DICTIONARY OF GEOPHYSICS, ASTROPHYSICS, and ASTRONOMY

egion in the nightside magnetosphere where
region 2 Birkeland currents apparently originate.
Magnetospheric plasma must be (to a high
degree of approximation) charge neutral, with
equal densities of positive ion charge and negative
electron charge. If such plasma convects
earthwardundertheinfluenceofanelectricfield,
aslongasthemagneticfieldstaysconstant(afair
approximation in the distant tail) charge neutrality
is preserved.
Near Earth, however, the magnetic field begins
to be dominated by the dipole-like form of
the main field generated in the Earth’s core, and
the combined drift due to both electric and magnetic
fields tends to separate ions from electrons,
steering the former to the dusk side of Earth
and the latter to the dawn side. This creates
Alfvén layers, regions where those motions fail
to satisfy charge neutrality. Charge neutrality
is then restored by electrons drawn upwards as
the downward region 2 current, and electrons
dumped into the ionosphere (plus some ions
drawn up) to create the corresponding upward
currents.
Alfvén shock See intermediate shock.
Alfvén speed In magnetohydrodynamics, the
speed of propogation of transverse waves in a
direction parallel to the magnetic field B. In SI
units,vA =B/ √ (µρ) whereB is the magnitude
of the magnetic field [tesla],ρ is the fluid density
[kg/meter 3 ], andµ is the magnetic permeability
[Hz/meter].
Alfvén’s theorem See “frozen-in” magnetic
field.
Alfvén wave A hydromagnetic wave mode
in which the direction (but not the magnitude) of
the magnetic field varies, the density and pressure
are constant, and the velocity fluctuations
are perfectly aligned with the magnetic-field
fluctuations. In the rest frame of the plasma,
energy transport by an Alfvén wave is directed
along the mean magnetic field, regardless of
the direction of phase propagation. Largeamplitude
Alfvén waves are predicted both by
the equations of magnetohydrodynamics and
the Vlasov–Maxwell collisionless kinetic the-
© 2001 by CRC Press LLC
Algol system
ory, without requiring linearization of the theory.
In magnetohydrodynamics, the characteristic
propagation speed is the Alfvén speedCA =
B/ √ 4πρ (cgs units), whereB is the mean magnetic
field and ρ is the gas density. The velocity
and magnetic fluctuations are related by
δV = ∓δB/ √ 4πρ; the upper (lower) sign applies
to energy propagation parallel (antiparallel)
to the mean magnetic field. In collisionless
kinetic theory, the equation for the characteristic
propagation speed is generalized to
V 2 A =C2
A 1 + 4π
B2
P⊥−P −
,
whereP⊥ andP are, respectively, the pressures
transverse and parallel to the mean magnetic
field,
= 1
ρ
ρα(Vα) 2 .
α
ρα is the mass density of charge species α, and
Vα is its relative velocity of streaming relative
to the plasma. Alfvén waves propagating
through a plasma exert a force on it, analogous
to radiation pressure. In magnetohydrodynamics
the force per unit volume is −∇〈δB〉 2 /8π,
where 〈δB〉 2 is the mean-square magnetic fluctuation
amplitude. It has been suggested that
Alfvén wave radiation pressure may be important
in the acceleration of the solar wind, as well
as in processes related to star formation, and in
other astrophysical situations.
In the literature, one occasionally finds the
term “Alfvén wave” used in a looser sense, referringtoanymodeofhydromagneticwave.
See
hydromagnetic wave, magnetoacoustic wave.
Algol system A binary star in which mass
transfer has turned the originally more massive
component into one less massive than its accreting
companion. Because the time scale of
stellar evolution scales as M −2 , these systems,
where the less massive star is the more evolved,
were originally seen as a challenge to the theory.
Mass transfer resolves the discrepancy. Many
Algol systems are also eclipsing binaries, including
Algol itself, which is, however, complicated
by the presence of a third star in orbit around
the eclipsing pair. Mass transfer is proceeding
on the slow or nuclear time scale.