Institute of Geophysics and Planetary Physics, University of California, Los Angeles, CA 90095-1567
It is widely recognized that Io, the innermost of the Galilean satellites, releases matter into the rapidly rotating Jovian magnetosphere at rates that may be as high as a ton per second. Following ionization, this iogenic, heavy-ion plasma dominates the dynamics of the Jovian magnetosphere. On average this plasma must be lost at a rate that balances its generation but we do not know whether this process is steady or intermittent. Measurements by the Galileo magnetometer suggest that this process is unsteady. By estimating the magnetic and particle stresses from these observations, we further can derive a mass density profile that is consistent with earlier measurements of the current sheet density and that is consistent with estimates of the radial transport of mass in the middle jovian magnetosphere.
The Jovian magnetosphere is known to be dynamic. Radio emissions, especially those at decametric wavelengths, have long been observed to be strongly time varying [Carr et al., 1983]. More recently it has become possible to monitor Jovian auroral emissions from 1 AU. They too undergo strong temporal variations [Ballester et al., 1996; Prangé et al., 1992]. The evidence of this dynamic behavior in the observations of the five flyby missions, Pioneers 10 and 11, Voyager 1 and 2 and Ulysses [Dessler, 1983; Planetary and Space Science, 1993] has not been as clear, apparently either because the time scales are long compared to the duration of the encounters or because the variability in the observations caused by the rotating magnetodisk current sheet obscured such secular variations.
A dynamic magnetosphere is expected because of the addition of a significant flux of ions to the magnetosphere by Io, amply demonstrated by the Galileo observations [Frank et al. 1996; Huddleston et al., 1997]. Nonetheless, the nature of the transport process has not been as obvious. Some authors have advocated a variety of circulation models for the jovian plasma: a circulation pattern involving a stationary line of X and O neutral points [Vasyliunas, 1983]; flux tube interchange transport [Southwood and Kivelson, 1988]; and predominantly co-rotating plasma with a dawnside layer escaping downtail [Cheng and Krimigis, 1989]. The insertion into orbit of the Galileo spacecraft on December 7, 1995 permitted the long-term monitoring of magnetospheric activity and the separation of periodic and secular changes. In this report we present the first evidence for a process at the inner edge of the Jovian magnetodisk that causes a major structural change in this region. The disruption event appears to be abrupt on the time scale of the rotation of the planet (-10 hours), and the time for restructuring much longer. In some senses this process is analogous to the terrestrial substorm that occurs at the earthward edge of the terrestrial magnetotail [Russell and McPherron, 1973] but we do not believe that reconnection has an important role in the initiation of this particular instability. We also examine the balance of stresses inferred from the magnetic field observations. This stress balance is consistent with modern notions of the composition of the plasma and the average rate of radial transport of the plasma.
The measurements reported herein were obtained by the fluxgate magnetometer [Kivelson et al., 1992]. Figure 1 displays 82 hours of the radial component of the magnetic field in four 24-hour panels overlapped by four hours. During this time Galileo moved from a radial distance of 48 Jovian radii (RJ) and a local time of 0645 to a radial distance of 17 RJ and a local time of 1030. Initially the radial component of the magnetic field reverses rapidly between two slowly varying levels, radially outward (positive Br) and radially inward (negative Br). This is the region of the magnetodisk where the north-south component of the field is small and the planetary magnetic field is stretched into a disk-like configuration. The tilt of the magnetic dipole axis to the rotational axis causes the current sheet in the center of the magnetodisk to cross the Galileo spacecraft as the planet rotates. Waves on the surface of the current sheet separating the two halves of the magnetosphere cause the occasional crossing to have multiple magnetic field reversals (e.g. June 23, 2100-2200 UT). As Galileo proceeded inward on this pass it eventually left the region of very stretched magnetic fields and entered a region in which the current sheet was thicker and "Aweaker" in the sense that the field was closer to a dipolar configuration. This transition occurred at about 23 RJ.
|Figure 1. The radial component of the magnetic field measured on the first inbound orbit just prior to Galileo’s first encounter with Ganymede. The pass begins 47 Jovian radii from the planet and ends 17 RJ from it. The periodic reversals of the radial component are due to the rotation of the warped and tilted current sheet over the satellite every 10 hours.|
Figure 2 shows the three components of the magnetic field and its strength in the region around the transition. Prior to the current sheet crossing about 0830 UT, the field was quiet in all components. However, after the current sheet is crossed the strong fluctuations begin that are largely compressional. These continue for a full revolution of Jupiter indicating that the event was truly global. During the next rotation the magnetic field is again disturbed but at a much lower level.
|Figure 2. The three components of the magnetic field radial, north-south or theta, and azimuthal or phi, for the period 0200 UT on June 26, 1996 to 0200 UT on June 27, showing the apparent abrupt change in the magnetic characteristics at about 23 RJ.|
Perhaps the most important change, from before 0830 UT to after it, is the change in the component of the magnetic field, B , crossing the current sheet. Figure 3 shows this component of the magnetic field measured at the current sheet crossing and the change in the radial magnetic field component, BR, from above the current sheet to below for each of the first four inbound passes, G1, G2, C3 and E4. The radial field change across the sheet measures the current in the magnetodisk. The radial profile of BR does not vary much from orbit to orbit. The radial variation of the normal component does vary from orbit to orbit. On G1 there is a very abrupt change at 23 RJ; on G2 there is a change in the radial range but it is not as abrupt. On C3 there is very little change if any in the region. On E4, there is an abrupt decrease in the field across the sheet but it is further out than on G1. In short then, the region around 24 RJ is quite variable from pass to pass and the abrupt change in the noise level seen in Figures 1 and 2 after the 0830 UT current sheet crossing on 26 June 1996 is most probably a temporal event and not simply a spatial variation. Such a change of noise level is only seen on one other pass, E4, and at a much reduced level. The local times at which Galileo crossed 24 RJ on these four orbits were 0851, 0828, 0805 and 0753 for G1, G2, C3 and E4 respectively. It is unlikely that variations over this one-hour range had much effect on the results presented here.
Estimating the Magnetic Force
We can attempt to understand the dynamic events such as this one by examining the stress balance in the neighborhood of the observed transition, both on this orbit and on subsequent passes. Extensive examination of the Voyager plasma and field stresses have been undertaken, notably by McNutt ; Mauk and Krimigis  and Paranicas et al. . These studies revealed much about the nature of the stress in the magnetosphere but, because the Voyager 1 and 2 spacecraft moved through the magnetosphere very rapidly compared to the Galileo spacecraft whose observations are reported here, they revealed little about the dynamics of the magnetosphere.
Acting in the radially outward direction are the centrifugal force, and magnetic and particle pressure forces. Acting in the radial inward direction are gravity and the magnetic curvature force. The gravitational force is negligible beyond a few RJ compared with the other forces. We can determine the magnetic or JxB force from the magnetic field measurements with a very simple model of the current sheet. We measure the azimuthal current from the change in the radial magnetic field (Br) across the current sheet shown in Figure 3. The current is then multiplied by the magnetic field component normal to the current sheet in the upper panel. This product gives the integrated inward force on the plasma due to the curvature and pressure in Newtons per meter along the circumference of the current sheet.
|Figure 3. The magnetic field component normal to the current sheet measured at each of the crossings (top and third panels) and the change in the radial component of the magnetic field across the current sheet (second and bottom panels) for each of the first four orbits of Galileo. The change in the radial field is a measure of the azimuthal current flowing in the magnetodisk. Points are plotted at the times of the current sheet crossings. Smooth curves drawn are not numerically fitted to the data.|
Figure 4 shows this magnetic force as a function of radial distance for each of the first four Galileo orbits. The measurements shown in Figures 1 and 2 correspond to the thick solid line of the Ganymede 1 (G1) pass. Measurements from other passes, Ganymede 2 (G2), Callisto 3 (C3), and Europa 4 (E4), are shown in contrasting line styles. The C3 pass has a completely smooth radial gradient in this region. The other passes all have transitions in the magnetic force at the inner edge of the current sheet, with the G1 transition being the largest. Thus it appears that the force needed to contain the outward expansion of the magnetodisk is highly variable, but the magnetic force by itself does not indicate which of the outward forces leads to this variability.
|Figure 4. The magnetic force (JxB) as a function of radial distance for the first four inbound passes of the Galileo spacecraft through the inner magnetodisk and quasi-dipolar middle magnetosphere.|
Using Pressure Estimates to Determine an Approximate Radial Mass Density Profile
The local stress balance in a magnetized plasma can be considered by examining the momentum equation:
(dV/dt) + P = j x B (1)
together with the two Maxwell's equations
·B = 0 (3)
In cylindrical coordinates with the assumption of isotropic pressure and azimuthal flow the momentum equation for a thin rotating current sheet can be rewritten (cf Vasyliunas, 1983)
- 2r + (P/r)z = (jxB) ·r (5)
where the subscripts r and z indicate which parameters are kept constant in the partial derivative. The coordinates r, , z form a right-handed system with r radially outward and z northward. Equation (4) governs the pressure balance along the normal to the current sheet while (5) governs the radial component. The right-hand side of (5) can be rewritten as:
(jxB) xr = [- (B2/2µ0 ) + (Bx )B/µ0 ] ·r
= - (B2/2µ0 )/r + (Br2/2µ0 )/ r + (B /µ0r)( Br/ )
+ (Bz/µ0 )( Br/ z) - B 2/(µ0r) (6)
Substituting in (5) and rearranging terms we obtain
2r = ( P/ r) + (Bz2/2µ0 )/ r + (B 2/2µ0 )/ r - (B /µ0r)( Br/ )
-(Bz/µ0 )( Br/ z) + B 2/(µ0r) (7)
In the jovian current sheet the left-hand term is an outward force. The first term on the right represents an outward force, since P decreases with increasing r, as does the second term because Bz decreases with r. The third term is small because B passes through zero in the current sheet and because the angle of the field to the radial direction increases with radial distance as the field is weakening, thus weakening the radial variation in B . The fourth term is zero if, as we assume, there is azimuthal symmetry. The fifth term is the curvature stress. It is an inward-directed force in the quiet time current when the magnetic field is southward and the radial component increases from a negative value below the sheet (inward) to a positive value above the sheet (outward). The last term is associated with the curved coordinate system and is negligible in the magnetodisk where Bf is small and r large. We also note that we have ignored inertial terms in the momentum equation because the steady-state radial flows should be much smaller here than the azimuthal flow.
We can use the stress balance equation to derive an approximate radial mass density profile with some further simplifying assumptions. Since the magnetic pressure in the lobes above and below the current sheet is in equilibrium with the pressure within the current sheet and since the plasma pressure in the lobes is very close to zero, we can use the radial variation in lobe magnetic pressure to estimate the radial gradient in the pressure in the current sheet. Since we will be using the integrated pressure or outward force across the current sheet and since the magnetic field in the field-reversing current sheet contributes some of that pressure (from nearly zero in the center to all at the edges), we assume for the purposes of this calculation that the pressure is equally distributed between particles and the field in the sheet. Since the magnetic force terms are all on the right-hand side of this equation we need not calculate them separately. Rather we estimate the JxB force that includes both the pressure and curvature forces. We estimate the centrifugal force and pressure forces by assuming that the current and plasma density and particle pressure are constant across the current sheet, that azimuthal variations are unimportant in this calculation and that the plasma rotates at a uniform rate around Jupiter. We can then integrate across the sheet and express the mass-per-unit radial distance in a ring around Jupiter as a function of radial distance in SI units.
where Br is the change in the radial component of the magnetic field from the northern to the southern lobe and T is the thickness of the current sheet measured as it swings back and forth due to the rotation of the planet. The change in Br is measured by subtracting the radial magnetic field observed well below the current sheet from that well above the current sheet. The BZ values are determined at the current sheet crossings and the radial gradients in these quantities are obtained by successive measurements at and between the current sheet crossings. The two terms on the right-hand side correspond to the magnetic force of the magnetic field, typically pulling inward; and our approximation to the plasma pressure force pushing outward. The factor 0.5 arises from our approximation that the magnetic field and plasma are equal contributors to the pressure inside the sheet. With the mass of the ring of plasma surrounding Jupiter expressed in metric tons per Jovian radius, the magnetic field in nanoTeslas, and the angular velocity that of Jupiter the constant of proportionality is 11.64. The result of this exercise is shown in Figure 5 for each of our four inbound passes. If the plasma is moving around Jupiter with a velocity that is less than the co-rotational velocity, the inferred density will be larger by a corresponding factor.
|Figure 5. The inferred mass-per-unit radial distance of the Jovian magnetodisk according to a simple model for the first four inbound passes, all in the midmorning sector of the Jovian magnetosphere.|
The estimated mass density of the magnetodisk is variable, but perhaps less so than the magnetic force. Part of this variability may be due to the approximations we have made. In any event these profiles provide a first order estimate of the radial fall off of the mass of the current disk that is very instructive, varying from about 4x104 tons/RJ at 18RJ to about 1000 tons/RJ at 30 RJ. This latter value appears to be the noise level of this analysis.
From the 1 ton/second that Io is thought to introduce into the inner Jovian magnetosphere [Hill et al., 1983] we can use this radial gradient in mass to estimate the outward velocity of the mass if it is in steady state. The resulting velocity estimates range from 1.8 km/sec at 18 RJ to 70 km/sec at 30 RJ. We recall that these values would be lower if the massloading rate at Io were less than the canonical ton/s we have used. The values would be higher if the rotation rate is less than that of co-rotation. Within these uncertainties this estimate is very consistent with the values of velocity (~50 km/sec) obtained by Kane et al.  using the Voyager low-energy charged particle [LECP] data from 30-60 RJ. These transport velocities in turn indicate that the middle magnetosphere should respond sluggishly to variations in the rate of mass added to the Io torus, perhaps requiring weeks to months to reach the magnetodisk. However, once in the magnetodisk region the mass should move outward to the edge of the magnetodisk in at most a few rotations of the planet. We can also estimate the number density of ions in the magnetodisk. Assuming that the average ion has atomic mass 20, as would ensue if iogenic sulfur dioxide were completely dissociated into its constituent atomic ions and that the thickness of the current sheet is 3 RJ consistent with our observations at a radial distance of 30 RJ, we obtain a density of 0.1 cm-3. This value lies in the middle of the range of densities determined from the Voyager plasma wave spectrum by Barbosa et al.  but is an order of magnitude greater than the density deduced from the LECP instrument on Voyager from data at energies above 28 keV. At our inferred density an ion temperature of about 20 keV would be required to provide the pressure needed to balance the magnetic field in the lobes above and below the current sheet. We do not expect the Jovian plasma to have a simple Maxwellian distribution in energy. In fact the Voyager plasma science experiment indicated that within 40 RJ the bulk of the plasma has energies below 6 keV with a contribution to the pressure by a smaller number of energetic ions [Bridge et al., 1979; Belcher et al., 1980].
Discussion and Conclusions
We appreciate that in this examination of the stresses in the magnetodisk current sheet we have made many approximations such as isotropic pressure, negligible radial outflow, and a particular balance of pressure between particles and fields in the current sheet. Nevertheless, we believe the results of our calculations are instructive as to the physics of the magnetodisk region.
We note some similarities to the terrestrial substorm process in which energy is stored in the Earth’s magnetotail during a growth phase and then suddenly released into the night magnetosphere producing aurora. In Jupiter’s middle magnetosphere the equivalent of the growth phase could be an increase in the mass of the inner magnetosphere that eventually leads to an imbalance of pressure that cannot be contained by the magnetic field. However, Figure 5 suggests that the radial density profile has long-term stability within about a factor of two. Instead the relative importance of the magnetic force and pressure gradient force varies from pass to pass. Nevertheless the mass density on the G2 pass does appear to be significantly less than on the other three passes. Clearly we need to examine more cases to establish the average behavior.
Even though we agree with the electron densities obtained by Barbosa et al. , we most certainly disagree with their estimate of when the centrifugal force becomes important. Barbosa et al.  assumed that the pressure-producing particles were solely protons in contrast to the present understanding of the particle composition. Barbosa  has relaxed that assumption in more recent work. Modern reductions of the LECP data indicate sulfur dominates at least at >30 RJ and above 28 keV in energy [Kane et al., 1995]. If we redo the calculation of Barbosa et al.  using an ion mass of 20 and not 1 amu, we do in fact obtain the conclusion that centrifugal force is important inside 30 RJ. On days in which the density is higher than usual it could easily be important in as close as 25 RJ where the sudden drop in inferred density often occurs. This inference is in accord with the conclusions of McNutt et al.  who found that the <6 keV ions provided the inertia of the plasma everywhere inside of 40 RJ.
These observations also suggest that the average energy of the plasma in the Jovian magnetodisk is intermittent. Perhaps this intermittence is associated with the dynamic injections of energetic particles observed near 11 RJ [Mauk et al., 1997]. However, these latter events appear to be localized in nature, whereas the events reported here appear to affect the entire current sheet for at least several days. Dynamic events have also been reported in the outer magnetosphere [Krupp et al., 1998; Russell et al., 1998]. Again these events appear to have limited angular extent. It is possible that the variability that is seen in the magnetodisk may in fact trigger these events in the outer magnetosphere. Furthermore, these events appear to be associated with reconnection across the current sheet. At the inner edge of the current sheet we neither expect nor observe evidence for such reconnection of magnetic field lines across the current sheet. Finally, we note that since such disruptions take place deep in the co-rotating plasma, they most naturally rotate with the plasma and should be independent of the geometry of the solar wind interaction. Such co-rotating features in the aurora have been observed [Ballester et al., 1996; Prangé et al., 1992].
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