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Comparison of Stark Broadening and Doppler Broadening of Spectral Lines in Dense Hot Plasmas. By Michael Zellner. Thanks to:. Dr. Charles Hooper Jeffrey Wrighton Mark Gunderson. Mission Statement.
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Comparison of Stark Broadening and Doppler Broadening of Spectral Lines in Dense Hot Plasmas By Michael Zellner
Thanks to: • Dr. Charles Hooper • Jeffrey Wrighton • Mark Gunderson
Mission Statement • Compare the relative effects of Doppler broadening to Stark broadening of spectral lines emitted by a radiator in a plasma
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.
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.
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 ~1*1023 per cm3) • A plasma can be neutral, positive, or negative in overall charge
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
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
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
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 (n=2 to n=1)
Types of Spectral Line Broadening • Natural Broadening (uncertainty principle) • Pressure Broadening • Stark Broadening • Doppler Broadening • Opacity Broadening
Natural Broadening DE DT £ hbar/2
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
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)
Stark Difficulties • Calculation of the free-free gaunt factor
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
Results • Neither Doppler or Stark Broadening can be neglected for Boron dopant in a plasma
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 Z’s need to be modeled