The Geoeffectiveness of Magnetic Clouds as a Function of
Their Orientation
C. Cid, T. Nieves-Chinchilla, M. A. Hidalgo, E. Sáiz and Y. Cerrato
Departamento de Física. Universidad de Alcalá. Alcalá de Henares, Madrid, Spain
Abstract. Trying to get light into the paradigm of forecasting geomagnetic activity, we have looked for a relationship
between geoeffectiveness and the orientation and helicity of magnetic clouds. During the years 1995-2000, we have
selected all the geomagnetic storms with Dst index less than -70 nT. Then, we have inspected WIND data looking for a
possible magnetic cloud related to every storm event. When a magnetic cloud is encountered, we have fitted to
experimental data a model that we have developed for the magnetic cloud topology in order to obtain the attitude of the
magnetic cloud and its helicity. On the basis of the results obtained, a close relationship is observed between the
orientation of the magnetic cloud and its helicity, and the geomagnetic activity.
In this paper we look for the response of the current
ring as a magnetic cloud (MC) passes through it.
Depending on the helicity of the MC and on the
orientation of its axis, the induced current is calculated
and related to the Dst index. We also compare the
theoretical expectations that we obtain with
experimental data.
INTRODUCTION
The defining feature of a geomagnetic storm is a
global decrease in the horizontal component, H, of the
geomagnetic field, and a gradual recovery to its
average level ([1], [2]). Analyses of magnetic storm
morphology have been made by Chapman [3],
Vestine et al. [4], and many others (see [5]). These
studies have shown that at equatorial and mid latitudes
the decrease in H during a magnetic storm can
approximately be represented by a uniform magnetic
field parallel to the geomagnetic dipole axis and
directed toward the South. The magnitude of the
decrease in H represents the severity of disturbance,
and the disturbance field is denoted as Dst index
([6],[7]). Thus, the Dst variation provides a
quantitative measure of geomagnetic disturbance that
can be correlated with other solar and geophysical
parameters (e.g. [8]).
THEORETICAL APPROACH
We consider a MC that passes through the ring current
located around the Earth at a distance Rrc, with a thick
δ Rrc. We assume that the magnetic field of the MC is
given by the model proposed by Hidalgo et al. [10]. In
this model the magnetic field vector can be
decomposed only in two components: an axial and a
poloidal one (there is no radial component). These
components of the magnetic field are obtained from
Maxwell equations, assuming a circular cross section
for the MC and a current density vector with no radial
component, and with axial and poloidal components
constants. The expressions obtained for the magnetic
field
components
are
the
following
The variation in H during a geomagnetic storm is
due to changes in the terrestrial ring current (see e.g..
[9]). This current ring consists in energetic charged
particles flowing toroidally around the Earth, and
creating a ring of westward electric current, centered at
the equatorial plane and extended from geocentric
distances of about 3 to 8 Re. This ring is a critical
element in understanding the onset and development
of space weather disturbances in geospace.
BMC
poloidal =
MC
Baxial
µ0
jaxial r
2
= µ 0 j poloidal (R MC − r )
CP679, Solar Wind Ten: Proceedings of the Tenth International Solar Wind Conference,
edited by M. Velli, R. Bruno, and F. Malara
© 2003 American Institute of Physics 0-7354-0148-9/03/$20.00
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(1)
(1) We suppose that the electric field has only one
component, Eϕ, that is, it follows the angular
direction in a cylindrical coordinate system, and
where RMC is the radius of the MC.
When the MC travels through the interplanetary
medium, its axis makes an angle θ (latitude) with
respect to the ecliptic plane and it presents a longitude
angle, φ, relative to the Sun-Earth line. Then, the
theoretical magnetic field of the MC has to be
expressed in the new reference system. As we assume
that the ring current lies on the ecliptic plane, we will
consider the GSE reference system as a proper system
for this analysis. The velocity of the MC is also
refereed to GSE system, obtaining two components in
the ecliptic plane: a parallel (vx) and a perpendicular
(vy) to the Sun-Earth line (see Figure 1).
(2) We consider that BGSE can be decomposed in two
different contributions: the terrestrial magnetic
field (that does not vary with time), and the MC
magnetic field (that varies with time). In order to
simplify the analysis, we only take into account
the z-GSE component due to the MC magnetic
field.
The electric field induced, Eϕ, obtained from
equation (3) produces a variation in the intensity of the
ring current, δI, given by
Rrc + δR rc
δI = σ ∫R
Ecliptic plane
Magnetic
cloud
rc
(4)
Eϕ dr
where σ is the conductivity of the ring current, that we
consider constant. This δI produces a magnetic field in
the z direction, δB, whose effect in the center of the
ring current can be approach as
µ δI
(5)
δB = 0
2 Rrc
This magnetic field, δB, is the responsible of the
perturbation of the geomagnetic field, and can be
compared with the Dst index. In this analysis we take
into consideration the term of the theoretical Dst index
that only depends on the longitude angle.
FIGURE 1. A schematic view of the ring current
(in brown colour) and the projection of the MC (in
blue) on the ecliptic plane. The orientation of the axis,
the radius and the velocity of the MC are also
indicated.
Then, from all the above theoretical considerations,
we obtain
[
Dst ≈ C0 sinφ (2a xt + v x0 ) − cos φv y
]
(6)
In experimental data we can see that vx decreases
linearly with time and vy is almost constant. Then, we
will consider that
v x = v x0 + a x t , v y = cte
(2)
Having into account the situation described above,
the electric field induced in the ring current due to the
passage of the MC is given by
ρ
ρ
∂B GSE
∇ × E GSE = −
∂t
(3)
FIGURE 2. Simulation of the Dst index obtained
from equation (6). For the simulation, we have taken a
Rrc=4.5Re, δRrc =2Re, | jaxial |=10-12 Cm-2s-1, vy=0,
v x0 =-800 kms-1, ax=5.8 ms-2 and. As the conductivity
has been assumed to be one, the Dst is expressed in
arbitrary units.
that we solve in cylindrical coordinates under the
following considerations:
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where C0 = µ 02 jaxial σRrc (δRrc )2 16 . Figure 2 shows a
simulation of the Dst index obtained.
Dst
vy=0
vy/vx=0.4
Influence of the MC Helicity in the
Geoeffectiveness
A MC will be geoeffective when a South magnetic
field disturbs the Earth magnetic field as it passes, that
is, when a negative value is obtained for the Dst index
(at this stage, we do not consider the magnitude of Dst
index, but just its sign). The influence of the MC
helicity in equation (6) is included in the sign of the
axial component of the current density. A left (right)
handed MC corresponds to a positive (negative) jaxial.
In order to explain clearly this influence, we will
analize separatelly the case when the velocity of the
MC as it goes away from the Sun presents only x-GSE
component, and when the velocity present a y-GSE
component not nule
2π
π
φ(rad)
0
FIGURE 3. Theoretical Dst index obtained at t=0 for
a left-handed MC with vy=0 (solid line) and vy= vx/4
(dotted line).
DATA ANALYSIS
We have analyzed Dst index from Space Physics
Interactive Data Resource (SPIDR) during the years
1995 to 2000. From this data, we have selected those
events where the index was less than -70nT unless for
one day, then, a sample of 61 events is considered for
this work. Once a “storm event” has been selected, we
examine magnetic field and plasma data from the
Wind spacecraft looking for a MC event in the solar
wind associated with the storm. Only for 11 storm
events (a 16 per cent) there was no MC associated. For
the rest of storms, we fit our model to magnetic field
data in the MC interval obtaining the axial component
of the current density and the longitude angle of the
MC axis, as well as other parameters that are not
related to this work.
The Magnetic Cloud Velocity Is Parallel To The XGSE Direction
If we assume that the MC moves parallel to the
Sun-Earth line ( vy=0), there are two possibilities to
obtain we obtain from equation (6) a Dst negative
value: (1) if it is left handed and its axis longitude
angle is included in the interval between 0 and π rad or
(2) if it is right handed and its axis longitude angle is
between π and 2π rad. Then we have obtained that the
helicity and orientation of a MC need to be considered
in order to analyze its geoeffectiveness.
Trying to check our theoretical results, we have
plotted the sign of the axial component of the current
density of all these MC events (as a measurement of
the helicity) versus the longitude angle of its axis
(Figure 4).
The Magnetic Cloud Velocity Is Not Parallel To The
X-GSE Direction
jaxial/|jaxial|
In the last section, in order to obtain the
geoeffective latitude intervals, we have considered that
the MC travels far away from the Sun, directed right to
Earth. Then, the function that let us obtain the
theoretical Dst value (eq. 6) is the same that sin
function. Anyway, if the cloud does not travel
following the Sun-Earth line, that is, if vy≠0, then a
shift in the longitude angles that gives a negative Dst
index is produced (Figure 3).
1
0
-1
0
90
180
270
360
phi (degrees)
FIGURE 4. The figure represents the sign of the
axial component of the current density versus the
longitude angle of the MC axis. The reference lines
indicate a shift of +25º from the Sun-Earth line.
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2. Adams, W. G., Phil. Trans. London (A) 183, 131 (1892).
The results obtained show a close relationship
between the helicity and the longitude of the MC axis
that is shifted from the Sun-Earth line direction (0º180º). Following the theoretical results, this shift could
be associated to the existence of a non-null component
of the solar wind velocity in the perpendicular
direction to the Sun-Earth line.
3. Chapman, S., Annali di Geofisica 5, 481 (1952).
4. Vestine, E.H., Laporte, L., Lange, I., and Scott, W.E.,
The geomagnetic field, its description and analysis,
Carnegie Institution of Washington Publication 580,
Washington D.C., 1947.
5. Akasofu, S.-I. and Chapman, Solar Terrestrial Physics,
Oxford University Press, Oxford, 1972.
SUMMARY AND CONCLUSIONS
6. Mayaud, P.N., Derivation, Meaning, and Use of
Geomagnetic Indices, Geophysical Monograph 22,
American Geophysical Union, Washington D. C., 1980.
In this work, we have analyzed the influence of a
MC in the magnetic field of the Earth. Using a model
that we have developed previously for the magnetic
field of a MC, we have calculated the electric field
induced on the ring current around the Earth, and the
influence of the appearance of this electric field on the
Earth magnetic field. We have compared the disturbed
magnetic field with the Dst index, trying to determine
the characteristics of a MC to be geoeffective. We
have focused our study on the influence of the
longitude angle of the MC axis. A close relationship is
obtained between this angle and the helicity of the
clouds for the events analyzed. Although this
relationship is clear, a shift from the expected values
of the longitude angles is obtained. We have explain
this shift as due to a component of the velocity
perpendicular to the Sun-Earth line, although a
detailed analysis of the velocity vector of these events
would be desirable. We will try this analysis in a
nearly future.
7. Rangarajan, G.K., "Indices of geomagnetic activity" in
Geomangetism, p.323, ed. By J.A. Jacobs, Academic
Press, London (1989).
8. Daglis, I. A., Kasotakis, G., Sarris, E.T., Kamide, Y.,
Livi, S., and Wilken, B., Influence of interplanetary
disturbances on the terrestrial ionospheric outflow,
Physics and Chemistry of the Earth 24, 229-232, 1999).
9. Williams, D.J., Planet. Space Sci. 21, 1195 (1981).
10. Hidalgo et al., J. Geophys. Res. 107, pp1-pp7 (2002).
ACKNOWLEDGMENTS
We want to thank K. Ogilvie, R. Fitzenreiter and R.
Lepping (Goddard Space Flight Center, Greenbelt,
Mariland) for permission to use Wind data, and Space
Physics Interactive Data Resource (SPIDR) for
providing Dst index data. This work has been
supported by the Comisión Interministerial de Ciencia
y Tecnología (CICYT) of Spain, grant ESP97-1776.
Consuelo Cid wants also to acknowledge to the Solar
Wind X organizing committee for their financial
support.
REFERENCES
1. Broun, J. A., “On the horizontal force of the Earth's
magnetism”, Proceedings Roy. Soc. Edinburg 22, 1861,
pp. 511.
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