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Some remarks on the structure of the distant neutral sheet
Planet.
Space Sci. 1975,
Vol. 23, pp. 723 to 726.
Persamon
Press.
Printed
in Northern
Ireland
RESEARCH NOTES
SOME REMARKS
OF THE DISTANT
ON THE STRUCTURE NEUTRAL SHEET (Received 10 May 1974)
Abstract---From Pioneer 7 observations the equilibrium of the neutral sheet is investigated, in the usual one-dimensional model. Deviations from this simple geometry are suggested to have important consequences on the stability of the sheet. The internal structure of the neutral sheet of the distant geomagnetic tail, as observed by Pioneer 7. at N 1000 Earth radii, is briefly discussed in this note. Our attention is limited to those crossings (5 out of 11, Walker ef al. 1973) for which a significant number of plasma observations internal to the sheet is available,
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Fro.1. MAGNETIC PIED (1Osec AVERAGES) AND PLASMA DATA AROUND THE NEUTRALSIWET. Magnetic field components (gammas) are related to the usual solar ecliptic (SE) coordinates with a Sunward Xsm axis and a northward Zsa axis. The number density is in particles/&; the thermal and bulk velocities are in km/set. 723
724
RESEARCH
The reversal of the x-component model
NOTES
of the magnetic field (see Fig. 1) is typically well represented by the simple B = &rgh(r/L)$
(1)
where & is the constant tail field, z the distance from the neutral sheet and L the half-thicknessof the sheet itself. Equation (1) is an exact solution of the Maxwell-Vlasov equations for a plasma sheet separating regions of opposite field lines (Harris 1962). Undetermined amplitude and velocity of the tail motions, so far from the Earth, do not allow any realistic estimate of the neutral sheet thickness. However, assuming a constant velocity of the spacecraft relative to the sheet, B is observed to vary linearly with .r (cross-correlation coefficient > 0.97) in the region z < L. A magnetic field as Equation (1) provides, in the magnetohydrodynamic approximation, a pressure profile as
P(‘) = PO-
$
cosh!(z,L)
1-
where p. is the plasma pressure at the null point. Equation (2) has usually been interpreted in terms of a density gradient; as matter of fact our results suggest also the presence of a more explicit temperature gradient around the neutral sheet. The agreement with this simple one-dimensional model is reinforced considering that the theoretical values of the magnetic field, requested for pressure balance (2), (assumingp = 2&J, are typically close to the observed Bt (Table 1). TABLE 1.
Btaeor 8.6 9.8 9.1 6.6 6.3
(b)
BOX, 9.4 10.0 105 6.6 5.3
t
F1o.2. THE DIRJJCXIONOF THE MAGNETIC FIELD IN THE XZsl PLANE. Versors are ordered in their temporal sequence (a). Observed features are indicative of a spatial magnetic topology as in (b).
RESEARCH
NOTES
725
Nevertheless, the observed deviations from the simplified model should be pointed out; indeed they are expected to have a remarkable influence on the stability of the neutral sheet. For example, as pointed out by Villante and Lazarus (1973). and confirmed in Fig. 1, there is a plasma velocity shear in the distant tail with a clear maximum at the neutral sheet. Dobrowolny (1972), showed that, in a straight magnetic field configuration, similar structures might be associated with Kelvin-Helmoltx instability processes. More particularly, the enhanced z-component values at the x-reversals suggest interconnection of field lines across the neutral sheet. When examined in detail as in Fig. 2(a) (showing the time signature of the field direction in a meridian plane passing through the Earth) these structures clearly suggest a more complex magnetic field topology (Fig. 2(b)). On the other hand, at the zeroth order, a non-zero z-component across the sheet only implies a ap/ax Z 0 undetectable with few crossings at about the same geocentric distances. These observations could be a consequence of the non-linear evolution of the tearing mode instability. This instability, indeed, as discussed by Biskamp et al. (1970), prevents the sheet from undergoing gross destruction leading to the formation of magnetic loops. The same conclusion was provided by Schindler and Ness (1972), who reported detailed evidence for closed magnetic loops in the near Earth tail. In this sense our results pose again the problem of a more general investigation of the stability of the neutral sheet. For example, Smith and Raduu (1973), suggested that a transversal component of the magnetic field could possibly stabilize the tearing mode of the geomagnetic tail. However, to the author’s knowledge, an analytical treatment of similar two-dimensional structures has not yet been made. Finally, the observation of simultaneous reversals of both the x- and the z-component (double crossing in Fig. 3). in a sharp region of more depressed field strengths, might be alternatively interpreted in terms of an x-null point sweeping back and forth past the spacecraft.
FIG. 3. h’fAc3NETIC FIELD (10 SeC AVERAGeS) AND PLASMA DATA AROUND THE NEWRAL. SHEET. Magnetic field components (gammas) are related to the usual solar ecliptic (SE) coordinates with a Sunward X, axis and a northward Zsl axis. The number density is in particles/co; the thermal and bulk velocities are in km/set. 11
726
mEARCH
NOTES
Acknawledgeme~fs-I wish to thank Dr. A. J. Lazarus of the Center for Space Research, M.I.T., and Dr. N. F. Ness of the NASA Goddard Space Flight Center, for the use of plasma and magnetic field data from Pioneer 7. The 10 see averages of the magnetic field were provided by the magnetic field group of the Laboratorio Plasma nello Spazio, CNR, Frascati. Thanks are due for helpful discussions and critical reading of the manuscript to Professors F. Mariani and M. Dobrowofny of the University of L’Aquila. Some aspects of the paper were also discussed with Dr. R. Pozzoli of the Laboratorio Fisica de1 Plasma, CNR, Milan. U. VI~LANTE Istifuto Fisico, Universitci, L’Aquila, and Laboratorio PIasma nello Spa&, CNR, Frascati, Ituly REFERENCES BISKAMP,D., SAGDEEV,R. Z. and SCHINDLER, K. (1970). Non-linear evolution of the tearing instability in the g~magn~ic tail. Cost. E~ectrudy~. 1,297. DOBROWOLNY,M. (1972). Kelvin-Helmoltz instability in a high @ collisionless plasma. Phys. FZuids 13, 2263. HARRIS, E. G. (1962). On a plasma sheath separating regions of oppositely directed magnetic field. Nuovo Cim. Xxm, 115. SCOUR, K. and NESS, N. F. (1972). Internal structure of the geomagnetic neutral sheet. J. geo@zys. I&s. 77,Pl. Sm, D. F. and tiw, M. A. (1972). Stability of a model current sheet with finite transverse field and finite 0080~velocity. Cosm. Electrodyn. 3, 285. VILLANTE,U. and LAZARUS, A. J. (1973). Double streams of protons in the distant geomagnetic tail. Submitted to J. geophys. Res. WALER, R. C., V-m, U. and L-us, A. J. (1973). Plasma flow and field revti regions in the distant geomagnetic tail. Submitted to J. geophys. Res. Planet. Space Sci. 1975, Vol. 23. Pp. 726 to 731.
Perpamon Press. Printed in
Northern Irehnd
WIND ESTIMATES NEAR 150 km FROM THE VARIATION IN INCLINATlON OF LOW-PERIGEE SATELLITE ORBITS (Received 1 July 1974) Abstract-Precise orbit determinations of five Air Force low-altitude satellites are used to estimate winds near 150 km from variations in the satellite orbital inclinations. Zonal winds determined by this method range from 25 to 200 m/se-c during quiet to m~e~tely disturbed geomagnetic conditions, to winds on the order of 300-600 m/set during active geomagnetic conditions. Comparisons are made with other wind data and appropriate theories. In recent years. mean rotational speeds of the upper atmosphere have been determined from the small variation of i&in&ion of satellite or&s (King-Hel~,*l970,1972). Satellite orbits studied thus far typically have nerieee heights above 200 km, orbitat period decavs of fess than 0.05 minldav, and decreases in inclination Gf abo;t 0.0005 deg/day. brbital i&linations &e usually not determined
range between 130 and 150 km, causing drag perturbations of typically decrease at the rate of 0.5 min/day, and inclinations accurate and well distributed in time. Orbital inclination is deg, making it possible to measure variations of O*OO2deg/day
there are some disadvantages
to the use of these particular satellites:
1. Satellite lifetimes are only 7-10 days. 2. Vehicle boosters adjust the orbit two to three times during a satellite’s lifetime, making it difftcult to find a sticiently long data sample (the minimum desired being about 3 days).
Space Sci. 1975,
Vol. 23, pp. 723 to 726.
Persamon
Press.
Printed
in Northern
Ireland
RESEARCH NOTES
SOME REMARKS
OF THE DISTANT
ON THE STRUCTURE NEUTRAL SHEET (Received 10 May 1974)
Abstract---From Pioneer 7 observations the equilibrium of the neutral sheet is investigated, in the usual one-dimensional model. Deviations from this simple geometry are suggested to have important consequences on the stability of the sheet. The internal structure of the neutral sheet of the distant geomagnetic tail, as observed by Pioneer 7. at N 1000 Earth radii, is briefly discussed in this note. Our attention is limited to those crossings (5 out of 11, Walker ef al. 1973) for which a significant number of plasma observations internal to the sheet is available,
I
l
l
.
l
.
. l
0
1
I
I
..‘-.-.,
-r
. _. _..... : *.
.
8
.
. ..‘f
4
i
.‘.._..
.A
-
IT
,.’
..:..
5.d” II.
__
,.-
-
,
%C.,
-T
. -. ..:.*.
t
.
I
I
...&”
. .
..I_# ..-
v-
. ..*..r I
*r
2
..P..*...
8
5 . .
Fro.1. MAGNETIC PIED (1Osec AVERAGES) AND PLASMA DATA AROUND THE NEUTRALSIWET. Magnetic field components (gammas) are related to the usual solar ecliptic (SE) coordinates with a Sunward Xsm axis and a northward Zsa axis. The number density is in particles/&; the thermal and bulk velocities are in km/set. 723
724
RESEARCH
The reversal of the x-component model
NOTES
of the magnetic field (see Fig. 1) is typically well represented by the simple B = &rgh(r/L)$
(1)
where & is the constant tail field, z the distance from the neutral sheet and L the half-thicknessof the sheet itself. Equation (1) is an exact solution of the Maxwell-Vlasov equations for a plasma sheet separating regions of opposite field lines (Harris 1962). Undetermined amplitude and velocity of the tail motions, so far from the Earth, do not allow any realistic estimate of the neutral sheet thickness. However, assuming a constant velocity of the spacecraft relative to the sheet, B is observed to vary linearly with .r (cross-correlation coefficient > 0.97) in the region z < L. A magnetic field as Equation (1) provides, in the magnetohydrodynamic approximation, a pressure profile as
P(‘) = PO-
$
cosh!(z,L)
1-
where p. is the plasma pressure at the null point. Equation (2) has usually been interpreted in terms of a density gradient; as matter of fact our results suggest also the presence of a more explicit temperature gradient around the neutral sheet. The agreement with this simple one-dimensional model is reinforced considering that the theoretical values of the magnetic field, requested for pressure balance (2), (assumingp = 2&J, are typically close to the observed Bt (Table 1). TABLE 1.
Btaeor 8.6 9.8 9.1 6.6 6.3
(b)
BOX, 9.4 10.0 105 6.6 5.3
t
F1o.2. THE DIRJJCXIONOF THE MAGNETIC FIELD IN THE XZsl PLANE. Versors are ordered in their temporal sequence (a). Observed features are indicative of a spatial magnetic topology as in (b).
RESEARCH
NOTES
725
Nevertheless, the observed deviations from the simplified model should be pointed out; indeed they are expected to have a remarkable influence on the stability of the neutral sheet. For example, as pointed out by Villante and Lazarus (1973). and confirmed in Fig. 1, there is a plasma velocity shear in the distant tail with a clear maximum at the neutral sheet. Dobrowolny (1972), showed that, in a straight magnetic field configuration, similar structures might be associated with Kelvin-Helmoltx instability processes. More particularly, the enhanced z-component values at the x-reversals suggest interconnection of field lines across the neutral sheet. When examined in detail as in Fig. 2(a) (showing the time signature of the field direction in a meridian plane passing through the Earth) these structures clearly suggest a more complex magnetic field topology (Fig. 2(b)). On the other hand, at the zeroth order, a non-zero z-component across the sheet only implies a ap/ax Z 0 undetectable with few crossings at about the same geocentric distances. These observations could be a consequence of the non-linear evolution of the tearing mode instability. This instability, indeed, as discussed by Biskamp et al. (1970), prevents the sheet from undergoing gross destruction leading to the formation of magnetic loops. The same conclusion was provided by Schindler and Ness (1972), who reported detailed evidence for closed magnetic loops in the near Earth tail. In this sense our results pose again the problem of a more general investigation of the stability of the neutral sheet. For example, Smith and Raduu (1973), suggested that a transversal component of the magnetic field could possibly stabilize the tearing mode of the geomagnetic tail. However, to the author’s knowledge, an analytical treatment of similar two-dimensional structures has not yet been made. Finally, the observation of simultaneous reversals of both the x- and the z-component (double crossing in Fig. 3). in a sharp region of more depressed field strengths, might be alternatively interpreted in terms of an x-null point sweeping back and forth past the spacecraft.
FIG. 3. h’fAc3NETIC FIELD (10 SeC AVERAGeS) AND PLASMA DATA AROUND THE NEWRAL. SHEET. Magnetic field components (gammas) are related to the usual solar ecliptic (SE) coordinates with a Sunward X, axis and a northward Zsl axis. The number density is in particles/co; the thermal and bulk velocities are in km/set. 11
726
mEARCH
NOTES
Acknawledgeme~fs-I wish to thank Dr. A. J. Lazarus of the Center for Space Research, M.I.T., and Dr. N. F. Ness of the NASA Goddard Space Flight Center, for the use of plasma and magnetic field data from Pioneer 7. The 10 see averages of the magnetic field were provided by the magnetic field group of the Laboratorio Plasma nello Spazio, CNR, Frascati. Thanks are due for helpful discussions and critical reading of the manuscript to Professors F. Mariani and M. Dobrowofny of the University of L’Aquila. Some aspects of the paper were also discussed with Dr. R. Pozzoli of the Laboratorio Fisica de1 Plasma, CNR, Milan. U. VI~LANTE Istifuto Fisico, Universitci, L’Aquila, and Laboratorio PIasma nello Spa&, CNR, Frascati, Ituly REFERENCES BISKAMP,D., SAGDEEV,R. Z. and SCHINDLER, K. (1970). Non-linear evolution of the tearing instability in the g~magn~ic tail. Cost. E~ectrudy~. 1,297. DOBROWOLNY,M. (1972). Kelvin-Helmoltz instability in a high @ collisionless plasma. Phys. FZuids 13, 2263. HARRIS, E. G. (1962). On a plasma sheath separating regions of oppositely directed magnetic field. Nuovo Cim. Xxm, 115. SCOUR, K. and NESS, N. F. (1972). Internal structure of the geomagnetic neutral sheet. J. geo@zys. I&s. 77,Pl. Sm, D. F. and tiw, M. A. (1972). Stability of a model current sheet with finite transverse field and finite 0080~velocity. Cosm. Electrodyn. 3, 285. VILLANTE,U. and LAZARUS, A. J. (1973). Double streams of protons in the distant geomagnetic tail. Submitted to J. geophys. Res. WALER, R. C., V-m, U. and L-us, A. J. (1973). Plasma flow and field revti regions in the distant geomagnetic tail. Submitted to J. geophys. Res. Planet. Space Sci. 1975, Vol. 23. Pp. 726 to 731.
Perpamon Press. Printed in
Northern Irehnd
WIND ESTIMATES NEAR 150 km FROM THE VARIATION IN INCLINATlON OF LOW-PERIGEE SATELLITE ORBITS (Received 1 July 1974) Abstract-Precise orbit determinations of five Air Force low-altitude satellites are used to estimate winds near 150 km from variations in the satellite orbital inclinations. Zonal winds determined by this method range from 25 to 200 m/se-c during quiet to m~e~tely disturbed geomagnetic conditions, to winds on the order of 300-600 m/set during active geomagnetic conditions. Comparisons are made with other wind data and appropriate theories. In recent years. mean rotational speeds of the upper atmosphere have been determined from the small variation of i&in&ion of satellite or&s (King-Hel~,*l970,1972). Satellite orbits studied thus far typically have nerieee heights above 200 km, orbitat period decavs of fess than 0.05 minldav, and decreases in inclination Gf abo;t 0.0005 deg/day. brbital i&linations &e usually not determined
range between 130 and 150 km, causing drag perturbations of typically decrease at the rate of 0.5 min/day, and inclinations accurate and well distributed in time. Orbital inclination is deg, making it possible to measure variations of O*OO2deg/day
there are some disadvantages
to the use of these particular satellites:
1. Satellite lifetimes are only 7-10 days. 2. Vehicle boosters adjust the orbit two to three times during a satellite’s lifetime, making it difftcult to find a sticiently long data sample (the minimum desired being about 3 days).