Comparison of Stark Broadening and Doppler Broadening of Spectral Lines in Dense Hot Plasmas

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Comparison of Stark Broadening and Doppler
Broadening of Spectral Lines in Dense Hot Plasmas

• By
• Michael Zellner

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Thanks to

• Dr. Charles Hooper
• Jeffrey Wrighton
• Mark Gunderson

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Mission Statement

• Compare the relative effects of Doppler
  broadening to Stark broadening of spectral lines
  emitted by a radiator in a plasma

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Astrophysics

• Many astrophysical systems, such as stars, are
  comprised of plasmas that emit spectra in the
  x-ray wavelength. The x-ray emission can be
  gathered with a spectrometer connected to a large
  telescope. By increasing our understanding of
  plasmas and their emitted line spectra, we will
  be able to better interpret the data and extend
  our knowledge of astrophysical systems.

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Fusion

• Temperatures and densities of fusion reactions
  can be modeled and measured in a similar fashion.
  By obtaining spectra from a fusion reaction, the
  broadened spectral lines can be matched with our
  models to accurately determine both quantities.

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What is a plasma?

• A plasma is a sea of positive and negative
  charged particles
• A plasma is very hot (10,000 K), and very dense
  (ne 11023 per cm3)
• A plasma can be neutral, positive, or negative in
  overall charge

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How do we create plasma?

• A micro-balloon is filled with deuterium,
  tritium, and a high Z (nuclear charge) dopant
• The micro-balloon is blasted symmetrically with
  60 laser beams from the OMEGA laser system at the
  Laboratory for Laser Energetics in Rochester, NY

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• The OMEGA laser delivers up to 30-kJ of
  ultraviolet (351 nm) light to the micro-balloon
  in a single pulse
• Through Bremmstrahlung radiation, energy is
  transferred from the photons of the laser to the
  plasma
• The electrons are stripped off of the deuterium
  and the tritium

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• Electrons are stripped from the outer shells of
  high Z dopants
• Inner electrons are held tightly and at the
  correct temperature, the high Z dopants become
  hydrogenic
• The outer surface of the micro-balloon is ablated
  causing the inner surface of the micro-balloon to
  compress the plasma

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Target bay of the OMEGA Laser.
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View of target shot in the OMEGA Target chamber.
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Measurements using a spectrometer.

• Excited ions within the plasma emit spectra which
  can be collected with a spectrometer
• Photons which create the spectra are emitted when
  and excited electron jumps from a higher energy
  orbital to an orbital of lower energy w(Ea -
  Eb)/hbar
• Concerned only with the Lyman a emissions (n2 to
  n1)

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Types of Spectral Line Broadening

• Natural Broadening (uncertainty principle)
• Pressure Broadening
• Stark Broadening
• Doppler Broadening
• Opacity Broadening

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Natural Broadening
DE DT hbar/2
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Stark Broadening

• A type of pressure broadening (greatly effected
  by the density of the surroundings)
• Calculates the effects due to the electric
  micro-field that surrounds the radiating atom
• Presence of an electric field turns degenerate
  states into non-degenerate states
• Is calculated using an ensemble average of the
  possible positioning of the electric micro-field

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Stark Broadening Calculations
P(E) is the micro-field probability
function J(w,E) is the Stark Broadened line
profile (Tighe, A Study of Stark Broadening of
High-Z Hydrogenic Ion Lines in Dense Hot
Plasmas, 1977)
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Stark Difficulties

• Calculation of the free-free gaunt factor

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Stark Broadened Line
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Doppler Broadening

• An effect of the thermal kinetic energy of the
  radiator
• Uses a Maxwellian distribution for the velocity
  of the radiator
• Dependent only on the temperature of the plasma,
  not the density

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Doppler Calculation
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Doppler Broadened Profile
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Results

• Neither Doppler or Stark Broadening can be
  neglected for Boron dopant in a plasma

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Where next?

• A convolution program needs to be written to
  combine the two mechanisms of broadening
• Gradients need to be accounted for (temperature,
  density, electric field)
• Systems with different Zs need to be modeled