Adv. Space Res. Vol. 8, No. 8, pp. (8)165—(8)173, 1988 Printed in Great Britain. All rights reserved.
0273—1177/88 $0.00 + .50 Copyright © 1989 COSPAR
TRANSPORT OF IONOSPHERIC IONS IN THE MAGNETOSPHERE: THEORY AND OBSERVATIONS J. B.
Lockheed Palo Alto Research Laboratory, 3251 Hanover Street, Palo Alto, CA 94304, U.S.A.
ABSTRACT A Monte Carlo transport code is described that follows the distribution functions of upward flowing ions (UFI) from a source location in the ionosphere into the magnetosphere. Examples of the guiding-center motion and the full gyration motion of ions from the cusp ionosphere are shown to describe the characteristics of the ions expected in the outer magnetosphere, and these characteristics are compared with measurements of ion streams in the lobes and plasma sheet. This comparison indicates that the ionospheric ions observed in the outer magnetosphere originate from the cusp ionosphere. Moreover, a comparison of ISEE-l measurements of the distribution functions of 11+ and 0+ in the ring current during a magnetic storm with the distribution functions of ions from the ionosphere, computed with an earlier version of the Monte Carlo transport code, indicates that the UFI from the cusp ionosphere may fully account for all the H~and 0~in the near-earth plasma sheet and ring current during stormtime conditions. It is also shown that if 0+ ions from the cusp ionosphere cross the center plane of the magnetotail at distances greater than about 9 RE, their magnetic moments are not conserved. INTRODUCTION The upward flowing ions (UFI) — beams, conics, upwelling flows observed in the upper polar ionosphere, including the auroral zone, have spurred the development of particle tracing and transport codes to study the motion of the ions in the magnetosphere /1—8/. A particularly important and interesting UFI source — the cusp ionosphere — has been identified. This source, which is connected along the magnetic field to the dayside cusp, is broad in longitude but narrow in latitude, and the ionospheric plasma is convected almost perpendicularly (anti-sunward) through the source. Hence, the UFI are separated spatially according to their velocity components along the magnetic field and their E x B drift. in effect this process is a velocity filter, as described below. It has been referred to in the literature as the cleft ion fountain /4/ and the geomagnetic mass spectrometer /2/. The latter term was used because different species of the UFI generally have similar energy-per-unit-charge spectra and are therefore separated spatially according to their mass. This source is important because it supplies the majority, if not all, the ionospheric ions observed in the outer magnetosphere. Moreover, during disturbed times the ions from this source supply a large energy to 9 cm2s1) /9the near-earth plasma sheet: not only is the UFI flux from this source very high (about i0 12/, but the ions are also appreciably accelerated along their paths through the lobes before being injected into the near-earth plasma sheet /5/. Additional interest in the transport of UFI arises from the importance of determining the role of ionospheric ions in global magnetosphere processes; and, conversely, the effects of magnetospheric processes on the UFI. For example, the UFI fluxes and the ionospheric ion densities in the outer magnetosphere have been found to be highly dependent on the convection electric field and magnetic activity /10,13,14/. Moreover, it is likely that magnetic substorms may be triggered by the enhanced injection of ionospheric ions into the near-earth plasma sheet /15,16/.
J. B. Cladis MONTE CARLO TRANSPORT CODE
Monte Carlo Transport Code Our Monte Carlo transport code computes a large number of ion trajectories in realistic models of the geomagnetic and geoelectric field, taking into account the effects of charge exchange reactions with neutral hydrogen and oxygen atonis of the atmosphere, and simulating, if desired, ion heating perpendicular to the magnetic field due to the presence of an incoherent transverse wave field. The distribution functions of the ions along their transport paths are constructed repeatedly from the case histories. Moreover, tests are included to switch the calculation from the guiding-center motion to the full gyration motion in regions where the magnetic moment is not conserved. The transport conditions are modelled as follows. The geomagnetic field model of Tsyganenko /20/, as coded by David Stern of NASA/GSFC, is presently incorporated in the code. This model has all the advantages of the earlier model of Tsyganenko and Usmanov /21/, but its validity in the magnetotail has been extended to about 70 RE. The corotation potential, ~R, and various models of the convection potential, ~ are specified in the earth’s ionosphere, and the electric field, E = — v (‘I’~+ ‘Pa), at a point along the ion path is determined by tracing three local magnetic field lines (assumed to be eqi.iipotentials) to the ionosphere to find the potentials ‘PR + ‘PJ of those field lines. Generally, the simple models of the convection potentials described by Heelis et al. /22/, are specified in the ionosphere. The probability of a charge exchange reaction with atomic oxygen or hydrogen occurring during each step length is computed using the atmospheric model of Chamberlain /23/ as modified by W. E. Francis of Lockheed. A stochastic process, utilizing a model of the power spectral density of the transverse wave field, simulates the perpendicular heating of the ions by the waves. Such models of the wave power have been devised using available wave measurements in the magnetosphere (e.g. /24-26/). At distances from the earth within about 10 RE, the guiding-center trajectories of the ions are computed by integrating the equations of motion described by Northrop /27/, viz.,
~e -. (V’PG~VB)+VE~
VD + V
de1 -. mV11-~-+ qE
anY 2 11
dVE e1 m—~-—- mVsII0] x -~
+ mL~P 0
here, R is the position vector of the guiding center; VD is the drift velocity of the guiding center perpendicular to the magnetic field B; and ê1 is a unit vector along B. V11 is the ion velocity component parallel to the magnetic field; and ‘P0 is the gravitational potential. VE is the drift velocity,
is the magnetic moment, 2 mV
Transport of Ionospheric Ions in the Magnetosphere In regions where the magnetic moment is not conserved (R computed by integrating the equation,
9 RE), the full gyration motion of the ion is
Of course, a deficiency of this code is that the plasma response (i.e., the collective effects of the ionized species) is not taken into account. Inclusion of such effects — if only the ambipolar electric field — would appreciably increase the complexity and running time of the code. This deficiency must be kept in mind in assessing
ChARACTERISTICS OF CUSP-IONOSPHERIC IONS Examples of the guiding-center trajectories of 0+ ions that move upward from the cusp ionosphere with velocities of 12 km/s and pitch angles of 150° at 1.2 RE are shown in Figure la projected in the X—Z plane (GMS coordinates). Trajectories 1—4 were computed using increasing values of the convection electric field. The dots along the trajectories are 1000 s time markers. In Figure lb the energy of the ions is shown as a function of time. The acceleration of the ions, which is principally along the magnetic field due to the 3rd term on the right hand side of Eq. (2), is caused by the centrifugal force arising from the motion /5/. As indicated in Figure ib, this acceleration is appreciable in regions where V~and the curvature of the magnetic field are large. The very rapid increase in energy shown in Figure lb occurs as the ions cross the central plane of the magnetotail.
\ -~ .—I
Fig. 1. Guiding-center trajectories projected on X-Z plane (a), and energy versus time (b), of O~ions started at R = 1.2 RE, 9 =22°, and 1200 LT, with V = 12 km/s and a = 30°. Curves 1 4 are for increasing values of the convection electric field. The dots on the trajectories are 1000 s time markers. (from /5/). Note that Eq. (2) is independent of the charge and mass of the charged particle. Hence, all charged particles that originate from the same point with the same velocity will continue to have identical velocities along the magnetic field, regardless of their charge or mass, as long as the particles do not experience different fields due to the differences of their cross-field drifts. These differences, which are mainly due to the 2nd
source location. That is, if the flow velocities of different ion species, measured simultaneously in the lobes, are the same, the ions most likely originated from the same localized region. The portions of the trajectories shown in Figure la near and beyond the center plane are not correct because the magnetic moment of the ions is not conserved in the vicinity of the center plane. For example, Figure 2 shows the full gyration trajectory of the O~ion on trajectory 2 of Figure la, continuing from the 5000 a time mark. Panels a, b, and c of this figure show the projections of the trajectory in the X—Z, X—Y, and Y—Z planes. At the point (—13, —1.3, 4.0 RE) the ion velocity was 49 km/s and its pitch angle was 177.4°in the VE frame. The convection potential drop in the polar cap was 15 kV. Clearly, the ion motion is radically different. The magnetic moment is not conserved until the ion moves to distances less than about 9.5 RE from the earth. Figure 2 also reveals that ion streaming should be expected in the central plasma sheet as well as in the lobes. In the central plasma sheet the ion streams should be directed tailward, duskward, and earthward. Moreover, since the ions rapidly gain energy as they cross the central plane, more energetic ions are expected in the streams directed toward the earth. 5
Dawn-Dusk Potential = 15 kV Initial Conditions: V = 49 km/s, a = 177.40
(X,Y,Z)GSM = (—13, —1.3, 4.0) —20
—10 . X ——> SUN
Fig. 2. Full gyration motion in magnetotail of O~ion on trajectory 2 of Fig. la. Panels (a), (b), and (c) show projections of trajectories in X-Z, X-Y, and Y-Z planes, respectively. On theoretical grounds the cusp ionosphere is considered to be the principal source of the ionospheric ions in the outer magnetosphere (R 7 RE). Not only is the outflux from cusp ionosphere high, especially during disturbed times /9-11/, but more importantly the ions are transported to— and injected in— the outer magnetosphere, as shown in Figures la and 2. Ions that originate from other regions of the polar are accelerated to a far smaller extent and reach much lower altitudes, as discussed by Cladis /5/. Moreover, ions that flow upward from the auroral zone, at local times other than about 12+3 hrs, generally do not reach L values higher than the L values of the source. The ion measurements in the outer magnetosphere, discussed in the following section, also indicate that the ions originated in the cusp ionosphere
COMPARISON OF EXPECTED ION CHARACTERISTICS WITH MEASUREMENTS
Transport of Ionospheric Ions in the Magnetosphere
The histograms in panels a, b, and c give the number of cases versus the velocity, angular width, and flux, respectively, of H+ in the lobes, O~in the lobes, and 0+ in the plasma sheet. Both the H~ and 0+ velocity distributions shown in panel a are in agreement with the velocities expected of ions from the cusp ionosphere, as based on their outflow velocities and their subsequent acceleration along their transport paths. However, the H+ outflow measurements indicate that much higher occurrence frequencies of 11+ streams with velocities below the 110 eV energy limit used in this study should be present.
30 ENERGY STEP 1 5 10 15 20 .4-..o.-~.-I-+.-~-.-.-.-.—4III
0 0.5 1 2 5
C I I I I 200400 680 800 1000120014801600 iI 0~LOBES <401
15 30 45
90 105 120
L I C 50100 ‘ 11 I I 150 2(X) 250 300 350 400
20 5 10 20 aID
0.15 1 2
90 105 120
__________________ 50100 150200250300350480 V (km/sI
0.51 2 51020 xlQ~ 2 sec ster eV)1 (cm
I I I I I 15304560 75I 90105120 FWHM (DEGREES)
Fig. 3. Distributions of ion streams versus ion flow velocity (a), peak flux (b), and angular width (full width at half maximum) (c). (from /28/). The angular widths of the streams in the lobes are much wider than those expected from the conservation of the magnetic moment, indicating the occurrence of wave heating or collective plasma effects (most likely a streaming instability). It is doubtful that the H~streams having the very large widths(> 90°)were in the lobes. They were probably in the plasma sheet even though their energies were low. The fluxes shown in panel
also indicate that the ions originated in the cusp ionosphere.
jc(wc, eac) above the cusp ionosphere at energy wa and pitch angle ac, assumed to be isotropic in the upper hemisphere, is approximately related to the flux jL(wL,aL) in the lobes at the energy w~and pitch angle aj~,by the equation,
w 0 jc(wc,ac)~jL(wL,aL)—. wj~, 1
J. B. Cladis
conservation of the magnetic moment.
By using representative values, say, for 0+ ; viz. wc = 10 eV, 2stsr’eV’, then wj~, =300 eV, B nT, BL = 10 nT, = 30°, from and jL(wL, caL)ionosphere iO’~cm have been observed jc(wc,ac) 1.1 0x =40,000 107cm2s’sr’eV~. Suchca~ outfiuxes the cusp during disturbed times /9-11/. Figure 4, from Orsini et al./29/, is a scatter plot of the flow velocities of H+ and 0+ streams that were measured simultaneously, using the EGD instrument on ISEE-2 to monitor the streams and the mass spectrometers on ISEE-1 to identify the ions. As shown in the figure, the ion velocities are approximately the same, indicating that the ions initially had the same velocities in the same localized region — the cusp ionosphere — as discussed above. Of course, since 11+ ions from the solar wind also enter the magnetosphere through the polar cusps, and many may flow upward after being degraded in energy by the atmosphere near their turning points, the origin of the observed H~is still uncertain. Note that the majority of the H~ flow velocities are lower than limiting velocity (about 140 km/s) used in the statistical study of Sharp et al. /28/. This result is in agreement with the ionospheric outfiux measurements mentioned above.
ISEE—l ICE 1978-1979 0+ VS H+ FLOW VELOCITY
Fig. 4. Scatter plot of flow velocity of O~ions versus flow velocity of H~as detected by ICE on ISEE-1 satellity during same time interval. (from/29). An early version of the Monte Carlo code (incorporating a dipole geomagnetic field) was used by Cladis and Francis /5/ to compute the transport of ions from the magnetotail to the ring current region during stormtime conditions. The source of the ions was taken to be the outfiux from the cusp ionosphere, transformed adiabatically to 15 RE in the magnetotail, and assumed to be uniform in longitude. As the ions were convected inward from the magnetotail, they were accelerated stochastically perpendicular to the magnetic field, simulating interactions with a broadband transverse wave field. The wave heating was discontinued at the Mcllwain injection boundary /30/ and the ions were convected adiabatically inward of this boundary. The H~and O~distribution functions given by the histograms in Figure 5 were computed using H~and 0+ ionospheric outfiuxes of 5.5x108 cm2s1 (w = .63 eV) and 2.8x108 cm2s1 (w = 10 eV), respectively, and wave power spectral densities near the H+ and 0+ gyrofrequencies of 0.16 (L/10)5/3 (mV/m)2/Hz and 2.5(L/10)5/3 (mV/m)2/Hz, respectively. The H~and O~distribution functions measured with the mass spectrometers on the ISEE-1 satellite during the main phase of the storm are given by the solid curves in the figure. Note that these calculated and measured distributions are in good agreement over a wide range of L. This agreement provides further evidence that the cusp ionosphere supplies an appreciable fraction of
Transport of Ionospheric Ions in the Magnetosphere 5/3 (mV/m)2/Hz for O~
7.00 ~ L 68.00 9.75 6 IT ~ 9.98 h 45° PA 135°
(bI 6.10 L 6 7.00 9.98 ‘ LT 6 10.22 h 45° 6PA 6135°
.16(L/1O)5/3 (mV/m)2/Hz for H~
7.00 o 1 ‘8.00 9.75 LT W 9.98 h
6.10 ~ L 7.00 9.98 IT oiO.22 h
85° 6 PA ~ 135°
< 9 ~ 1.0 10
10.606 6PALT o 0135° 11.04 05°
10.22 PA 6 IT 6135° 10.83 h 45°o
~ ~ 10 6 z
5.50 L ~ 6.10 10.22 5 IT 10.43 1, 95° PA s 135°
11.06 6 1 4.94 10.64 6 IT 11.04 h 115° PA s 135°
~ 10~ a ~FTTT
10~ _________________________ _________________________ 0 4 8 12 16 20 0 0 8 12 16
20 ENERGY (kay)
Fig. 5. Phase space densities of 0+ (panels a-d at left) and 11~ (panels a-d at right) measured (curves) with ISEE-l satellite and computed (histograms) in bin dimensions given in panels. (from /3/). CONCLUSIONS The flow velocities and fluxes of the 0+ streams detected in the lobes and plasma sheet are in general agreement with the values expected for 0+ ions that flow upward from the cusp ionosphere. However, the angular distributions of the 0+ streams measured in the lobes are broader than the ones inferred from the conservation of the magnetic moment. This result in not unexpected because at high altitudes (beyond a few RE) the ions are highly aligned with the magnetic field; hence, their distribution is susceptible to streaming instabilities that tend to relax (widen) the angular distribution. These conclusions can also be made for the H+ streams described here, which do not include the streams of solar-wind 11+ in the mantle. However, even though these H+ ions were most likely among the UFI from the cusp ionosphere, they might have included an unknown fraction of 11+, of solar-wind origin, which entered the magnetosphere through the dayside cusp and mirrored at depths of the atmosphere where their energies were appropriately degraded. The calculation of the full gyration motion of O~ions in the near-earth magnetotail reveals that the magnetic moment is not conserved and that the ions tend to become isotropized by their motion in the magnetic and electric fields in the vicinity of the central plane. Hence, calculations of the guiding-center motion of ions at distances greater than about 9 RE may be seriously in error. The calculation of the transport of H+ and O~ions into the ring current during a magnetic storm /3/ indicates that the UFI from the cusp ionosphere during stormtime conditions may entirely account for the presence of these ions in the plasma sheet and ring current. During quiet times, however, the UFI fluxes as well as the O~abundances in the plasma sheet and ring current are reduced considerably, and the H+ /He~ density ratio in the plasma sheet indicates that much of the H~may be from the solar wind /13/.
J. B. Cladis
Finally, it must be emphasized that all the transport studies performed to date have been based on the assumption that the particles move individually in the modeled fields. That is, collective plasma effects have
been neglected. The comparison of observed and calculated ion stream characteristics in the lobes indicate that this assumptions may not be seriously flawed for some conditions. Nevertheless, the next generation of transport codes should include some of the multi-species plasma effects, especially the ambipolar electric field. Acknowledgment. The author is grateful to W. E. Francis, G. T. Davidson, W. Lennartsson, and Y. T. Chiu of the Lockheed Palo Alto Research Laboratory for helpful discussions and assistance. The effort was supported by the Lockheed Independent Research Program. REFEREN CES 1.
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