Plasma Spectroscopy and Atomic Physics

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Plasma Spectroscopy and Atomic Physics

• Yuri Ralchenko

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Plasma SpectroscopyDo we really need it?..

• Classical approach
• Coulomb interactions between the plasma
  constituents (charged balls) govern the plasma
  history.
• Spectroscopic approach
• Agree but Plasma history affects the internal
  properties of the plasma constituents (many-body
  systems, not balls!) which are revealed via
  emitted photons.

• Advantages
• Non-intrusive methods
• Remote diagnostics
• Extremely versatile
• High resolution in time and space

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Typical Experiment
Plasma
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Questions

• Atomic Physics
• What are the (free) ion properties?
• Why and how does an ion become excited?
• Why and how does an excited ion emit a photon?
• What are the properties of the emitted photon?

• Plasma Spectroscopy
• How are the free ion properties being affected by
  the plasma environment?
• How many excited ions are there? (What are the
  populations?)
• What happens to a photon traveling through the
  plasma?

What can the registered photons tell us about
plasma properties ? Electron and ion densities,
electron and ion temperatures, ion stage
distributions, magnetic and electric fields,
turbulent fields, shock waves, energy losses,
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History

• Before 1950s
• atomic physics, astrophysics
• After 1950s
• fusion experiments
• 1964 H. R. Griem, Plasma Spectroscopy
• 1974 H. R. Griem, Spectral Line Broadening in
  Plasmas
• There is no journal on plasma spectroscopy!

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References

• Griem H.R. Principles of Plasma Spectroscopy,
  Cambridge Univ. Press, 1997.
• Shevelko V.P. and Vainshtein L.A. Atomic Physics
  for Hot Plasmas, IOP Publishing, 1993.
• Cowan R.D. The Theory of Atomic Structure and
  Spectra, Univ. California Press, 1981.

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Units

• Energies/temperatures
• 1 eV 1.602x10-19 erg
• 11 604 K
• Ionization potential for H
• 1 Ry 13.61 eV
• T(room) 1/40 eV
• T(photosphere) 0.5 eV
• T(JET) 25 000 eV

• Wavelengths
• 1 Å 10-8 cm 1 nm 10 Å
• Size of the H-atom 1 Å
• Visible light
• ? 3500-7000 Å
• ?Ehc/? ? ?E 2-4 eV
• X-rays down to 1 Å

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Hydrogen Atom

• Coulomb potential (non-relativistic)
• H?i(r) Ei?i(r)
• quantum numbers n, l, j
• En-1/n2 lt 0 discrete spectrum
• with g2n2
• E?0 continuum
• The higher n, the larger r rn n2
• Bohr radius a0 0.529 Å

One-electron (hydrogen-like) ions ?E ? Z2 r
? Z-1
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Multielectron Ions

• Computational Methods
• Hartree-Fock (self-consistent field)
• Model potentials
• Perturbation theory
• Typical accuracy for level energies and
  wavelengths ?3-5
• Some notations
• O I O0, O II O1,
• Configuration 1s22s22p53s (n1l1an2l2ß)

• Still Coulomb forcebut many-body problem we
  just cannot solve it exactly!
• Approximations
• Central field ? non-central interaction
  (directexchange) ? spin-orbit (ls) interaction ?
  relativistic corrections
• Rigorous conservation laws
• Total angular momentum J
• Energy E
• Approximate conservation laws
• Orbital angular momentum L?li
• Total spin S?si
• Approximate quantum numbers
• ni, li, L, S

Spectroscopic charge
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Multielectron Ions contd

• LS coupling
• (light medium ions)
• L Sili S Sisi
• J LS
• Term 3P 2S1L
• Level 3P1 2S1LJ

• jj coupling (heavy ions)
• ji li si
• J Siji

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Radiative Processes
Strong transitions E1 (electric dipole) A108
s-1 for neutrals AZ4108 s-1 for ions Weak
transitions M1 (magnetic dipole), E2 (electric
quadrupole), some E1 (?S?0) A 1-100 s-1 for
neutrals A Z6-12 for ions Accuracy 10
E1
h?E1-E0
E0
spontaneous emission
absorption
stimulated emission
A ?E2 ?-2 Light intensity I(?)NuAh?
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Radiative Processes contd
O I lines 3P1-1D2 3P2-1D2 1D2-1S0
M1
E2
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EM fields Zeeman

• Magnetic field Zeeman effect

?E ? B
J
J
?
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EM fields Zeeman contd
Time-dependent spatially-resolved picture of
magnetic field penetration
BkG 0-2 2-4
4-6 6-8
8-10
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EM fields contd

• Electric field Stark effect
• Hydrogen ?E ? E (linear)
• Non-hydrogenic ions ?E ? E2 (quadratic)

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Collisional Processes

• Ion impact
• Excitation
• Aq Br ? Aq Br
• Ionization
• Aq Br ? Aq1 Br e
• Charge exchange (transfer)
• Aq Br ? Aq1 Br-1
• Normally ion-impact processes are less important

• Electron impact
• Excitation
• Aq e ? Aq e
• Deexcitation
• Aq e ? Aq e
• Ionization
• Aq e ? Aq1 e e,
• Aq e ? Aqn e ne
• 3-body recombination
• Aq1 e e ? Aq e
• Radiative recombination
• Aq1 e ? Aq hv
• Dielectronic capture
• Aq1 e ? Aq

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Collisional Processes contd
dO
n
n0
Area (cm2)
dsfi
outflux/solid angle
f2

dO
influx/unit area
Differential cross section
Total cross section
Scattering amplitude
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Collisional Processes contd
Asymptotics logE/E, 1/E, 1/E3
can help to find hot electrons!
Typical s pa02 10-16 cm2
Electron energy distribution function
velocity
Rate coefficient
Rate (s-1) RNe
Accuracy lt30
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Atomic Physics conclusions

• Basic principles are known, improving details
• Achieved accuracy lt1 or even better (!) for
  energies and wavelengths, lt10 for transition
  probabilities, lt20-30 for collisional cross
  sections
• and still some puzzles are discovered! (e.g.,
  radiative recombination cross sections for
  extremely small energies)

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Line Shapes and Shifts
Power spectrum
signal
infinite
sin(?0t)
infinite, decaying
Lorentz profile
exp(-?t/2)sin(?0t)
finite
sin(?0t), 0 ? t ? T
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Line Shapes and Shifts contd
I0
line core
G for Lorentz
FWHM full width at half maximum
I0/2
line shift
line wings
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Line Shapes and Shifts contd
Natural broadening Uncertainty principle
Lorentzian with G ? ?? 1/t and negligibly
small line width ??/? 10-8 Doppler effect (ion
temperature) Doppler shift ?? ? ? - ? 0 ?
0v/c ? I(?) ? f(?/?0-1c) Maxwellian ?
Gaussian I(?) I0exp-(?-?0)2c2/2v2?02
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Line Shapes and Shifts contd

• Convolution of (independent!) broadening effects
• Gauss Gauss Gauss
• ?2 ?12 ?22
• Lorentz Lorentz Lorentz
• ? ?1 ?2
• BUT

Gauss Lorentz Voigt!
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Line Shapes and Shifts contd
Collisional (Stark, resonance,) broadening
electrons and/or other ions interrupt or modify
the light train
Collisionally broadened line profiles depend on
particle densities!
u
l
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Plasma Environment Effects
Ionization potential lowering, ?I
High-n electrons do not see the ion!
Debye radius
Interparticle distance
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Radiation Transfer
I0
I1
plasma
emission
absorption
optical depth
optically thick
optically thin
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Radiation Losses

• Importance
• Magnetic fusion research
• Solar corona

• Free-free (bremsstrahlung)
• e Aq ? e Aq hv
• Free-bound (radiative recombination)
• e Aq1 ? Aq hv
• Bound-bound (spectral lines)
• Aq ? Aq hv

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Types of Equilibria
h? Planck
Complete Thermodynamic Equilibrium
ions Boltzmann
e Maxwell
Saha
Local thermodynamic equilibrium (LTE)
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Types of Equilibria LTE
Dense (or very dense) plasmas Collisional
processes radiative processes Ne 1013 Te1/2
?E3 cm-3 (Te, ?E in eV)
No atomic collisional data are needed!
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Types of Equilibria Corona
Low density plasmas (mainly) solar corona
Population balance equation NgRexcNuA I NuA
NgRexc Ioniz. and recomb. Ne
Depends only on excitation from the ground state!
spontaneous emission
excitation
ionization equilibrium is independent on Ne
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If theres no equilibrium?
ionization limit
ionization
excited states
recombination
ground state
ground state
Z1
Z
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Collisional-Radiative Modeling
All possible processes

• Rate equations

Rate Matrix (atomic data!)
State Vector
Source Function
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Ionization equilibrium C
Solid Ne 1019 cm-3 Dashed Ne 1010 cm-3
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Example Diagnostics
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Example X-Ray Lasers

• Ordinary visible lasers long wavelengths
  2,000-10,000 Å
• X-ray lasers short wavelengths ? 500 Å
• ?E hc/? ? ?E ? 25 eV
• Neutral atoms small ?Es only (lt20 eV)
• Solution use highly-ionized atoms because ?E
  Z2
• Source of multiply-charged ions
• only very hot plasmas!
• High density is required (i) to reach high
  ionization stages quickly and (ii) to have high
  lasing
• Z-pinch plasma is hot and dense enough
• T 200 eV (2106 K) N 1020 cm-3

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Conclusions

• Plasma Spectroscopy
• interesting, useful, thought-provoking