GEOPHYSICAJ• RESEARCH LETTERS, VOL. 12, NO. 5, PAGES 287-290, MAY 1985
MAGNETOSPHERIC COUPLING OF HYDROMAGNETiC WAVES - INITœAL RESULTS
W. Allan, S.P. White and E.M. Poulter
Physics and Engineering Laboratory,
Department of Scientific and Industrial Research,
Lower Hutt, New Zealand
Abstract. Recently, emphasis in modelling ULF
pulsations has begun to shift away from
steady-state driving mechanisms towards impulsive
and non-steady sources. We propose a model
allowing numerical solution of the coupled
hydromagnetic wave equations with arbitrary
azimuthal asymmetry in a cylindrical
magnetospheric geometry. General time-dependent
in the magnetosphere can be impulsively stimulated
to ring simultaneously at their eigenperiods.
Allan et al. [1985] examined in detail such a
transient pulsation seen by STARE, ground-based
magnetometers, and GEOS-2. They interpreted the
observations as showing that the field lines were
excited by a (compressional) fast-mode impulse
with m = -2.3. Thus a low m-value is sufficient
stimuli can be applied at the outer (magnetopause) to couple significant energy into field-line
boundary, an arbitrary Alfven speed distribution
can be defined within the boundary, and
ionospheric Joule dissipation is included.
Initial results are presented which show that
impulsive stimuli at the magnetopause can set up
compressional cavity resonances which drive
transverse field-line resonances within the
magnetosphere, in general agreement with recent
predictions. For a realistic ionospheric
oscillations.
A theoretical model is required to investigate
the effect of impulsive and non-steady driving
mechanisms, in particular the coupling of energy
from compressional waves into field-line guided
modes for arbitrary m-valueß In this paper, we
propose a simple model to achieve this, and
present some initial numerical solutions to
demonstrate the model's possibilities. In
dissipation, and azimuthal wavenumber ~3, it is principle, our model is similar to that outlined
found that transient transverse mode solutions are recently by Kivelson and Southwood [1985]. Our
of comparable importance to monochromatic results support the general predictions of their
solutions near the resonant field line. model.
Introduction
Description of model
Since Dungey's early work on hydromagnetic We employ a model based on that of Radoski
waves in the magnetosphere [Dungey, 1955], much [1974, 197•]. The magnetosphere is represented by
emphasis has been laid on the so-called "toroidal" an infinitely long half-cylinder in which magnetic
and "guided poloidal" field-line resonance modes, field lines are circles centered at r = 0 (the
which have natural frequencies arising through equator), magnetic field strength decreases as
reflection at the conjugate ionospheres The r -1 and the magnetopause is taken to be the field
ß
modes are decoupled solutions of the coupled line at r = r 0. The field-aligned coordinate is
hydromagnetic wave equations, the decoupling being 8, with the southern and northern ionospheres at
through axisymmetry for the toroidal mode, and
large asymmetry for the guided poloidal mode.
For typical magnetospheric conditions, coupled
modes involving moderate asymmetry of the wave
fields are likely to be the norm. Much
observational work [eg Olson and Rostoker, 1978;
Hughes et al., 1978] has shown, that, for
pulsations in the frequency range 1 < f < 50 mHz,
the azimuthal wavenumber m is typically < 10, and
is often ~2. The field-line resonance theory [eg
Southwood, 1974] is normally invoked to explain
such pulsations. In this theory, toroidal
field-line resonances are driven by a
monochromatic steady-state source (with fairly
large m), usually taken to result from the
Kelvin-Helmholtz instability at the magnetopause.
Recent work [Kivelson and Southwood, 1985] has
suggested that some monochromatic toroidal
resonances are driven by impulsively stimulated
cavity eigenoscillations. Also, STARE
8 = 0 and • respectively. The azimuthal
coordinate in the real magnetosphere is
represented by using a periodic boundary condition
on the axial variable s.
The electric field components of a
hydromagnetic wave in this model are defined by
E r = T(r,t) f(8) exp (ils),
E s = iP(r,t) f(8) exp (ils).
(1)
E 8 is taken to be zero, the azimuthal wavenumber
is •, and
f(8) = cosh•(•/2-8) sin(nS)
-i sinh•(•/2-8) cos(nS). (2)
This represents a standing-wave structure along
the field line, equivalent to the standing waves
observations [Poulter and Nielsen, 1982] have described in Allan and Knox [1979]. The
demonstrated clearly that geomagnetic field shells field-line harmonic is n ( = 1,2,3,...), while •
can be identified with the damping decrement y/•.
The form in (2) forces a field-aligned Poynting
Published in 1985 by the American Geophysical flux into the ionospheres at • = 0 and •
Union. (consistent with ionospheric Joule dissipation),
the energy being extracted from the wave fields in
Paper number 5L6468. the magnetosphere.
287
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