Next: Introduction
Abstract
It has been very surprising to discover in recent years that some of the
energy dissipated by lightning can couple upwards into the upper atmosphere
driving some very impressive phenomena. These phenomena are grouped under
the name ''high altitude lightning'' and include: red sprites, blue jets,
gamma ray flashes, radio pulses, and more? To understand these phenomena
requires modeling of nonlinear processes driven by high electric power
densities.
The objective of this thesis is to provide the physics framework within
which some of the observed phenomena can be studied and quantitatively
understood and modeled. The first part of the thesis deals with red sprite,
the millisecond-long optical flashes predominantly in the red that stretch
at altitudes between 50 - 90 km, with horizontal extent of a few tens of
kms. In this thesis we set forth the hypothesis that the fractal nature of
the lightning discharge is responsible for the presence of localized regions
of high power density in the upper atmosphere while maintaining low average
integrated power. We demonstrate that the inhomogeneous, highly localized,
spatial structure in the power density is ultimately responsible for the
spatially structured optical emissions observed in red sprites.
To understand the radiation pattern generated by the tortuous structure of
lightning, fractal antennae are studied in detail, with special emphasis on
the concept of spatially inhomogeneous antenna gain that depends on the
fractal characteristics -the fractal dimension- of the discharge. The
fractal nature of lightning gives rise to an increase in the radiated power
density incident in localized regions compared with the homogeneous power
density generated with dipole, non fractal, models of lightning discharges.
Such an increase in the local power density naturally reduces the required
current threshold for sprites to values closer to measurements.
The concept of fractal antennae is applied to the generation of red sprites.
The procedure starts with lightning modeled as a self-similar fractal
discharge antenna, parametrized by its fractal dimension, that generates an
inhomogeneous radiation pattern in the upper atmosphere. The radiated fields
heat the electrons in the lower ionosphere creating the spatially structured
emission pattern observed in red sprites. The electric field propagation and
absorption in the ionosphere is computed self-consistently with the help of
a Fokker-Planck code. Since the spatio-temporal emission pattern, typical of
red sprites, depends strongly on the fractal dimension of the discharge,
discharges of different dimensions require different current amplitudes to
obtain similar emissions intensities. This threshold current strength may
vary by as much as a factor of 10 among the different discharges.
Furthermore, we developed the first spectral model of the emissions
generated by red sprites. Comparison of the results with ground and airborne
observations of sprite spectra results in an estimation of the power density
at the sprite. Proper care was taken to account for the wavelength dependent
atmospheric attenuation.
The second part of the thesis addresses the issue of the generation of the
observed gamma-ray flashes. The gamma-rays observed are consistent
with the generation of runaway electron beams generated by a runaway
discharge. Runaway discharges have been studied only in the absence of a
magnetic field. The magnetic field effect on the runaway discharge may be
important at heights consistent with HAL since the gyromotion becomes more
important than the other $B=0$ time scales, e.g. collisions, ionization,
etc. We developed the theory of the runaway discharge for B different from 0. Results
indicate that the threshold conditions for the runaway discharge are changed
radically in the presence of the Earth's magnetic constraining the electron
acceleration between the ionizing collisions, hence inhibiting the
discharge. In the Earth's atmosphere, such effects become very important for
heights above 20 km, thus, making them extremely relevant in the modeling of
blue jets, gamma ray flashes, and radio bursts, which seem to be related in
some way to these relativistic beams. Consequently, runaway discharges
driven by static electric fields are a very unlikely source of gamma-rays and red sprites, requiring extremely large electric fields with
amplitudes at least 10 times larger than expected.
There is still much to be done.
Next: Introduction