Magnetic Fluctuations in the Middle Magnetosphere of Jupiter
C. T. Russell,1 X. Blanco-Cano,2 and R. J. Strangeway1
The ions added to magnetic flux tubes in the vicinity of Io must be removed from those field lines in steady state because the magnetic flux threading the jovian core is constant on the time scales of plasma circulation in the jovian magnetosphere. These ions can be removed by scattering so that the particles diffuse in pitch angle and ultimately are lost into the atmosphere or they can survive transport to the near tail region where reconnection forms magnetized islands of zero net magnetic flux that travel down the jovian magnetotail. Which loss process prevails depends on the speed of radial transport of the ions versus the degree of scattering present. The radial transport process seems not to be steady and thus fluctuating field-aligned currents arise that can enhance the scattering. Nevertheless it appears that many of the ions added to the magnetosphere by Io eventually experience loss by reconnection in the tail.
The engine that drives the jovian magnetosphere is massloading at Io. The ions added to the Io torus are accelerated to corotational energies and remain at close to corotational energies throughout the torus and for some distance beyond. The force that maintains corotation despite the outward transport is the Lorentz force maintained by coupling to the ionosphere and atmosphere with a field-aligned current system that closes at high altitude in the equatorial magnetosphere and at low altitudes in the ionosphere. The mass added at Io has been observed directly [Frank et al., 1996; Bagenal, 1997] and indirectly through the ion cyclotron waves generated [Huddleston et al., 1998]. The transport rate outwards has been estimated from the Galileo data using the radial density profile in the torus and assuming it is in steady-state equilibrium with the massloading rate, by observing the displaced wake of Europa and by assuming centrifugal force balance in the magnetodisk [Russell et al., 1999a]. In the torus the radial flow velocity is very low, only m s-1 in the inner torus rising to about 1 km s-1 at 15 RJ and reaching about 50 km s-1 near 40 RJ.
In the near tail region sporadic reconnection is observed [Russell et al., 1998] dumping the ions into the magnetotail and forming nearly empty magnetic flux tubes that then return to the inner magnetosphere to reenter the outward flux transport again, once they receive a new load of ions at Io [Russell et al., 2000a].
This substorm-like process would not be necessary if the magnetosphere could empty the magnetic flux tubes of the heavy ions by pitch angle diffusion into the loss cone at a rate sufficiently fast that the ions were lost before the flux tube reached the tail. In fact if the ions were lost this way then the centrifugal force that drives the radial convection would be weakened and the circulation process would stop. It is of some interest therefore to determine how fast ions can be lost from the flux tubes as they transport outward and we examine the amplitude of waves capable of causing this scattering in this paper.
Ring Current Impoundment Paradigm
The Voyager observations of the Io torus density profile shown in Figure 1 led to a paradigm for plasma transport in terms of centrifugally-driven flux tube diffusion within the torus [Siscoe and Summers, 1981] and ring current impoundment on the outer edge of the torus [Siscoe et al., 1981]. The ledge region is where the number of ions per unit magnetic flux integrated over a flux tube changes only slowly with radial distance. The slow drop density with radius is assumed to drive the diffusion. It is also evidence for loss of particles from the field lines. From 7 to 8 RJ there is a sudden drop in the plasma density. To explain this sharp discontinuity Siscoe et al.  suggested that the hot plasma had an oppositely directed pressure gradient that balanced the outward centrifugal force of the torus at this point. If this were true there must be a mechanism for remaining ions within the torus and the ramp to maintain steady-state as Io is continually pumping ions into the torus at its inner edge. Further if the torus is impounded by the ring current, its radial motion should stop at the ramp. This will aid in the loss of plasma at this point because flux tubes have longer to be emptied here.
|Figure 1. Radial profile of total flux tube content from Bagenal  compared to profile of Siscoe et al. . A radial profile with a power law exponent of 2 is shown for comparison. After Bagenal .|
As noted above the substorm process seen in the tail and the wake of Europa at closer radial distances all suggest that the ramp is not a barrier to the flow and that flow goes from Io, even more quickly, outward. In this scenario one expects the ramp region to have enhanced loss processes because particles are being lost quickly in this region. Thus it is of some interest to focus our attention on the ramp region if we want to understand how particles are lost in the jovian system.
The Outer Torus/Ramp
The outer torus was crossed twice by Galileo when high resolution data were being obtained on the J0 pass and on the C23 pass. The data on the I0 pass are shown in Figure 2 with the background field removed. The magnetic field is very active here with many step functions. The turbulence is nearly isotropic at low frequencies with transverse fluctuation having similar amplitudes to the compressional component. Figure 3 shows the corresponding data on pass C23. The waveforms appear quite similar to those on J0 but the turbulence is about a factor of 2 smaller in amplitude.
|Figure 2. Magnetic field fluctuations at the location of the ramp on the J0 pass on December 7, 1995. The data is displayed in corotational coordinates.|
|Figure 3. Magnetic field fluctuations at the location of the ramp on the C23 pass on September 14, 1999.|
|Figure 4. Power spectrum of the compressional and transverse fluctuations for the period shown in Figure 3. The spectral estimates shown are averaged over 11 individual Fourier estimates. An arrow marks the S+ gyrofrequency.|
Figure 4 shows a power spectrum of the transverse and compressional components of the fluctuations for the interval shown in Figure 3. The arrow shows the location of the local S+ gyrofrequency. A corresponding spectrum has been published for the J0 pass by Russell et al. .
The power spectral density at the gyrofrequency of S+ ions can be calculated from the wave power by
Where D is given in radians2 s-1 and b2/D f is the power spectrum at the S+ gyrofrequency measured in nT2/Hz [Russell et al., 2000b]. Applying this formula to the spectra corresponding to Figures 2 and 3 gives values of 2.3x10-5 and 8.6 x 10-6 respectively.
Beyond the Ramp
We have data at high resolution beyond the ramp near the radial distance of Europa. Figure 5 shows such a spectrum. The spikes seen are harmonics of the Galileo spin period and should be ignored for our calculation. The arrow shows the S+ gyrofrequency. The corresponding diffusion coefficient here is 2 x 10-7 radians2 s-1 much smaller than in the ramp region.
|Figure 5. Power spectrum of the compressional and transverse fluctuations near the orbit of Europa on November 6, 1997 on pass E11. The spikes seen at 5x10-2 Hz and harmonics are due to the spin of the spacecraft that has not been completely removed here.|
|Figure 6. Sample power spectra in the middle magnetosphere. A bar marks the location of the S+ gyrofrequency [Russell et al., 2000].|
If we move out further in the magnetosphere we have very little coverage at high resolution but we can use lower time resolution data and extrapolate to higher frequencies near the S+ gyrofrequencies. This has been done for the region 10 RJ to 28 RJ by Russell et al. [2000b]. Figure 7 shows these data and our added points in the ramp and near Europa. The three points in the ramp are clearly much higher than anywhere beyond this distance out as far as 18 RJ.
To determine whether loss rate of the scattered cold torus ions is limited by the size of the loss cone we need to determine if the scattering time into the loss cone is comparable to the transport time. To reach the loss cone the pitch angle of a particle must be scattered 1.57 radians. With the diffusion coefficient found in the ramp and plotted in Figure 7 a particle would diffuse into the loss cone in about 1.5 days. Estimating the radial velocity through this region to be about 50 m s-1 [Russell et al., 2000b] and the ramp thickness to be about 0.5 RJ, the transport time through the ramp is about 9 days. Thus we would expect the ions to be in the strong diffusion limit here and the loss cone to be full. Beyond the ramp where the diffusion coefficient is an order of magnitude smaller, we would expect the particles to be in the weak diffusion limit.
|Figure 7. The pitch angle diffusion coefficient for cold S+ ions as a function of radius from the wave power measured by Galileo both on and off the equator. Also shown is the area of loss cone. This histogram gives the medians of the diffusion coefficient in overlapping 4 RJ bins.|
In the strong diffusion limit the loss rate is determined by the size of the loss cone. A particle at the equator and in the loss cone will be lost in one-quarter bounce time. The probability of a particle being in the loss cone is the area of the loss cone in radians2 divided by 2p . At the ramp the size of the loss cone is about 0.0064 sq. radians. Since the quarter bounce time of a torus ion at 8 RJ is about 8000s the decay time of the ions in the strong diffusion limit is about 90 days. Thus we expect some loss of plasma but to cause an effect as large as that shown in Figure 1, the transport time would, through the ramp, have to be somewhat larger than we estimated above by perhaps a factor of 4. We emphasize in closing this discussion that the fluctuations in the ramp are quite large enough to keep the particles’ pitch angle isotropy. The controlling factor on the loss rate is the size of the loss cone and the bounce time. They both vary with radius so the ramp is where loss times are the shortest. In addition the diffusion coefficient is lower than in the ramp from the ramp out to about 16 RJ. This also lessens the loss rate.
Discussion and Conclusions
The inner torus is very quiet except right at Io. The noisiest place in the torus is in the ramp at its outer edge. The signals here are strong enough to place the plasma in the strong diffusion limit and so that its loss is limited by the size of the loss cone. The size of the loss cone is so small even at L=8 RJ that expected lifetimes are greater than the time to transport the plasma radially through the wave region. Thus we expect minimal losses of plasma to the atmosphere through pitch angle scattering. We note that Figure 1 that shows the size of the ramp is drawn from Voyager data and we used Galileo wave amplitudes for our diffusion analysis. It is possible that the transport times through the ramp was somewhat longer for Voyager than for Galileo because the density of the torus was greater in December 1995 than during the Voyager pass [Gurnett et al., 1997]. In short we conclude that pitch angle diffusion occurs in the Io torus and throughout the middle magnetosphere but, while particles are lost, a large number of them appear to survive the scattering process and are ultimately transported into the tail and lost there through reconnection.
This work was supported by the National Aeronautics and Space Administration under research grant NAG5-8064 and through JPL grant 958510.
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