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 xray 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 microballoon 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 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
inf
I ( w) =  P( E ) J ( w, E )dE
0
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
IDopper( w) = 1 /(   ) exp( ( w  wo)^ 2 /  ^ 2)
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