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