plasma modeling
Plasma Spectral Modeling
Calculating X-ray and UV spectra of hot plasma requires knowledge of the atomic transition rates and energies, as well as a code to evaluate the precise model required. Scientific usefulnessrequires that the database of atomic information, as well as the codes, be robust, .documented, and deterministic
The following processes are important in this calculation
Continuum emission processes
-
Free-bound emission (radiative recombination)
-
2-photon emission
-
Line emission processes
-
Non-Auger processes
- Satellite lines emitted from excited states above the first ionization potential
-
Impact excitation of inner-shell electrons above the ionization limit
- Dielectronic capture
-
Plasma Emission Models
The appropriate model depends not only on the temperature of the plasma, but also its density. At sufficiently high densities, collisions completely determine the level population. As the density drops, a collisional-radiative model must be used and finally the purely radiative nebular approximation can be used. The breakpoints between these models are discussed below
Local Thermodynamic Equilibrium (LTE)
Level populations determined only by collisional processes
Applies for
-
At
K for H-like Fe
cm
-
At
K for H-like O
cm
Collisional-Radiative Model (CR Model)
- Most general case
-
Needed for
cm
cm
-
Also needed for complex ions at somewhat lower densities
Coronal and Nebular Models
-
Applicable for
to
cm
- Low density approximation
- Equilibrium established
Common Simplifying Assumptions
-
Most of these assumptions break down somewhere in astrophysics
-
In fact, most of them break down in our own Sun!
- The ability to calculate more general cases is limited by availability and accuracy of atomic
-
The ability to parameterize an astrophysical plasma in full detail is a different, often more difficult, problem
- Ionization/recombination may be solved separately from excitation/de-excitation
-
Either collisional processes dominate or radiative processes dominate
-
Optical depth effects may be treated in a simple way
-
ignored
-
escape probability formalism
- Low density
-
Ion population mostly in the ground state
- Coronal approximation (collisionally ionized plasmas)
- Nebular approximation (photoionized plasmas)
- Rate coefficients are not
-sensitive
-
- Time-independent
- Maxwellian electrons
- Electric and magnetic field effects are ignored
- No diffusion
Calculating Line and Continuum Emission
| 1) |
| 2) |
| 3) |
| 4) |
| 5) |
emissivity
level population density
transition probability from upper level
to lower level
.
sum of photoionization and collisional impact ionization rates
sum of radiative, dielectronic, and 3-body recombination rates
individual charge exchange rate coefficient
population density of the interacting species
includes stimulated absorption (photo-excitation) as well as spontaneous radiative decay
the collisional rate coefficient for interaction with species
and
radiative source terms for photoexcitation and photoionization, resp.
,
and
collisional, photo-, and charge exchange ionization coefficients, resp.
photo-excitation probability
,
,
, and
radiative, dielectronic, three-body, and charge exchange recombination rate coefficients, resp.
and
collisional excitation and de-excitation rate coefficients, resp. for impact with species
(electrons and sometimes protons)
Atomic Database
To calculate all these rates, we need a database of the atomic transitions. This database must include the following parameters:
- Collision Strengths :
,
- Ionization/Recombination Rates
- Ionization
- Auger ionization
- Recombination
- Dielectronic recombination
- Radiative Processes
- Absorption
- Emission
- Photoionization
- Atomic Energy Levels
- References for all of the above
Collisional Excitation
Ions may be excited by collisions with electrons, protons, or other ions. Collisions with electrons are the most common, since they have the highest velocity, but in some cases proton excitation can be important.
Electron Collisional Excitation
- Fundamental calculation is the cross section, which becomes a dimensionless quantity :
- Averaging this over a Maxwellian gives the ``collision strength''
- High-temperature approximation (see Burgess & Tully 1992, A&A, 254, 436)
- Electric dipole:
- Multipole :
- Spin-change :
- Electric dipole:
- Threshold effects; R-MATRIX vs DW (from McLaughlin et al, 2001, J. Phys. B. in press)
Proton Collisional Excitation
- Similar notation
- In equilibrium,
slower than electrons
- Affects mostly low-lying levels
Comparing Excitation Rates: He-like and Hydrogenic
Collision strengths for hydrogenic iron (Fe XXVI). The Sampson calculations use a non-relativistic distorted wave calculation, while the Kiselius calculations was fully relativistic. Fe XXVI exists in equilibrium between










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