 0 CPU TIME= 3.851 MIN -- processors=: 250 sub world 1 CPU TIME= 3.990 MIN -- processors=: 250 sub world 2 CPU TIME= 6.496 MIN -- processors=: 250 sub world 3 Suggested Proc distribution: 89 245 253 413
CPU TIME= 3.563 MIN -- processors=: 245 sub world 1 CPU TIME= 3.868 MIN -- processors=: 413 sub world 3 CPU TIME= 3.869 MIN -- processors=: 89 sub world 0 CPU TIME= 3.977 MIN -- processors=: 253 sub world 2 -------------------------------------------------------------
Another 2.5 mins saved .... better balance of resources
RECAP
We can also adapt the distribution of processors to energy points in the outer region
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Photoionisation of Mid-Z atomic ions
Posters : Thu 140,Thu 143Posters : Thu 140,Thu 143
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An overview of the parallel DARC dipole photoionisation codes
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An overview of the parallel DARC dipole photoionisation codes● The parallel dipole suite of codes, benefit from the changes made from excitation
All the eigenvectors from a pair of dipole allowed symmetries are required for bound-free dipole matrix formation
●The current approach ensures that every dipole matrix pair is carried out concurrently with groups of processors assigned to an individual dipole.
RESULT : ALL photoionisation, dielectronic-recombination or radiative-damped excitation takes the time for a single dipole formation
● The capacity to perform photoionisations calculations with over 500 levels, improves the residual ion structure, the ionisation potential and resonance structure associated with over 3500 channels.
● As the code scales to 100,000 processors , we can have a resolution of 10^(-8) Rydbergs ie (6-30 million pt) in the incident photon energy, which is vital when comparing with ALS measurements at 4,6,9 meV.
● Of course, theoretical calaculations can guide experimental measurement and determine metastable fractions in experimental measurement.
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Example : Groundstate Photoionisation of Ca II (work in progress)
Target : 3p^6, 3p^5[4s-5p] 3p^4 3d 4s 3p^4 3d 4p 3P^4 3d 4d which gives rise to 513 levels
Theoretical : DARC R-matrix
Experiment : Lyon (1987) ALS(2010)
Currently, the theoretical modelis only from the groundstate,with metastable calculations ongoing.
hv + Ca II (^2 S) 3p^64s
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Example : Photoionisation of Kr II and Xe II
● Used a 326 level model for the residual ion in both cases
● Target configurations for K III include : 4s^2 4p^44s 4p^5 4p^64s^2 4p^2 4d^24s^2 4p^3 4d4s 4p^4 4d 4p^4 4d^2
● Target configurations for Xe III (exactly the same : switching n=4 to 5)
● In the following graphs the R-matrix results have been statistically averaged over the initial p^5 levels
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The agreement with Xe II is equally good
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Come by the poster for more details … TH 143
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Thank-you for your attention