Energetic ion phase space densities in Neptune's magnetosphere

ICARUS

99,

420-429 (1992)

Energetic Ion Phase Space Densities in Neptune’s Magnetosphere ANDREW F. CHENG Applied Physics Laboratory,

The Johns Hopkins University, Laurel, Maryland 20723

C. G. MACLENNAN AT&T Bell Laboratories,

Murray Hill, New Jersey

07974

BARRY H. MAUK AND S. M. KRIMICIS Applied Physics Laboratory,

The Johns Hopkins University, Laurel,

Maryland 20723

AND L. J. LANZEROTTI AT&T Bell Laboratories,

Murray Hill, New Jersey

07974

Received March 16, 1992;revised June 15, 1992

1. INTRODUCTION Ion intensities measured by the Voyager 2 Low Energy Charged Particle (LECP) experiment at Neptune have been analyzed to determine ion phase space densities at fixed values of the first and second adiabatic invariants of charged particle motion. The phase space densities are broadly peaked near L = 10 and generally show a rapid decline going toward Neptune, although there is a gap in data coverage at the Proteus (1989Nl) minimum L-shell. These profiles are interpreted as indicating generally inward radial diffusion with an energetic ion source near L = 10. There is excellent agreement between inbound and outbound phase space density profiles at the same values of the invariants, suggesting quasistationary and roughly axisymmetric radiation belts. If absorption by Neptune’s moons and rings is an important loss process, then the radial diffusion coefficient D, is on the order of lo-’ L3 see-‘, consistent with the Voyager Plasma Science determination for a T&on-associated proton source of lo*’ set-‘. The LECP ion phase space density profiles are consistent with relatively weak L-dependence of DLL, provided that loss rates increase toward the planet; for an extreme case of a loss rate independent of L, DLL = L6.03. Weaker L dependence of DLL is found for a loss rate T- ’ increasing toward the planet (DE = L3 when T- ’ = L -3.63), suggesting interchange diffusion. With DLL = 6 x lo-* L3 set-‘, the inward diffusing power carried by energetic ions is estimated as 2 X lo9 W, which would be adequate to power Neptune’s aurora if a substantial portion of the ions is lost into Neptune’s atmosphere. o 1992Academic Pws, Inc.

Presented at NeptunefTriton January 6-10, 1992.

Conference

0019-1035192 $5.00 Copyright 0 1992 by Academic Press, Inc. All rights of reproduction in any form reserved.

in Tucson,

Arizona,

during

420

The Voyager 2 spacecraft made the first in situ observations of Neptune’s magnetosphere in August 1989. The Voyager 2 Low Energy Charged Particle (LECP) experiment measured ions above 28 keV and electrons above 22 keV, with ion composition measurements above 0.6 MeV per nucleon. Initial LECP observations were given by Krimigis et al. (1989), and a more detailed overview of the encounter including the special instrument modes and the spacecraft orientation and trajectory was presented by Mauk et al. (1991). Energetic ions and electrons were observed by LECP primarily within the orbit of Triton, suggesting the importance of Triton interaction for the magnetosphere (Krimigis et al. 1989). Nevertheless, no heavy ions were detected above 0.6 MeV per nucleon, although evidence for an approximately corotating, heavy-ion population was found in energetic ion anisotropies outside the orbit of Triton (Mauk et al. 1991). A cold plasma density as high as 1.4 cmm3 was detected by the Voyager Plasma Science (PLS) experiment, and a heavy-ion component was identified, probably N+ from a Triton torus (Belcher et al. 1989). Neptune’s magnetic field can be approximated by offset, tilted dipole models, where the dipole moment is tilted by a large angle to the rotation axis and the dipole center is offset more than half a planetary radius from the planet center (Ness et al. 1989). Weak ultraviolet aurora1 emissions were observed over large areas of Neptune’s surface, including regions far from the magnetic poles

NEPTUNE

ION-PHASE

(Broadfoot et al. 1989). These aurora1 emissions may be explained, at least in part, by particle precipitation into the global-scale magnetic anomaly (weak-field region at the top of the atmosphere) created by Neptune’s dipole offset (Cheng 1990b). This anomaly precipitation also produces a loss signature, or “atmospheric drift shadow,” observed as a sharp dropout of energetic particles during the low-altitude pass of Voyager 2 near Neptune’s rotational pole (Stone et al. 1989, Krimigis et al. 1989, Cheng 1990b, Selesnick and Stone 1991~). The initial Voyager results on Neptune’s magnetosphere raise important issues regarding sources, losses, and radial transport of energetic particles and plasma. These issues bear on the importance of Triton as a source of magnetospheric plasma and on mechanisms for powering Neptune’s aurora. In the following, we address these issues by analyzing Voyager LECP ion data to calculate phase space densities at fixed first and second adiabatic invariants. Phase space density analysis (e.g., Schulz and Lanzerotti 1974; see also Section 2) has been used to study plasma sources, losses, and transport in the magnetospheres of Earth, Jupiter, Saturn, and Uranus. Voyager LECP data have previously been used to determine ion and electron phase space densities at Jupiter (Armstrong et al. 1981; Cheng et al. 1983, Paonessa 1985), Saturn (Armstrong et al. 1983, Paonessa and Cheng 1986), and Uranus (Cheng et al. 1987). Near a first invariant of 100 MeV/G, ion phase space densities in the magnetospheres of Earth, Jupiter, Saturn, and Uranus are very similar (Cheng et al. 1985, 1987). At all four planets, phase space densities show a rapid, approximately exponential decline going toward the planet, indicating inward radial transport from a source at large radii, as well as losses in the inner magnetosphere. At Jupiter, phase space density analyses have shown that energetic ions are lost at nearly the strong diffusion rate, and that inward radial diffusion of energetic ions and their precipitation may suffice to power Jupiter’s UV aurora if trapped intensities are sufficiently high (Gehrels and Stone 1983, Thorne 1982, Cheng et al. 1983, Cheng 1986). At Saturn, phase space density analyses have established losses in the Dione-Tethys-Rhea region, but the relative importance of wave-induced precipitation and satellite sweeping (absorption by solid bodies such as moons and ring particles) remains unclear (Paonessa and Cheng 1986, Hood 1985). At Uranus, low-energy proton and electron profiles, 5100 MeVIG, show evidence for absorption at the minimum L values of Ariel, and highenergy proton profiles, ~200 MeV/G, show evidence for injection events, suggesting substorms at Uranus. Highenergy electron profiles show evidence for distributed sources of energetic electrons as well as absorption occurring near the minimum L values of Miranda and Ariel

SPACE DENSITIES

421

[Cheng et al. 1987, 1990, Hood 1989, Selesnick and Stone 1991a]. This paper presents and analyzes ion phase space densities determined from Voyager 2 LECP data at Neptune. Electron phase space density analysis will be deferred to a later study. The offset, tilted dipole model OTD2 (N. F. Ness, private communication) is adopted as an adequate approximation to the magnetic field for the phase space density analysis. The region where the field model is approximately valid excludes the high-latitude polar pass very close to Neptune, but otherwise extends out to beyond the orbit of Triton since plasma stresses do not significantly distort Neptune’s magnetic field (Krimigis et al. 1989). The OTD2 model is characterized by a dipole moment of 0.13 CR&, a tilt angle of 45”, and an offset of 0.55R, (N. F. Ness, private communication; Mauk et al. 1991). The ion phase space density analysis in this paper assumes a proton composition consistent with LECP composition measurements above 0.6 MeV per nucleon energy. However, there are indications of a heavy-ion composition in the outbound LECP data beyond the orbit of Triton, from anisotropy analysis (Mauk et al. 1991), and heavy ions were detected in the cold plasma (Belcher et al. 1989). Presence of a heavy-ion component affects the absolute normalization of the phase space density (e.g., Cheng et al. 1985, Section 2), but does not change the shape of a phase space density profile (the form of its radial dependence) if the abundance ratios are constant. Hence, even if heavies are present, the inferred diffusion rates are unaffected if the proton/heavy ratio is fixed. 2. OUTLINE OF METHOD Energetic particle sources, losses, and radial transport in planetary magnetospheres can be studied by the technique of phase space density analysis. This technique uses measurements of charged particle intensities (particles cm-’ set-’ sr- ’ keV- ‘) to calculate phase space densities at fixed values of the first and second adiabatic invariants (defined below). When the electromagnetic fields are sufficiently slowly varying that the first and second adiabatic invariants are conserved, the guiding center drifts have the property that the total magnetic flux through an ensemble of guiding centers is conserved, when all members of the ensemble have the same first invariant and second invariant (Roederer 1970). Hence the phase space density, which is just the number of particles per unit magnetic flux in a flux tube for fixed first and second invariants, is also conserved unless injection, loss, or scattering occurs. Calculation of phase space density is therefore a useful technique for identifying where particles are injected, where they are lost, and how they are transported. The first adiabatic invariant M is defined by

422

CHENG ET AL.

M = p2/2mB,,

(1)

where p is momentum, m is the rest mass, and B, is the mirror point magnetic field. The second invariant K is K=

‘*(B, - B)“’ ds, I$1

(2)

where s is the arc length along the guiding center field line and s, and s2 are mirror points. This K is independent of particle energy. The third invariant is 4 = 2rrB,R;L-’

(3)

in the offset, tilted dipole 0TD2 magnetic field model, where B, = 0.13 G for Neptune (Ness et al. 1989, Ness, private communication) and L is the distance in units of R, from the dipole center to the field line at the magnetic equator. When the third invariant is violated by stochastic electromagnetic disturbances such as electric or magnetic impulses or flux tube interchanges, the particle transport can be described by radial diffusion (e.g., Schulz and Lanzerotti 1974). When in addition there is particle loss, injection, or scattering, the phase space density can be described by the lossy radial diffusion equation

(4) which includes a phenomenological net loss termf/T (the excess of losses over sources). Heref(M, K, (D)is defined as the number of particles within dM dK da, andfcan be determined from the experimentally measured intensityj (particles cmd2 see-’ sr-’ keV_‘) by f = 4,rrj(2m3M)“2/(p2).

(5)

Since M is constant for each profile, the quantityj/(p2) is proportional tofand is basicallyfexpressed in new units. We simply refer to it as “phase space density.” The present result (5) corrects the Eq. (5) given by Cheng et al. (1987). Equation (A5) of that paper should also have an additional factor of y = p/mu in the denominator. The relativistic corrections have no practical effect on ion phase space densities. However, the electron phase space densities of Cheng et al. (1987) should be multiplied by y, which is typically less than 3. This correction would not change any of the earlier conclusions. The development thus far applies to a single-ion species (e.g., protons). If a mixture of ions is present, f should in principle be determined separately for each species. In what follows, Eq. (5) is evaluated using values for proton mass and proton energy in each channel, since the compo-

sition is in fact proton-dominated at higher energies. However, the total ion intensity j is used in (5) rather than the proton intensity jp. Hence phase space density as calculated here differs from proton phase space density by a factor j,,/j or proton abundance. If the ratio j,/j is a constant, it cancels out of the radial diffusion equation (4) and is immaterial. However, if j,/j is a variable, then a systematic error is introduced in the phase space density analysis. In the following, as in previous Voyager phase space density analyses, composition data are not available and jr/j is assumed constant. 2.1. Coverage of Invariant Space Calculation of phase density specifically requires determination of j at the particular energy and pitch angle corresponding to the desired invariants M and K at the spacecraft location. This j is determined by interpolation within the measured pitch angle distributions and energy spectra, using the method described by Cheng et al. (1987). At Neptune, LECP obtained complete angular scans (within seven 45” sectors, with the eighth blocked by a metal shield) at 6-min intervals. A detailed description of the Neptune trajectory, instrument orientation, and operating modes was given by Mauk et al. (1991). In each scan the energy spectra and angular distribution are measured within 48 sec. These scan data allow computation of phase space densities at 6-min intervals. The Voyager encounter geometry relative to Neptune’s magnetic dipole and the range of pitch angles and energies measured by LECP determine the values of M and K that were sampled. At any L, there is a minimum K that can be observed, corresponding to particles mirroring at the spacecraft latitude; particles with smaller K never reach the spacecraft. There is also a maximum K corresponding to the smallest local pitch angle, or highest mirror latitude, sampled at any L. Likewise there is a minimum and a maximum M observed at any L corresponding to the measured energy range. For radial diffusion studies using Eq. (4), it is desirable to have large ranges of L where a fixed K can be sampled. Moreover, it is interesting to compare inbound and outbound measurements at the same M, K, and L. On the outbound pass, values of 0.3 I K 5 0.8 G’12RN were sampled from L = 2 to L = 9, and progressively lower values of K were measured as L increased from L = 6 to L = 13. The range of K values 0.02 5 K I 0.05 G”‘RN was sampled both inbound and outbound in the range 9 5 L 5 11. Also K in the range 0.1 5 K 5 0.8 G’j2R, was sampled near L - 8 to 9 both inbound and outbound. The range of M values sampled extended from a minimum of 2 MeViG for L 5 4 up to a maximum of 500 MeVlG for L 2 8. In the following, phase space densities are analyzed mainly for the invariant ranges mentioned above.

NEPTUNE 104

1

INi

I

I

I

I

1

! 1

1

I

I

I

I

6

6

10

12

14

16

18

10-a10-4 0

2

4

I

II

TRITON

I

ION-PHASE I

20

l-8 HN FIG. 1. Ion phase space densities at fixed values of first invariant M and second invariant K. Several profiles are shown for M values ranging from M = 2 MeV/G to M = 500MeV/G, all at K = 0.8 G”*&.,. The minimum L values for Proteus (1989Nl) and for Triton are indicated at the top. Curves are drawn to guide the eye across the gap in coverage from L = 4 to L = 7.

During the low-altitude polar pass near closest approach, extremely large K > 1 G1’2R, was sampled over a large (but highly uncertain) range in L. These data are not analyzed by the present method owing to the known inaccuracies of the offset, tilted dipole field models in this region (Ness et al. 1989, Connerney et al. 1991). Finally, during both the inbound and the outbound ring plane crossings at Neptune, the Voyager LECP detectors were fixed in sector seven so as to avoid the possibility of damage from ring particle impacts. As no scan data were obtained during these periods, phase space densities were not calculated. The inbound ring plane crossing occurred at a very high K value for which the OTD2 field model is inapplicable anyhow, as mentioned above. However, the outbound ring plane crossing occurred at moderate K and includes the minimum L-shell crossing of Proteus (1989Nl), where an apparent absorption signature is observed (Krimigis et al. 1989, Mauk et al. 1991). Further analysis of this feature is deferred to subsequent work. 3. ION PHASE SPACE DENSITY

423

SPACE DENSITIES

and shifting to smaller L for higher M > 200 MeV/G. The generally positive radial gradient in the inner magnetosphere is extreme, yielding a five order of magnitude drop between L = 3.5 and L = 8 at M = 20 MeV/G. Also evident in Fig. 1 is the gap in coverage between L = 4 and L = 7, corresponding to the outbound ring plane crossing where no scan data were obtained. Since an apparent absorption signature is found in the intensities near L = 5 corresponding to the Proteus (Nl) minimum-L values (Mauk et al. 1991), a local minimum or an inflection point would be expected in the phase space densities there. If present, this feature would lie within the gap in coverage shown in Fig. 1. Outside this gap, there is a generally positive radial gradient out to L - 10. Such a radial gradient in f is also found in the inner magnetospheres of Earth, Jupiter, Saturn, and Uranus (Cheng et al. 1985, 1987, 1990). In all cases, the steep decline infis interpreted as indicating inward radial transport with rapid losses occurring mainly in a region of relatively high plasma density and plasma-wave activity, suggesting the importance of wave-particle interactions. For Uranus, Hood (1989) has suggested that losses are dominated by satellite absorption for some particle parameters. The ion phase space densities in the inner magnetospheres of these planets are quantitatively similar when given in absolute units, and not just similar in form (Cheng et al. 1985). To emphasize this quantitative similarity, Fig. 2 compares Neptune and Uranus ion phase space densities given in the same absolute units at a fixed M = 100 MeV/G and two fixed values of K in planetary units (K = 0.05 G1’2R and K = 0.3 G1’2R, with R the respective planet’s radius). 104

,

1

I

r’”

K = 0.05 .A-+--

.>~

PROFILES

Figures l-4 show ion phase space densities calculated from Voyager LECP data in Neptune’s magnetosphere. These profiles consistently indicate generally positive radial gradients within L I 10, with a broad maximum in phase space density near L = 10, as can be seen in Fig. 1, The precise location and width of this maximum appear to vary systematically with particle energy, being typically broader at lower M (corresponding to lower energy)

10-I 1 4

I

I 6

I 8

I 10 L

1 12

14

RN

FIG. 2. Comparison of Uranus phase space density profiles (U, points connected with lines) and Neptune profiles (N) at the same M = 100 MeV/G and at two K values, K = 0.05G"*R and K = 0.3 Gu2R, with R the planetary radius.

424

CHENG ET AL.

6

6

10

12

14

16

18

20

L, R, FIG. 3. Same as Fig. I, except that several K values in G”*RN are shown at the same M = 500 MeVIG. One curve is sketched to guide the eye.

Finally, we note that data from both the inbound and outbound passes are shown in Figs. l-4. No attempt is made to distinguish inbound from outbound points in Figs. 1-4, because the inbound and outbound profiles tend to overlie one another within the experimental scatter, especially at low energies, so that use of separate symbols or curves would be too confusing. In general, there is excellent agreement between inbound and outbound profiles at the same values of M, K, and L. This is consistent with radiation belts at Neptune that are essentially time-stationary and axisymmetric. The absence of observed magnetospheric activity at Neptune has been discussed previously by Mauk et al. (1991) and contrasted with the magnetospheric activity observed at Uranus (Mauk et al. 1987, Cheng et al. 1987, Coroniti et al. 1987, Sittler et al. 1987). 4. INTERPRETATION AND ANALYSIS

The generally positive radial gradients inf for L 5 10 and the rapid declines in f going toward the planet are consistent with lossy, inward radial diffusion, where losses increasingly overwhelm radial transport within the inner magnetosphere; that is, T-’ % D,, for small L. Farther from the planet, the diffusion coefficients D,, increase and losses may be expected to decrease, so eventually inward transport and losses begin to balance, &T 1, and the f profiles level off. Calculated loss rates T-’ from satellite and ring absorption do tend to decrease at sufficiently large L (e.g., Paranicas and Cheng 1991a and 1991b). If an attempt is made to model thefprofiles with lossfree radial diffusion (7-i = O), then the inferred D,, will show a rapid, exponential rise toward the planet. This

However, Fig. 2 also shows that the Neptune K = 0.3 G”*R profile displays a broad maximum near L = 10, whereas the Uranus profile at the same M, K, and L does not. Figure 3 shows several Neptune profiles at different values of K but at the same value of M = 500 MeV/G, contrasting with Fig. 1, which showed a wide range of A4 values at a fixed value of K. The shift in the width and location of the phase space density peak near L = 10 can be seen clearly in Fig. 3 as K increases. This is essentially the same effect as that noted in Fig. 1 and appears to be primarily due to energy dependence (as K of a particle increases at fixed L and M, its energy must increase). The profiles in Figs. 1 and 3 also extend across the Triton 104 I minimum L values, L - 14. There are suggestions of a I I phase space density minimum at the lower energies (K 5 0.15 G”*R at M = 500 MeVlG and A4 I 50 MeV/G at 0.8 ______ K = 0.8 G”*Z?) but not at higher energies. It is cautioned 1 that beyond L 2 14 the OTD2 field model becomes increasingly inaccurate (Connerney et al. 1991) and that there are suggestions of heavy-ion plasma in that region (Mauk et al. 1991). Figure 4 shows a selection of profiles from the innermost region L I 4. It is in this region that losses due to interactions with Neptune’s rings (Paranicas and Cheng 1991a) and atmosphere (Cheng 1990a, 1990b) are expected to become most important. The profiles show drastic declines in phase space density going toward the planet. The data in Fig. 4 were obtained on the outbound pass after 1.5 2.0 2.5 3.0 3.5 4.0 hour 0420 on Day 237. In this region, the 0TD2 field model L RN agrees fairly well with the more accurate multipole field models (Connerney et al. 1991). FIG. 4. Same as Fig. 3, showing several K values for M = 2 MeV/G.

lo.22

NEPTUNE

ION-PHASE

behavior was also found at Saturn (Armstrong et al. 1983) and Uranus (Cheng et al. 1987) and is physically implausible, All known radial diffusion mechanisms (e.g., Schulz and Lanzerotti 1974, Hood 1989) predict that D,, should increase rapidly going away from the planet. If DLL is constrained to rise going away from the planet, then the profiles in Figs. l-4 imply lossy inward radial diffusion, T-’ > 0, within L = 10. The phase space density peak near L = 10 is interpreted as indicating a local source of energetic ions. While a peak in the observed profiles can in principle be caused by effects of time dependence and/or longitudinal variation, the observed agreement between inbound and outbound profiles and the absence of evidence for magnetospheric activity argue in favor of a quasi-steady-state, axisymmetric magnetosphere. In that case, the phase space density peak implies a local source driving inward radial transport within L = 10 and outward radial transport outside that radius. However, the fundamental mechanism responsible for this source is unknown. 4.1. Convective Electric Fields Two distinct models of plasma convection in Neptune’s magnetosphere have been proposed, predicting inflows and outflows of plasma within particular longitude sectors. Hill and Dessler (1990) predicted a quadrupolar convection pattern based on a model of mass loading in the Triton torus. In their model outflows were predicted in two longitude sectors, namely within 140”-210” W and within 310”-25” W, and inflows were predicted in the complementary sectors. Selesnick (1990) predicted a different model based on a solar wind-driven convection system, in which case outflow was expected within the hemisphere centered on 76” W (346”-166” W), and inflow was expected in the opposite hemisphere. Richardson et al. (1991) have already pointed out that the PLS phase space density profiles did not support the predictions of either model. They inferred inward radial transport of plasma within L = 10 from both inbound and outbound PLS data, inconsistent with the predicted outflow sectors of either the Hill and Dessler (1990) model or the Selesnick (1990) model. However, at LECP energies the ions are trapped on drift shells, and convective electric fields of the magnitude suggested by Selesnick (1990), up to 0.01 mV/m, do not lead to transport on open drift trajectories. Instead, such convective electric fields induce distortions in the drift shells that may be observable as longitudinal asymmetries. The dominant form of radial transport at LECP energies can be radial diffusion even with convective transport dominant for the cold plasma. The magnitude of the energetic particle drift shell distortion can be roughly estimated as follows for equatorially mirroring particles. The distorted drift shell is deter-

425

SPACE DENSITIES

mined by an equation of the form MB,Lw3 + e@ = constant, where B, = 0.13 G, @ is the electrostatic potential, and M is the constant first invariant. This expression assumes a steady state in the corotating frame and is valid for the Hill and Dessler model but not the Selesnick model in which @ is time dependent. However, this expression still yields an estimate of the drift shell distortion if the energy change is small during a drift period. If @ is supposed to vary by up to 4 keV around a dipole drift shell at L = 8, then the effect of the convective potential for a 30-keV particle is to distort the drift shell by up to AL = 0.36. The Hill and Dessler (1990) model predicts convective fields typically greater than that for the Selesnick (1990) model. It is unclear whether these drift shell distortions would produce observable inbound-outbound asymmetry in the LECP phase space density profiles. No such asymmetry is evident, so the LECP data do not support the convection models but do not rule them out either. Stronger evidence against the convection models is provided by the PLS results (Richardson et al. 1991) that suggest inward radial diffusion of cold plasma. 4.2. Estimates

of Radial Diffusion Coejjicient

The radial diffusion equation (4) provides a relation between the particle net loss rate 7-l and the radial transport rate determined by D,, and the phase space density gradient written f’ = df/dL. Both D,, and T-’ are in principle unknown functions related by the single equation (4), but with additional information on 7-l and simplifying assumptions, estimates can be given for the rate of radial diffusion. For example, if a conventional power law dependence is assumed for D,, , such that D,, = D,L” (Schulz and Lanzerotti 1974, Hood 1989), then Eq. (4) in the steady state becomes -= 1

F'

+

F” + (F’)2,

(6)

DLL?

where F = In f and prime means dldL. The derivatives F’ and F” can be determined directly from the phase space density profiles, so Eq. (6) determines the balance between radial transport and losses as parameterized by DLL7. If DLL7 B 1, transport dominates, but if DLL7 4 1, losses dominate. Table I shows the results of such an analysis of the M = 2 MeV/G, K = 0.8 G”2R, profile. Two cases are considered in Table I. The first is IZ = 3, characteristic of the relatively weak L dependences for D,, expected for flux tube interchange driven radial diffusion. There are two types of radial diffusion driven by flux tube interchange motions; the first is driven by neutral winds in the upper atmosphere of the planet and the second is driven

426

CHENG ET AL. TABLE

sis of Voyager PLS data. Arguments given below favor the n = 3 case (interchange diffusion) for Neptune.

I

Analysis of M = 2 MeV/G, K = 0.8 G*‘2R, L

hn (“I

(I%,

(n = 3)

(n = 10)

3.7 1.8

42.9 38.8

51.5 295

2.1 0.0175

0.645 0.0107

DLLT

DLLT

Note. Radial diffusion coefficient DLr. = DOLn.

by centrifugal interchange instability. These types of interchange may differ in their detailed dependence of D,, on L, but both are typically characterized by a weak L dependence (see review by Hood 1989). Jupiter’s magnetosphere may exhibit both types of interchange diffusion, with centrifugal interchange instability operating outside IO’S orbit and wind-driven interchanges dominating well inside it (e.g., Siscoe and Summers 1981). Relatively weak dependence of D,, on L has also been inferred for Saturn and Uranus (e.g., Hood 1985, Paonessa and Cheng 1986, Hood 1989), suggestive of interchange diffusion. The nature of interchange diffusion at Saturn is unclear, but at Uranus, atmospheric wind-driven interchanges most likely dominate owing to the lack of evidence for a negative radial gradient of cold plasma phase space density outside L = 5. A separate class of diffusion processes is shown in the second case given in Table I, for which 12= 10, typical of the steeper L dependence expected for diffusion caused by solar wind-driven impulsive electric or magnetic disturbances (Schulz and Lanzerotti 1974). This second class of radial diffusion appears to predominate at Earth. Table I indicates that for either class of diffusion, DLL7is on the order of unity near L = 3.7 but decreases to values el near L = 1.8. Table I also shows the mirror latitude A, and the kinetic energy KE for protons with the indicated values of the invariants. The results in Table I now lead to quantitative estimates for &,, , g iven estimates of the loss rate T- ‘. If absorption by Neptune’s rings and satellites is the dominant loss mechanism in the inner magnetosphere, then the calculations of Paranicas and Cheng (1991a, 1991b) indicate that 7-i near L = 1.8 is 7-i - 2 x 10m5set-‘. With this loss rate and the value of DLL7 from Table I, DLL is estimated to be D LL = 6 x 1O-8 L3 set-’

4.3. Lossy Radial Diffusion Models Additional information on the functional form of DLL and quantitative constraints on n can be obtained by fitting numerical solutions of Eq. (4) with a/at = 0 to the M = 2 MeV/G, K = 0.8 G”*R, profile analyzed above. Figure 5 shows two different numerical solutions to the lossy radial diffusion equation, one solution for II = 3 and one solution for n = 6.03, both assuming (different) power law forms for 7-i. It can be seen that both solutions fit the phase space density profile typically to within a factor of 2, less than the probable systematic error as judged from the scatter of the points (see Fig. 1). The statistical errors are completely negligible. Figure 5 leads to the following constraint on the value of n and therefore on the nature of the radial diffusion. Specifically, Eq. (6) and Table I show that DLL7 increase rapidly with L, with the rate of increase determined by the phase space density profile. Moreover, the loss rate T- * is expected to be largest near the planet, whether due to ring and satellite absorption or plasma wave scattering (Kurth and Gurnett 1991). Charge exchange with hydrogens of a Triton torus can be shown to be negligible provided the H density is less than lo3 cmm3 (Cheng 1990a); greater H densities should have been observed by the Voyager ultraviolet spectrometer.

‘04) 104

I

- - -

MODEL

FIT, DLL = D,L6-03 -

CONSTANT

Z

D,,T = ~xIO-~ ““..“’

MODEL

FIT, DLL = D,L3

z = 7, L3.6 D,z~ = 3.6~10.~

(7)

for the IZ = 3 case. This is regarded as a lower limit because other loss mechanisms may be important in addition to ring and satellite absorption. This value of D,, is in good agreement with that estimated previously by Richardson et al. (1991), DLL = 10e7 L3 set-‘, from analy-

L, RN FIG. 5. Comparison of numerical solutions to lossy radial diffusion equation (two nearly identical curves) with M = 2 MeV/G, K = 0.8 G”2R, profile (points connected with lines). Numerical solutions assume power law forms for D,, and 7 as shown.

NEPTUNEION-PHASE

Hence r should generally increase with L going away from Neptune. However, the rate of increase of DLL7with L is basically fixed by the phase space density profile. Thus an upper limit to the rate of increase of D,, can be obtained for the extreme case of constant 7, one of the solutions shown in Fig. 5. If D,, m L”, then n 5 6.03

(8)

is obtained. Indeed, when n = 3, Fig. 5 shows that 7 = r L3.63with D r = 3.56 x 10e4. Given D,, = 6 x 1O-8 L?’ see- l, this’firm for 7 yields T- ’ = 2 x lo-’ set- ’ at L = 1.8 and 7-l = 1 x 10m6 set-’ at L = 4, generally consistent with calculated values for sweeping by Neptune’s rings (Paranicas and Cheng 1991a). We conclude that D,, in Neptune’s inner magnetosphere has a relatively weak L dependence, consistent with flux tube interchange diffusion. 4.4. Estimate of Power from Inward Radial Diffusion Inward radial diffusion of energetic ions implies an energy flow into the inner magnetosphere. If some of these ions are lost by precipitation into Neptune’s atmosphere, the inward radial diffusion may provide a power source for Neptune’s UV aurora which requires an energy input of -lo9 W (Broadfoot et al. 1989). This power requirement is now compared with the power carried by inward diffusing energetic ions, which is estimated by Pd = 2rrLR;Hu,DLLF’,

(9)

where the thickness along the field lines of the ion distribution is H, the energy density is up, and RND,,F’ is the “diffusion velocity” (Schulz and Lanzerotti 1974). This inward diffusion power is estimated at L = 8, where up = 1.1 x lo-i0 erg cmp3 was the measured proton energy density (Mauk et al. 1991) at a magnetic latitude of almost 30”. Representative values of F’ at L = 8, smoothed over a 1 R, interval, are F’ = 0.9 for M = 100 MeV/G, K = 0.3 G1”RN; F’ = 1.5 for M = 500, K = 0.15 in the same units; F’ = 1.0 for M = 500, K = 0.3. Then with D,, from Eq. (7), H - L, and F’ - 1, the inward diffusion power becomes P, = 2 x 109 w,

(10)

close to, but exceeding, the aurora1 input power requirement . Hence if a substantial fraction of the inward-diffusing protons precipitate into Neptune’s atmosphere, then inward diffusion can be an important power source for Neptune’s aurora. However, other loss processes for protons may be important, such as absorption by Neptune’s rings

427

SPACEDENSITIES

and moons. In addition, other mechanisms may contribute to excitation of Neptune’s aurora, including precipitation of energetic electrons (Cheng 1990b) and photoelectrons (Sandel et al. 1990). 5. DISCUSSION Energetic ion phase space densities have been calculated from Voyager 2 LECP measurements in Neptune’s magnetosphere. The phase space densities show a broad peak near L = 10 and generally decline rapidly toward the planet, although there is a gap in radial coverage that includes the Proteus minimum L values. These profiles are interpreted as indicating lossy inward radial diffusion with an energetic ion source near L = 10. The excellent agreement between inbound and outbound profiles supports a steady-state, axisymmetric interpretation. The phase space density peak near L = 10 is not plausibly explained as resulting from any systematic error. If the peak were attributed to a change in proton abundance, then the proton fraction must increase drastically for L > 10. However, the results of Mauk et al. (1991) indicate precisely the opposite; the heavy-ion fraction evidently increases outside L = 10. If absorption by Neptune’s rings is an important loss process in the inner magnetosphere, then analysis of the M = 2 MeVIG, K = 0.8 G”‘R, profile leads to a radial diffusion coefficient of D,, = 6 x 10e8 L3 set-‘, corresponding to a loss rate of 7-l = 2 x lo-’ set-’ near L = 1.8 that decreases to 7-l -L 1 x 10m6 set-’ near L = 4. This loss rate is generally consistent with calculated loss rates for ring sweeping (Paranicas and Cheng 1991a) in this region. Sweeping by Neptune’s moons is less important than ring sweeping within L cr 4, although there are sharp peaks in the moon sweeping rate, e.g., at minimum L values, where moon sweeping can be locally competitive with ring sweeping (Paranicas and Cheng 1991b). There may be additional important loss processes, such as wave-particle interaction (see below). If loss processes in addition to ring and satellite sweeping are important, then the estimate for D, would be increased. Nevertheless the suggested value of D,, = 6 x 10e8 L3 set-’ is in good agreement with the estimate D,, = low7 L3 set-’ obtained by Richardson et al. (1991) from Voyager PLS analyses assuming a Triton torus source of 1O25protons per second. This Triton torus proton source is roughly consistent with the recent calculations by Summers and Strobe1 (1991), who found total neutral hydrogen escape rates of 3.4 x lo*’ H set-’ and 1.8 x 10z5H, set-’ from Triton’s upper atmosphere. The escaping hydrogens form a gigantic neutral torus, and only a fraction of them are ionized within the magnetosphere (Cheng 1990a). The direct escape of protons from Triton’s atmosphere is relatively negligible (Summers and Strobe1 1991). While a

428

CHENGETAL.

detailed calculation of neutral cloud ionization and ion partitioning remains to be done, it appears that the total proton source in Neptune’s inner magnetosphere could exceed 102j see- ‘. The most likely mechanism balancing the proton source is radial transport (Richardson et al. 1991); if inward radial diffusion at L = 10 is to carry 102j fprotons set-‘, and if n = 3, then the PLS phase space density profiles imply D,, = lo-‘fL3 set-‘. The Voyager PLS results can be consistent with a smaller D,, < lo-’ L3 see-’ if there is significant outward radial diffusion of cold plasma at large L 2 12. In that case, the inward radial diffusion at L = 10 need only balance some fraction of the Triton torus proton source so D, can be smaller. The Voyager PLS results do not rule out this possibility (Richardson et al. 1991). The LECP phase space densities reported here do in fact indicate outward radial transport outside L = 10, but the directions of radial diffusion can be opposite at PLS and LECP energies. Such is known to be the case outside the 10 torus, where there is outward diffusion of cold plasma but inward diffusion of hot plasma (above about 300 eV; Smith et al. 1988). The LECP phase space density profiles provide independent evidence in favor of a relatively weak L dependence for DLL. Specifically, if the loss rate 7-l is constrained to be greatest near the planet, then n I 6.03, where DLL x L”. A generally decreasing 7~’ with increasing L is characteristic of ring and satellite sweeping. Moreover, observed plasma wave intensities were greatest near Neptune (Kurth and Gurnett 1991). The limiting case n = 6.03 is obtained for 7-l constant; if 7-l decreases with L as suggested here, then n must be smaller. A lossy radial diffusion model with IE = 3 quantitatively fits the M = 2 MeV/G, K = 0.8 G”2RN profile. These results suggest flux tube interchange as the main diffusion mechanism at Neptune, most likely driven by atmospheric winds as has been suggested previously for Uranus (Hood 1989). Finally the suggested D,, - lo-’ L3 set-’ implies a power carried by inward-diffusing protons which is estimated as 2 x IO9W At L = 8. This power would be sufficient to maintain Neptune’s UV aurora, if a substantial fraction of the inward-diffusing protons is lost to Neptune’s atmosphere. The large offset of Neptune’s magnetic dipole produces a global scale magnetic anomaly analogous to, but relatively much larger than, Earth’s South Atlantic anomaly (Cheng 1990b). Particle precipitation occurs within the weak-field region of the anomaly because the mirror point of a drifting particle descends into the atmosphere. This precipitation loss produces severe flux depletions which were observed by Voyager approximately at the predicted time along the trajectory (Krimigis et al. 1989, Mauk et al. 1991), and it should furthermore excite UV emissions at roughly the observed locations for Neptune’s aurora (Cheng 1990b). Precipita-

tion loss in the anomaly should act in conjunction with absorption by Neptune’s rings, and crude estimates (Cheng 1990b) indicate anomaly precipitation loss rates on the order of 10-j set- ‘, roughly competitive with ring sweeping (both processes produce substantial absorption probability within a single azimuthal drift period). Anomaly precipitation occurs mainly at high K values and produces a loss-cone distribution of pitch angles, Strong excitation of plasma waves may result and may cause rapid pitch angle scattering loss of smaller Kparticles (by raising their mirror latitudes enough to cause them to precipitate in the anomaly). Cheng (1990b) suggested that this plasma wave scattering process could be responsible for observed particle bursts in the atmospheric drift shadow. A detailed calculation is needed to determine how anomaly precipitation, mediated by plasma wave scattering, compares with ring absorption as a loss process. In summary, a radial diffusion coefficient D,, = IO-’ L3 set- ’ would be consistent with both PLS and LECP results. This D,, would allow inward radial diffusion to balance injection of protons from the Triton torus at PLS energies, and it would allow inward radial diffusion to maintain the radiation belts at LECP energies against losses to ring and satellite absorption, as well as to anomaly precipitation, which may be comparably important. The total power carried by inward-diffusing protons meets or exceeds the aurora1 input power requirement. An independent argument based on the shape of an LECP profile suggests n 5 6.03, where D,, 0~L”. These results are difficult to reconcile with those of Selesnick and Stone (1991b), who inferred D,, = 2 x 1O-8 (L/5)’ set-’ from Voyager Cosmic Ray Subsystem (CRS) data. This CRS analysis was based on modeling of a Proteus absorption signature in megaelectron volt electron data, while the Voyager LECP and PLS analyses used lower energy ion data that did not include the time of this Proteus signature. Nevertheless, the CRS diffusion coefficient would lead to severe difficulty in understanding LECP and PLS data, as its magnitude is much lower and its L dependence much steeper than those suggested here. An unknown loss process for hydrogens or protons would be required to account for PLS data, and unknown mechanisms would be needed to maintain the radiation belts against ring and satellite absorption and anomaly precipitation. Selesnick and Stone (1991b) did suggest that their D,, resulted from solar wind-driven disturbances, in which case D,, could be different for electrons and ions of different energies. However, the present results favor interchange diffusion, at least at LECP energies. Another possibility is that the CRS absorption signature is not actually caused by Proteus absorption but by some additional and much more potent process, such as loss due to ring material, co-orbital material, or plasma wave scattering. Selesnick and Stone (1991b) did note that the CRS

429

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absorption signature was displaced by 0.3 in L from its expected location based on Proteus absorption. If additional losses are present, then D,, can be increased from the value estimated by Selesnick and Stone. However, if Dt, (L = 8) were as much as -10M5 set-’ as suggested here, then these additional losses are not plausibly attributed to solid absorbers, as a total area -lo3 times that of Proteus would be required. An absorption signature coincident with the CRS signature was observed in LECP ion and electron data (Krimigis et al. 1989, Mauk et al. 1991). Detailed analysis of this signature will be reported in future work. ACKNOWLEDGMENT This work was supported by NASA under the Neptune Data Analysis Program and under Task I of Contract N00039-91-C-0001. REFERENCES ARMSTRONG,T. P., M. PAONESSA, E. BELL, AND S. M. KRIMIGIS 1983. Voyager observations of Saturnian ion and electron phase space densities. J. Geophys. Res. 88, 8893-8904. ARMSTRONG,T. P., M. PAONESSA,S. BRANDON, S. M. KRIMIGIS, AND L. LANZEROTTI1981. Low energy charged particle observations in the 5-20 R, region of the Jovian magnetosphere. J. Geophys. Res. 86, 8343-8356. BELCHER, J., ef al. 1989. Plasma observations near Neptune: Initial results from Voyager 2. Science 246, 1478-1483. BROADFOOT,A. L., et al. 1989. Ultraviolet spectrometer observations of Neptune and Triton. Science 246, 14.59-1466. CHENG, A. F. 1986. Energetic neutral particles from Jupiter and Saturn, J. Geophys. Res. 91,4524-4530. CHENG, A. F. 1990a. Triton torus and Neptune aurora. Geophys. Res. Left. 17, 1669-1672. CHENG, A. F. 1990b. Global magnetic anomaly and aurora of Neptune. Geophys. Res. Lett. 17, 1697-1700. CHENG, A. F., C. MACLENNAN,L. LANZEROTTI,M. PAONESSA,AND T. P. ARMSTRONG1983. Energetic ion losses near IO’S orbit. J. Geophys. Res. 88, 3936-3944. CHENG, A. F., S. M. KRIMIGIS, AND T. P. ARMSTRONG1985. Near equality of ion phase space densities at Earth, Jupiter, and Saturn. J. Geophys. Res. 90, 526-530.

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