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