Transcript Time-Dependent Studies of Atomic Ionization

Calculation of atomic collision data for
heavy elements using perturbative and
non-perturbative techniques
James Colgan, Honglin Zhang,
Christopher Fontes, and Joe Abdallah,
Los Alamos National Laboratory, NM, USA
Layout of Talk
• Atomic data needed
• What elements we aim to examine
• Los Alamos suite of codes for collisional data
production
– Plane-Wave-Born Approximation
– Distorted-Wave Method
• Time-dependent close-coupling approach to
excitation/ionization
– Recent examples of TDCC calculations and
comparisons with other work
• Conclusions
Atomic data Needed
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Collisional excitation
Collisional ionization
Recombination
Photo-induced processes
These processes all produce cross
sections and/or rate coefficients
• These data must be constructed in such a
way that plasma modeling codes can
easily use the data (e.g. IPCRESS,
random-access binary file format)
Los Alamos Atomic Physics Codes
LTE
Structure +
Oscillator
strengths +
Slater integrals
Non-LTE
CATS/
RATS
CATS/RATS/ACE
Photoionization
GIPPER
Populations from
Saha equation
+ UTA’s = spectrum
ATOMIC
Structure +
Oscillator
strengths +
Slater integrals
Collisional excitation
Photoionization/
Collisional ionization/
Auto-ionization
Populations from
rate equations
+ UTA’s = spectrum
Los Alamos Atomic Physics Codes
• CATS: Cowan’s semi-relativistic atomic structure code
– Now available to run through the web: http://aphysics2.lanl.gov/tempweb/
– Hartree-Fock method developed by Bob Cowan used for the atomic
structure calculations
– Plane-Wave-Born excitation data
– Various semi-relativistic corrections included
• RATS: Relativistic version of the atomic structure code
– Uses a Dirac-Fock-Slater (DFS) potential for atomic orbitals (cf Doug
Sampson)
– Calculates energy levels and configuration average energies
– Oscillator strengths
– Plane-Wave-Born excitation collision strengths
– New “fractional occupation number” capability to significantly speed up
large calculations
• GIPPER: Ionization cross sections
– Semi-relativistic and fully relativistic
– Photo-ionization cross sections
– Electron-impact ionization cross sections
– Auto-ionization rates
Los Alamos Atomic Physics Codes
• ACE: Electron impact excitation cross sections/collision strengths
– Electron-impact excitation cross sections calculated using either First-order
many-body theory (FOMBT) or using the distorted-wave approximation
(DWA)
• TAPS: Display code
– Displaying data from IPCRESS files and calculating rates
– Designed to take input from any/all of the above codes
• ATOMIC: plasma modeling code (LTE and non-LTE)
– Reads in data from all of the atomic collision codes above
– Can replace PWB collisional data with distorted-wave data from ACE, if
required
– Produces populations and plasma quantities for a given
temperature/density. Also produces spectra for comparison with other
codes/experiment
– Ongoing participation in NLTE-4 workshop to compare various plasma
modeling codes with each other and with experiment
– Recently parallelized and modularized to significantly improve speed up.
Los Alamos Atomic Physics Codes:
Strengths/Weaknesses
• Consistent treatment of all
states and ion stages; accurate
and fast calculations for highly
ionized species
• Storage of atomic data in a
compact binary format
(IPCRESS files) which allows
very large amounts of data to be
stored in a manageable form
• Codes are now in a mature
state, are portable, and well
tested on a variety of platforms
• PWB/DW approximations may
produce inaccurate collisional
data, especially for neutral or
near-neutral systems (less of a
problem for hot plasmas where
ions are likely to be more
stripped)
• No current ability to insert
(more accurate) data from other
calculations instead of
PWB/DW, if required
• Complications can arise due to
problems with consistent
treatment of resonance
contribution from autoionizing
states when combining different
types of calculations
Los Alamos Atomic Physics Codes:
Recent Highlights
• Comparisons have been made with a
recent experiment measuring a
germanium X-ray spectrum from
laser pulse experiments performed
in Italy
• LANL plasma kinetic code
ATOMIC used to simulate spectra
• Good agreement found
• A configuration-average model used
to calculate populations
• Detailed fine-structure spectrum
obtained by statistically distributing
the populations over the
corresponding level structure for
each configuration
Blue lines are ATOMIC
Red lines are experiment
Los Alamos Atomic Physics Codes:
Recent Highlights
• Comparison with a recent Xe
emissivity experiment
(shown) and with a
calculation from an
independent plasma kinetic
code
• Agreement only fair in this
case
• More recent hybrid finestructure (level to level)
calculations are in better
agreement
Los Alamos Atomic Physics Codes:
Proposed Work
• We now propose using these LANL atomic physics codes
to generate a comprehensive collisional data set for silicon
• Only sporadic calculations available for this element:
– Ionization cross sections measured for Si+, Si2+, Si3+, Si6+, Si7+
– DW calculations for Si+, Si2+, Si3+, also some non-perturbative
calculations (TDCC/CCC/R-matrix) available for Si3+
• Very little excitation cross section data seems to be
available
• No collisional data available for excitation or ionization
from excited states of these ions
• No calculations available for the neutral Si atom
• Our proposal is to benchmark these DW calculations with
selected TDCC calculations for Si, Si+, Si2+
Background to time-dependent
approach
Why is a time-dependent approach useful?
– We ‘know’ the solution at t=- and t=+: just product
of an electron wave packet and target atom/ion
– We then time evolve this t=- solution by direct
numerical solution of the Schrödinger equation
– Allows (in principle) a numerically exact description of
3-body Coulomb problem of two electrons moving in
field of atomic ion
– Allows accurate calculations of
• Total integral cross sections
• fully differential cross sections
– Electron-impact ionization
– Straightforward extraction of excitation cross sections
– Data necessary for modeling of plasma fusion devices
as well as astrophysical modeling
Development of time-dependent approach
• Bottcher (1982) studied e-H system near threshold by following
time evolution of a wave packet
• Was one of the earliest time-dependent approaches to ionization
using a wave packet approach
• Ihra et al (1995) performed similar calculations in the s-wave
model. Also Odero et al (2001) performed time-dependent e-H
scattering calculations
• Pindzola and Robicheaux, Pindzola and Schultz (1996)
formulated the time-dependent close-coupling method to study
e-H at the peak of the ionization cross section
• This was followed by Temkin-Poet studies of the threshold law
for e-H (Robicheaux et al, 1997), and differential cross sections
(Pindzola and Robicheaux, 1997)
• Electron scattering cross sections for many atomic species have
now been calculated including H, He, Li, C, Ne, Li+, Li2+, Mg+,
Al2+, Si3+; more currently underway
Time-Dependent Close-Coupling Method
• Angular reduction of the Schrödinger equation for a 2-electron
wavefunction results in
• A set of radial, coupled differential equations
• Initial state is a product of a one-electron bound orbital and a
wavepacket representing the incoming electron
• We propagate on a uniform radial mesh for suitable time interval
Electron scattering: Temkin-Poet model
(no angular momenta in problem)
• Not antisymmetrized
• Final state shows
– elastic scattering
– exchange scattering
– ionization
Time-Dependent Close-Coupling Method
• Obtain bound and continuum radial orbitals
by diagonalization of one-dimensional
Hamiltonian:
• (eg, e-Li scattering) use pseudopotential to
generate 2s orbital
• Frozen-core orbital so that only two active
electrons in system
• Obtain probabilities by projecting propagated
wavefunction on to one-electron bound orbitals
Recent TDCC calculations
• Detailed study of excitation and ionization cross
sections and rate coefficients for Li and Be
isonuclear sequences
• Initial studies made of heavier ions, such as Mo+
• New calculations of electron-impact double
ionization (and including ionization-excitation) of
He
• New calculations of electron-impact ionization of
H2+, the first electron-impact molecular timedependent calculation
Electron-impact ionization of Li2+
Computed ionization cross
sections for first 4 ns states of
Li2+
We compare TDCC (squares)
with RMPS calculations (solid
red line), and with 2 DW
calculations (dashed lines)
DW calculations are well above
close-coupling calculations for
the excited states
Demonstrates that inter-channel
coupling effects on ionization
from excited states are important
Electron-impact ionization of Beq+
Computed ionization cross
sections for ground and first
excited state of all ions of Be
For neutral stage; DW cross
sections higher than nonperturbative methods
This disagreement gets worse
for excited states
Non-perturbative methods
TDCC, RMPS, and CCC are all
in good agreement
Electron-impact excitation of Beq+
Completing our comprehensive
study of Be isonuclear sequence
collisional processes
Computed excitation cross
sections for ground and first
excited state of all ions of Be
Non-perturbative methods are
again in good agreement
Conclusions/Future Work
• Los Alamos suite of codes are well suited for producing large
amounts of collisional atomic data for heavy elements
• We will use this capability to generate an extensive database of
excitation and ionization cross sections for several elements of
interest to fusion, beginning with Si
• Time-dependent non-perturbative calculations will be used to
benchmark these perturbative methods, especially for nearneutral systems
– This approach can also compute differential cross sections if necessary.
• This approach will result in a comprehensive database of
excitation and ionization cross sections (and rate coefficients),
with some indication of the accuracy of the data produced
• Future years will extend these calculations to other heavier
systems of interest to fusion