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 (n e ~1*10 23 per cm 3 ) 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  E a - E b )/h bar 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  h bar /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

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

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