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Comparison of Stark Broadening and Doppler Broadening of Spectral Lines in Dense Hot
PlasmasBy
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
Target bay of the OMEGA Laser.
View of target shot in the OMEGA Target chamber.
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 Ea - Eb)/hbar
• Concerned only with the Lyman 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
E T 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
inf
0
),()()( dEEwJEPwI
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
Stark Broadened Line
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
Doppler Calculation
)2^/2)^(exp()/(1)( owwwIDopper
Doppler Broadened Profile
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