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Dust in the Earth’s Magnetosphere
P. Molyneux
Date
Updated Reference Number
change
07/08/2007
PLM-PAY-MagnetDust-008-1
first version issued
1. Sources and Sinks
External
1) Interplanetary Dust
Primary
Internal
1)Electrostatic blow-off from the
surface of the moon.
2) Al2O3 grains etc. from solid rocket
motors
Sources
Secondary
1) Impact of interplanetary dust with moon.
2) Disruption of particles by electrostatic force/rotation
of interplantary dust.
3) Fragments of artificial satellites from
explosions/collisions etc.
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Sinks
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Ref: PLM-PAY-MagnetDust-008-1
Date: 07/08/2007
1) Impact with Earth/satellite.
2) Gradual erosion due to sputtering (bombardment causing atoms to
be ejected into gas phase) by energetic ions.
Adapted from fig. 1 in [1]
2. Motion of particles in the magnetosphere
The motion of a charged dust particle of mass m in an Earth-centred inertial frame is
described by the following equation:
  F  F  F ,
mR
G
LP
L
where FG is the gravitational force, FLP is the light pressure force and FL is the Lorentz force.
The light pressure force is described as FLP 
rg2 J 0 Q pr
c
, where rg is the grain radius, Qpr is
the light scattering efficiency (assumed to be 1) and J0 is the solar energy flux at 1AU, which
has a value of approximately 1.36 x 106 erg-2 s-1 [2].
The Lorentz force is given by FL  Q( E  R 
B
) , where Q is the charge on the dust
c
particle. Assuming that the particle is small (its radius is much smaller than the Debye
shielding length of the plasma) and isolated (the Debye length is much smaller than the
distance between dust grains), Q = φrg, where φ is the electrostatic potential of the grain.
Assuming that R  0 , the effect of the magnetic field on the particle can be ignored. The
electric field can be split into two components; Eco-rotation (related to the rotation of the Earth)
and Ecross-tail (related to the solar wind; also called the convection field). Assuming rigid corotation (meaning that the plasma in the magnetosphere rotates with the same speed as the
3
1
R 
magnetic field), E co rotation   (  R)  B 0  E  , where Ω is the angular velocity of the
c
 R 
Earth, B0 is the surface magnetic field at the equator, and the magnetic field is assumed to
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University of Leicester
PLUME
Ref: PLM-PAY-MagnetDust-008-1
Date: 07/08/2007
be a simple dipole field aligned with the axis of rotation. Ω and B0 are quoted in [2] as having
values of 7.272 x 10-5 rad s-1 and 0.31G respectively. The authors calculate a value for Eco-6
-1
rotation at geosynchronous orbit of approximately 3.36 x 10 V cm pointing towards Earth,
and a value for Ecross-tail of 2.5 x 10-6 V cm-1 pointing in the dawn to dusk direction. Using
these values to calculate the Lorentz force, it can be shown that for particles with radii
around 0.1μm or smaller the Lorentz force becomes similar in magnitude to the gravitational
and light pressure forces. However, calculating the exact value of the Lorentz force is difficult
because charging currents change the particles charge as it moves through the plasma
environment. For a detailed look at these currents see [2].
The orbital evolution of a particle in the magnetosphere depends on its size, its velocity, its
conductivity, any charge it is already carrying and the altitude at which it is injected into the
magnetosphere. The polarity of the charge on the grain also has an effect, because the
presence of the co-rotational electric field causes positive and negative charges to behave
differently. As a result of this, the Earths magnetosphere is more effective at trapping
positively charged grains. Negatively charged grains penetrate deep into the magnetosphere
before being ejected, unless the magnitude of charge is very large [1].
Orbital paths are plotted in [2] for particles of radius 0.1μm injected at two different heights:
one inside and one outside geosynchronous orbit. Conducting and dielectric grains are
considered separately. Charged dielectric grains are found to stay in the magnetosphere for
around 6 days if injected inside geosynchronous orbit before hitting the atmosphere,
although this falls to around 4.5 days if they are injected outside this orbit. Conducting grains
behave differently, crashing into the Earths atmosphere after just under 2 days when
injected inside geosynchronous orbit, and leaving the magnetosphere altogether after just
over a day if they are injected from a higher altitude than this.
The paper these results were taken from was based around the study of man-made particles
that are released by the burning of solid-rocket motors. Natural micrometeoroids may
behave differently. Natural particles are injected into the magnetosphere with a relative
velocity approximately equal to the escape velocity, and are already charged when they
enter. As a result of this, the authors of [2] suggest that they would experience larger
electrodynamical effects which may cause them to be lost, either by impact with the Earths
atmosphere or by ejection, faster than man-made particles.
3. Dust from comets/ meteor showers
The authors of [3] investigated the possible effects of the Earths magnetosphere on the
motion of submicron-sized dust grains associated with the Leonid meteor stream. The parent
comet of the Leonids is 55P/Tempel-Tuttle, which has an eccentric retrograde orbit. This
causes the dust grains moving towards Earth to have large approach velocities (~70km s-1).
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The authors of [3] found that magnetospheric perturbations are not strong enough to change
the orbits of dust with such high velocities. This is true for dust particles produced by the
parent comets of most meteor showers.
4. Lunar ejecta
The authors of [4] suggest that the moon is the primary source for all particulate matter in the
magnetosphere with radii less than 0.5μm. The particles are thought to be ejected from the
moon after lunar impacts by interplanetary material. The percentage of ejected matter that
ends up in the Earths magnetosphere depends on the phase angle of the moon, but at
certain times in the lunar cycle may be up to 80% [3]. The dust particle experiment on the
1959 Eta (Vanguard III) satellite detected a particularly large number of events over a period
which coincided with the Leonid meteor shower. It has been suggested that this was due to
dust being ejected from the lunar surface into the near-Earth environment after impacts by
Leonid meteors.
References
[1] D.A. Mendis: Entry of Dust Particles into Planetary Magnetospheres, Advances in Space
Research, vol. 4, no. 9, 1984, p. 111-120
[2] M. Horanyi, H.L.F. Houpis, D.A. Mendis: Charged Dust in the Earth’s Magnetosphere1. Physical and Dynamical Processes, Astrophysics and Space Science, vol. 144, no. 1-2,
May 1988, p. 215-229
[3] A. Juhász, M. Horányi: Magnetospheric Screening of Cosmic Dust, Journal of
Geophysical Research, Volume 104, Issue A6, June 1999, p. 12577-12584
[4] W.M. Alexander, J.D. Corbin: Interaction of Lunar Ejecta and the Magnetosphere of the
Earth, Solid particles in the solar system; Proceedings of the Symposium, Ottawa, Canada,
August 27-30, 1979. Dordrecht, D. Reidel Publishing Co., 1980, p. 425-428.
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