atomic physics with supercomputers. darío m. mitnik
TRANSCRIPT
1Winter Workshop on Computational Atomic Physics
04/21/23
Atomic Physics with Supercomputers
Darío M. . Mitnik
2Winter Workshop on Computational Atomic Physics
04/21/23
Electron-Ion scatteringcalculations
Darío M. . Mitnik
3Winter Workshop on Computational Atomic Physics
04/21/23
Atomic Physics with Supercomputers
Darío M. . Mitnik
4Winter Workshop on Computational Atomic Physics
04/21/23
M. S. Pindzola, F. Robicheaux, J. Colgan,Auburn University, Auburn, AL
D. C. Griffin,Rollins College, Winter Park, FL
N. R. BadnellStrathclyde University, Glasgow, UK
Outline
What are we calculating?
Why do we need supercomputers for such calculations?
How do we use the supercomputers in these calculations?
What are we calculating?
Rate Coefficients
Cross Sections
Electron-Impact Excitation
ki
Nelectron ion
kf
Eth
b
a
Electron-Impact Excitation
<ai| V | bf>
a
b
i
f
(N1) – electron ionkf
ke
Electron-Impact Ionization
ki
EI
N – electron ion
a
Electron-Impact Ionization
<ai| V | ef>
a
e
i
f
Radiative Recombination
N – electron ion
EI
(N+1) – electron ion
ki
a
b
Radiative Recombination
Mba= <b| D | ai >
b
a+ i
Photoionization:
Radiative Recombination:
Mab = 42c2/(2ki) |Mba|2
Dielectronic Recombination
Mba= <b| D | ai >
b
a+ i
Photoionization:
b
a+ i
n n
+
<b| V | n > <n| D | ai >
n + i n/2+
N – electron ion
bEI
(N+1) – electron ion
Dielectronic Recombination
ki
n
a
Dielectronic Recombination
EI
1s22s
1s22s2
Li-like
Be-like
1s22p
1s2 2
pnl
1s22p3/2
1s2 2
p 3/2n
l
Dielectronic Recombination
D.M. Mitnik et al, Phys. Rev. A 61, 022705 (2000)
Dielectronic Recombination
D.M. Mitnik et al, Phys. Rev. A 57, 4365 (1998)
Electron-ion Recombination
D.M. Mitnik et al, Phys. Rev. A 59, 3592 (1999)
Excitation-Autoionization
EI
1s22s
1s22s2
Li-like
Be-like
1s22p
1s22p3/2
1s2 2
p 3/2n
l
Excitation-Autoionization
D.M. Mitnik et al, Phys. Rev. A 53, 3178 (1996)
Excitation (resonances)
EI
1s22s
1s22s2
Li-like
Be-like
1s22p
1s22p3/2
1s2 2
p 3/2n
l
Excitation (resonances)
D.M. Mitnik et al, Phys. Rev. A 62, 062711 (2000)
Excitation (resonances)
D.C. Griffin et al, J. Phys. B 33, 4389 (2000)
Why supercomputersin Atomic Physics?
only a few atomic physicists are using supercomputers
“Collisional breakup in a quantum system of three charged particles”
M. S. Pindzola and F. Robicheaux, Phys. Rev. A 54, 2142 (1996).
Why supercomputersin Atomic Physics?
T. R. Rescigno et al., Science 286, 2474 (1999).
Electron-Impact Ionization of Hydrogen
even the simplest example: e + H H + e + e
has resisted solution until now
Methods
Perturbative methods
Non-Perturbative methods
Distorted Waves
Time-independent
Time-dependent
Time-independent: R-matrix method
P. G. Burke and K. A. Berrington
27 key papers reprinted
Short Bibliography list:
547 references
Time-independent: R-matrix method
Internal Region External Regiona
Target
H = E
~ sin(kr) + Kcos(kr)
1
( )a
R a ar
Why supercomputers?
Size of (N+1)-Hamiltonian:
MXMAT = MZCHF x MZNR2 + MZNC2
# scattering channels
# of continuum orbitals for
given L
# (N+1) terms for given SL
158 x 50 + 100 = 8000 ~ 512 Mb
Why supercomputers?
• Thousands of points are needed in order to map the narrow resonances.
Energy (eV)
Col
lisio
n S
tren
gth
D.C. Griffin et al, J. Phys. B 33, 4389 (2000)
Time-Dependent method
Time-dependent Schrodinger equation:
1 21 2 1 2
( , , )( , ) ( , , )
r r ti H r r r r t
t
������������������������������������������������������������������������������������
1 2
2 21 2 1 2
1 2
1 1 1 1( , , ) ( , )
2 2r rH r r t V r rr r
��������������������������������������������������������
Time-Dependent method
Time-dependent close-coupled equation:
1 2
2 21 1 1 1
1 2 2 2 2 21 2 1 1 1 2
1 1 ( 1) ( 1) 1 1( , )
2 2 2 2l l
l l l lT r r
r r r r r r
1 2
1 2 1 2
1 21 2 1 2
( , , )( , ) ( , , )
LSl l LS
l l l l
P r r ti T r r P r r t
t
1 2 1 2 1 2
1 2
' ' 1 2 ' ' 1 2' '
( , ) ( , , )L LSl l l l l l
l l
U r r P r r t
Why supercomputers?
16 x 250 x 250 = 1000000
1 2 1 2( , , )LSl lP r r t
250 x 250 = 62500
# coupled channels
# partial waves# points in
spatial lattice
Why supercomputers?
Memory
Time
What is a supercomputer?
Distributed-Memory
Shared-Memory
Glossary
functional parallelism
parallelization
data parallelism
Example of data parallelism
• we have 10000 cards• we want to pick up the highest card• each comparison takes 1 second
Example of data parallelism
1 processor10000 1 sec
Tim
e (s
ec)
Processors
2 processors5000 11 sec
10 processors1008 sec 100 processors
198 sec
10000 processors10000 sec
Example of a simple program
print*, ‘hello world’stopend
call mpi_initcall mpi_ rank(iam,nproc)print*, ‘hello world, from process # ’,iamcall mpi_finalizestopend
Example of a simple program
hello world
hello world, from process 2hello world, from process 0 hello world, from process 4 hello world, from process 1 hello world, from process 3
The R-matrix I package
Inner-Region
STG1 : calculates the orbital basis and all radial integrals
STG2 : calculates LS-coupling matrix elements. solves the N-electron problem. sets the (N+1)-electron Hamiltonian
STG3 : diagonalizes the (N+1)-electron Hamiltonian in the continuum basis
The R-matrix I package
Outer-Region
STGF : solves the external-region coupled equations.
STGICF : calculates level-to-level collision strengths by doing an intermediate- coupling frame transformation.
Diagonalization Timing
Example
191 x 34 + 506 = 7000
62-state calculation:
191 coupled channels
34 continuum-box orbitals
506 (N+1)-electron bound configurations
55-state calculation (Dell 603):
59 h and 41 min
62-state calculation (T3E-900) :
64-processors - 69 min.
Parallelization of the external-region codes
processor 1
processor 6
Time-Dependent method
Time evolution of a single-channel:
1 2 1 2 1 2( ) exp ( )LS LS LS
l l l l l lP t t i tH P t
Time-dependent Schrodinger equation:
1 2
1 2 1 2
1 21 2 1 2
( , , )( , ) ( , , )
LSl l LS LS
l l l l
P r r ti H r r P r r t
t
Time-Dependent methodInitial condition for the solution:
1 2 1 1 2 1 2 1
1( , , 0) ( ) ( ) ( ) ( )
2 i is k s kP r r t P r G r P r G r
Initial condition for the solution:
Time-Dependent method
Propagated wavefunction:
Time-Dependent method
Cross Section:
2
22 1 2 1
4LS LSnlm nlm
LS
L S Ak
Projection of the wavefunction:
1 2, ' ' ' 1 ' ' ' 2( , , ( ) ( ))LSnlm n l m nlm n l m
LS r r rtA r
Parallelization of the time-dependent codes
processor 1
processor 6
Conclusions
Atomic Physics is still alive