ISSN 1063-780X, Plasma Physics Reports, 2007, Vol. 33, No. 5, pp. 391–398. © Pleiades Publishing, Ltd., 2007.
Original Russian Text © P.N. Mager, D.Yu. Klimushkin, 2007, published in Fizika Plazmy, 2007, Vol. 33, No. 5, pp. 435–442.
391
1. INTRODUCTION
Among the vast variety of Alfvén waves in the
Earth’s magnetosphere, there are two limiting cases:
toroidally and poloidally polarized waves. In the first
case, the magnetic field lines oscillate in the azimuthal
direction (along the binormal to them), whereas in the
second case, they oscillate in the radial direction
(across the magnetic shells). Accordingly, the electric
field oscillates in the radial direction in the first case
and in the azimuthal direction in the second. The ques-
tion arises of what are the sources of such waves. It is
suggested that toroidally polarized Alfvén waves are
generated resonantly by fast magnetosonic waves com-
ing from the outer regions of the magnetosphere [1]. As
for the poloidally polarized Alfvén waves, they are
thought to be excited by the particles injected into the
magnetosphere during magnetic substorms. There is
some experimental evidence in support of this hypoth-
esis [2, 3]. It is widely believed that the waves are
excited by unstable populations of 10- to 150-keV pro-
tons via the bounce-drift resonance mechanism (the
bounce-drift instability) [4, 5].
In terms of this mechanism, however, it is impossi-
ble to explain a number of important features of the
waves under discussion. First, the observed waves have
quite definite azimuthal wavenumbers m. For the most
commonly observed unstable high-energy proton dis-
tributions, however, the instability growth rate weakly
depends on the azimuthal wavenumber [6]. Therefore,
the instability cannot select a narrow range of azi-
muthal wavenumbers. Second, the direction of the
phase velocity of the observed poloidal Alfvén waves
usually coincides with that of proton drift in a nonuni-
form magnetic field. However, the instability can
equally well generate waves propagating in the oppo-
site direction [6]. Finally, as was shown in [7, 8], the
poloidal waves are rapidly converted into toroidal ones,
so the instability amplifies toroidal, rather than poloi-
dal, waves.
It is therefore necessary to consider not only reso-
nant but also nonresonant mechanisms for generating
poloidal Alfvén waves. The excitation of MHD waves
by an external alternating current was studied in [9, 10].
For magnetospheric conditions, this mechanism was
considered in [11], where Alfvén waves were assumed
to be generated by the current of particles injected into
the magnetosphere. In the nonuniform magnetic field of
the Earth, such particles drift azimuthally, producing an
alternating current, because they are injected in the
form of a cloud that has a finite size in the azimuthal
direction. This alternating current generates an Alfvén
wave. The clouds can also be regarded as nonuniformi-
ties of the magnetospheric ring current. The excitation
of Alfvén waves by an unsteady external current was
considered in [12], where additional arguments in sup-
port of this mechanism were presented.
In [9–12], the plasma was assumed to be homoge-
neous (although, in [11], it was additionally assumed to
be bounded along the magnetic field lines). However,
the magnetospheric conditions are inherently nonuni-
form: in particular, the plasma density and magnetic
field strength vary both along the magnetic field lines
SPACE
PLASMA
Generation of Alfvén Waves by a Plasma Inhomogeneity Moving
in the Earth’s Magnetosphere
P. N. Mager and D. Yu. Klimushkin
Institute of Solar–Terrestrial Physics, Siberian Division, Russian Academy of Sciences, Irkutsk, 664033 Russia
Received April 19, 2006; in final form, November 23, 2006
Abstract—The generation of an Alfvén wave by an azimuthally drifting cloud of high-energy particles injected
in the Earth’s magnetosphere is studied analytically. In contrast to the previous studies where the generation
mechanisms associated with the resonant wave–particle interaction were considered, a nonresonant mechanism
is investigated in which the wave is excited by the alternating current produced by drifting particles. It is shown
that, at a point with a given azimuthal coordinate, a poloidally polarized wave, in which the magnetic field lines
oscillate predominantly in the radial direction, is excited immediately after the passage of the particle cloud
through this point. As the cloud moves away from that point, the wave polarization becomes toroidal (the mag-
netic field lines oscillate predominantly in the azimuthal direction). The azimuthal wavenumber m is defined as
the ratio of the wave eigenfrequency to the angular velocity of the cloud (the drift velocity of the particles). It
is shown that the amplitudes of the waves so generated are close to those obtained under realistic assumptions
about the density and energy of the particles.
PACS numbers: 52.35.Bj, 52.35.Py, 94.30.Gm, 94.30.Ms
DOI: 10.1134/S1063780X07050042