Complexity Of The 18 October 1995 Magnetic Cloud
Observed by Wind and the Multi-Tube Magnetic Cloud
Model.
V.A. Osherovich1, J. Fainberg2, A. Vinas2 and R. Fitzenreiter2
1
EER Systems Inc., NASA/GSFC, Greenbelt, MD 20771,
2
NASA/GSFC Greenbelt, MD 20771, US
Abstract. The notion that a magnetic cloud may consist not of one but of a few closely interacting magnetic tubes came
from the analysis of the relation between the electron temperature Te and plasma density Ne (1Fainberg et al. 1996). The
log-log plot of Te versus Ne of data in the 10-13 June 1993 Ulysses magnetic cloud revealed two polytropes (both with ge
< 1) which have been attributed by 2Osherovich, Fainberg and Stone (1999a) to two helices embedded in the same
cylindrical flux rope. In contrast to configurations with cylindrical symmetry, magnetic configurations with helical
symmetry allow a description of many helices which in cross section look like distorted flux ropes. We present elements
of the magnetic and thermodynamic structure of the Oct 18-21, 1995 magnetic cloud observed by Wind. Our research is
complementary to previous studies of this cloud by other authors (3Larson et al. 1997; 4Lepping et al. 1997; 5Janoo et al.
1998). The log-log plots of Te vs Ne suggest that this cloud consists of eight magnetic tubes with polytropic indices
below unity and a few non-coherent structures for which the polytropic relation is not valid. The solar wind quasiinvariant (6Osherovich et al., 1999b) for this cloud strongly anti-correlates with the Dst index for the resulting magnetic
storm.
MAGNETIC STRUCTURE OF THE
CLOUD AND SELF-SIMILAR (OFB
MODEL) FOR A SINGLE FLUX ROPE
B2f = -(R / 2)
df
dR
B2z* = f - B2f
The October 18-21, 1995 cloud observed by Wind
has all three magnetic cloud elements which according
to Burlaga [71981] are: a) a significant enhancement of
the total magnetic field B (figure 1, blackr line), b) a
smooth rotation of the total magnetic field B (figure 2,
red line) and c) a low proton temperature Tp. The front
sheath is marked by the shock at 11.111h (hours
referenced
r to start of October 18). Starting from the
shock, B rotates (blue line in figure 2), but the rotation
in the z-y plane is not smooth. Only on entering the
cloud at 19.1h, can one see the beginning of the
smooth rotation during
r the period 19.104-48.917h.
After this period, the B rotation continues in the back
sheath (orange curve in figure 2), but the smoothness
typical for inside the cloud is lost.
(1)
(2)
where (z*, f, R) are cylindrical coordinates with z*
along the axis of the flux rope. Thus, for a "flat top"
df
cloud like the Oct 18-21,1995 cloud,
ª 0 and
dR
therefore Bf should be close to 0. In fact, we see a
large Bf component (green curve in Figure 1).
The self-similar model of Osherovich, Farrugia and
Burlaga (OFB 1993) has
r
r
r
B = B 0 (h)y -2 (t) ez* + B f (h)y -1 (t) e f (3)
r y' r
r
(4)
v = R eR + v 0 (h) ez*
y
where h = R / y(t) is a self-similar parameter. The
evolution function y(t) obeys the equation
The magnetic structure of the October 18-21,1995 cannot be described by any force-free magnetic flux rope
(neither constant nor non-constant alpha). The general
solution for a force-free rope [Lust and Schluter, 1954]
can be expressed through a generating function where
d 2y
dy
(5)
= Sy-2 - Qy-1 + Ky (-2g +1 ) - n
2
dt
dt
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
733
where S, Q, K and n are constants; g is a polytropic
index. In order for the OFB flux rope to expand, g
Figure 1. Total magnetic field components for
October 18-21, 1995 magnetic cloud observed by
Wind.
Figure 4. Three types of structures inside the magnetic cloud.
Figure 2. Rotation of Magnetic Field Vector in October
18-21,1995 Magnetic Cloud Observed by Wind.
Figure 5. Position of three structures inside the magnetic cloud
must be below unity for either v 0 (h) = 0 or
v 0 (h) ≠ 0 which we include for purpose of generality.
The OFB model does accommodate a flat top B profile
for an old cloud, when y(t) is large enough and Bf max
is comparable to B z* max (over-grown pinch).
Figure 3. Total electron temperature vs. density in the
magnetic cloud and the sheath
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ANTI-CORRLELATION OF Te AND Ne
IN THE CLOUD AND THE SHEATH
correlation with Dst drop during related magnetic
storms.
The dependence of Te on Ne in the cloud (red dots
in figure 3) show eight extended periods with
significant anti-correlation (cc > 0.7) between Te and
Ne, for which the polytropic relation
g e-1
Te = FN e
(6)
holds. Between those regions (which we interpret as
magnetic tubes) there are non-coherent structures with
cc < 0.7. For the whole cloud (including non-coherent
structures), F=5.87x105 cgs units and ge = 0.39. For the
sheath (orange and blue points in figure 3), F is lower
and ge is somewhat higher than in the cloud, but is still
less than unity. For the back sheath, for example, ge =
0.75 and F = 2.66x105. Three types of structures
(highly coherent, coherent and non-coherent) inside
the cloud are illustrated in figure 4. The corresponding
correlation coefficients are cc =0.93 (blue color) cc =
0.84 (black) and cc = 0.1 (green). Figure 5 illustrates
the position
r of the corresponding regions on the z-y
plane of B rotation. The magnetic structure of the
back sheath includes two regions: (strong field region
– gray color in figures 6 and 7 and the weak field
region – black color on the same figures). Thus,
magnetically and thermodynamically, such regions can
be separated from each other. Further division (fine
structure) is possible.
Figure 6. Rotation of magnetic field in back sheath
ANOMALY OF SOLAR WIND QUASIINVARIANT (QI) AND MAGNETIC
STORM INDUCED BY THE OCTOBER
18-21, 1995 CLOUD
Recently, a new index of solar activity, the solar
wind quasi-invariant
QI ≡ (B 2 / 8p) /(rv 2 / 2)
(7)
Figure 7. Structures inside the back sheath of the magnetic
cloud.
has been suggested (Osherovich, Fainberg and Stone,
1999). QI is based only on parameters measured in the
solar wind, namely magnetic field strength B, solar
wind speed v and density r. While the yearly median
values of QI follow yearly sunspot numbers with cc =
0.98, every magnetic cloud can be viewed as a
violation of QI (increase by a factor of 20-100). Figure
7 illustrates this increase and also the strong anti-
735
with cc > 0.7 and a number of non-coherent structures
between tubes with cc < 0.7.
2. For the whole cloud (including non-coherent
regions), ge = 0.39 and F = 5.87x105. For the back
sheath, these values are ge = 0.75 and F = 2.66 x105.
Thus, for both the cloud and the sheath ge < 1 but g e is
significantly larger in the sheath as was previously
observed in the June 10-13, 1993 Ulysses cloud
[Fainberg et al. 1996; Osherovich and Burlaga 1997].
3. The cloud is old (expansion subsided) and as such
is in agreement with the OFB model where it has an
overgrown Bf component which leads to a flat profile.
4. We interpret the complexity of this cloud (8 tubes)
as a case of interacting helices embedded in one
cylindrical flux rope (our multi-tube model).
Figure 8. Solar wind quasi-invariant increase for the
magnetic cloud and the related drop in Dst index.
5. The abnormally large QI for this cloud closely anticorrelates with the Dst index, which dropped during
the associated magnetic storm.
DISCUSSION AND CONCLUSIONS
From the analysis of total Te as a function of Ne, we
infer that most of clouds consist of a few magnetic
tubes wrapped up in a magnetic flux rope (container).
Our exact bounded MHD solutions have depicted such
configuration as multiple helices embedded in the
cylindrical flux rope (Krat and Osherovich, 1976;
Osherovich, Fainberg and Stone, 1999b). The
topological complexity of such solutions depends on
the magnetic flux function (ground-statersolution, first
excited state, etc.). The continuity of B everywhere
and finite magnetic energy per unit of length of the
main tube, makes such solutions, mathematically,
similar to eigen-functions in quantum mechanics
(Osherovich, 1975). The complex structure of
magnetic clouds like the October 18-21, 1995 cloud,
we believe has consequences for the interaction of
such clouds with planetary magnetospheres and
comets. The strongly non-Maxwellian distribution of
electrons in magnetic clouds (discovered by Fainberg
et al. 1996) leads to an abnormally high population of
highly ionized heavy ions, which in turn can cause
soft-x-rays during the collision with comets. This
internal complexity could be a source of additional
variability of such x-rays.
REFERENCES
1. Fainberg, J. et al., Solar Wind 8, 554, 1996.
2. Osherovich, V.A., J. Fainberg and R.G. Stone GRL
26(3), 401, 1999a..
3. Larson, DE et al., Adv. Space Res. 20 (4-5), 655, 1997.
4. Lepping RP et al., J Geophys Res-Space 102 (A7):
14049, 1997.
5. Janoo, L et al., J Geophys Res-Space 103 (A8): 1724917259, 1998.
6. Osherovich, V.A., J. Fainberg and R.G. Stone GRL
26(16), 2597, 1999b.
7.
Burlaga, L.F., E. Sittler, F. Mariani and R. Schwenn, J.
Geophys. Res. 86, 6673, 1981.
8.
Lust, R. and A. Schluter, Z. Astrophys. 34, 263, 1954.
9.
Osherovich, V.A. C. Farrugia and L.F. Burlaga, Adv.
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1978.
CONCLUSIONS
11. Osherovich, V.A., Soln. Dann. 8, 1975.
12. Osherovich, V.A. and L.F. Burlaga, in Coronal Mass
Ejections, eds N. Crooker, J. Joselyn and J. Feynman,
157, 1997.
1. The October 18-21, 1995 cloud contains eight
magnetic tubes, for which Te anti-correlates with Ne
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