DICTIONARY OF GEOPHYSICS, ASTROPHYSICS, and ASTRONOMY

static equilibrium, air parcels have zero vertical
acceleration. There is no absolutely zero vertical
acceleration in real atmosphere, especially in
small scale weather systems. However, for large
scale weather systems, comparing to the gravitational
acceleration, the vertical acceleration is
very small and can be neglected, and thus the
quasi-hydrostatic approximation is appropriate.
quasi-linear theory In plasma physics, a theory
based on perturbation theory; interactions
between waves and particles are considered to
be first order only. As in perturbation theory, all
terms of second order in the fluctuating quantities
should be small enough to be ignored. Only
weakly turbulent wave-particle interactions can
be treated this way: The particle distribution is
only weakly affected by the self-excited waves
in a random-phase uncorrelated way. This requirement
not only corresponds to small disturbances
in perturbation theory but even directly
results from it as the waves are described in the
framework of perturbation theory. The waves
generatedbytheparticleswillaffecttheparticles
inawaythatwilltendtoreducethewaves. Thus,
the plasma is assumed to be a self-stabilizing
system: Neither indefinite wave growth happens
nor can the particles be trapped in a wave well.
The basic equation of quasi-linear theory is
the Vlasov equation. All quantities then are split
into a slowly evolving part and a fluctuating part.
The long-term averages of the fluctuating part
vanish. In quasi-linear theory, the slowly evolving
quantities give the evolution of the system
under study, while in case of the plasma waves
the fluctuating quantities are of interest because
they describe the wave.
With the index ‘o’ describing the slowly
evolving quantities and the index ‘1’ giving the
fluctuating quantities, the average Vlasov equation
as the basic equation of quasi-linear theory
can be written as
∂fo
+
∂t+ v ·∇fo
q v × Bo
·
m c
∂fo
∂v
=− q
v × B1
E1 + ·
m
c
∂f1
.
∂v
with f being the phase space density, v the
plasma speed, q the charge, m the mass of the
charged particles, E the electric, and B the magnetic
field. The term on the right-hand side con-
© 2001 by CRC Press LLC
quasi-viscous force
tains the non-vanishing averages of the fluctuations
and describes the interaction between the
fluctuating fields and the fluctuating part of the
particle distribution. These interactions, combined
with the slowly evolving fields on the lefthand
side lead to the evolution of the slowly
evolving part of the phase space density. Note
that no assumption about the smallness of the
fluctuations enters: The only limitation is a clear
separation between the fluctuating part and the
average behavior of the plasma. See perturbation
theory.
quasi-neutral equilibrium A plasma condition
apparently occurring on magnetic field lines
in the auroral oval, in which a parallel electric
field is balanced by the mirror force on precipitating
electrons. The parallel voltage may originate
in the circuit that powers Birkeland currents
linking the auroral ionosphere with the distant
magnetosphere. It accelerates the auroral electrons
and at the same time expands the loss cone,
allowing an increase in the current intensity.
quasi-separatrix layer Generalizations of
magnetic separatrices to magnetic configurations
with a non-zero magnetic field strength
everywhere in a given region. They are the locations
where drastic changes in field-line linkages
occur in the solar atmosphere.
quasi-single-scattering approximation A
radiative transfer model that accounts for only
single scattering of photons with the assumption
that forward-scattered light is treated as unscattered.
quasi stellar object See QSO.
quasi-viscous force A force transferring momentum
through the magnetopause, from the solar
wind flowing past Earth to the plasma inside
the geomagnetic tail. A quasi-viscous force was
proposed in 1961 by Ian Axford and Colin Hines
as a possible mechanism for causing global convection
in the Earth’s magnetosphere. Magnetic
reconnection, proposed the same year by James
Dungey, is an alternative mechanism, and many
researchers believe both mechanisms are active,
with the quasi-viscous force being the weaker
but steadier factor.
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