Protons are studied in the global depression of the earth's horizontal magnetic field. It is shown that 10 to 100 keV protons dominate ring current energetics in two preferred regions of cyclotron instability, which serve as stable trapping boundaries for ring current protons. The only apparent means of removing this stably trapped belt of particles are considered to be by charge exchange interactions, or by outward expansion of the plasmapause to erode the ring current. Both of these processes require about two days, which is the characteristic decay period of the main phase depression. Questions whose answers are necessary to formulate a quantitative theory of geomagnetic storms which relates main phase depression to solar wind parameters are included

Kennel, C. F.

Thorne, R. M.

English

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PLASMA PHYSICS GROUP
DEPARThMIEI T OF: PHY61SC
VNIVER81 TYS OF: CALIFORI
L.OS ANGE-LES 90024 02
(NASA-CR-127769) LOCATING THE N72-2
MAGNETOSPHERIC RING CURRENT R.M. Thorne,
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Locating the Mlagnetospheric Ring Current
Richard M. Thorne and C. F. Kennel
March, 1971 R-88
Plasma Physics Group
Department of Physics
University of California
Los Angeles, California 90024
This work was partially supported- by the Office of Naval Research,
Grant #N000O -69-A-0200-4023: the National Science Foundation, Grant
#GP-2281_ the AtofEc inergy Commission, Contract A4i03-3)4, Project
#1t; and the National Aeronautics and Space Administration, Contract
#NGL-05-007-190.
l
LOCATING THE MAGNETOSPHERIC RING CURRENT
The most pronounced feature of a geomagnetic storm is the global
depression of the Earth's horizontal magnetic field. This main phase decrease
is generally considered to result from an enhanced injection of energetic plasma
into the region of trapping within the Earth's radiation belts. Theoretical argu-
ments have shown that the field depression AB measured at low latitudes on the
ground depends almost entirely on one single property of the injected plasma;
namely its total energy content ET( AB has been shown to be independent of
the type of the injected charged particles, their individual energies, or their
(2,3)
spatial distribution in the magnetosphere 2 . The general solution for the main
phase depression given by Sckopke(2 ) is
AB 2 T(1)
B 3 EM
where B
o
(, 0.3 Gauss) is the equatorial magnetic field at the Earth's surface
and E, ( i1025 ergs) is the total geomagnetic energy contained above the Earth.
This result has been extended to include the effects of a bounded magnetosphere(4'5'6)
but the additional contributions (from boundary currents, etc.) are generally small.
Ground-based observations of the geomagnetic field give no clue about
the location of the ring current as is clear from equation (1). Furthermore, we have'
little idea whether or not there is an upper limit to the total energy content, ET.
From observational results it appears that the kinetic energy density of trapped
particles does not exceed that of the geomagnetic field at the equatorial point
2on the field line where the particles are measured. This limitation of particle
energy density may be due to such large scale instabilities as the interchange
instability (89)or the finite p ballooning mode. ) However, observations
and theory have yet to converge on this point.
Microscopic instabilities, involving resonant interactions with waves
whose frequency matches thie cyclotron frequency or bounce frequency, cause
trapped particles to diffuse in velocity space towards the atmospheric loss cone,
whereupon they are removed from the magnetosphere by atmospheric collisions.
It is the purpose of this note to point out that 10-100 KeV protons, which
dominate ring current energetics, have two preged regions of cyclotron instability,
and consequently loss, which serve as stable trapping boundaries for ring current
protons. The pertinent electromagnetic ion cyclotron instability therefore limits
the ring current location, and, using the empirical notion that within the stable
region the energy density does not exceed the geomagnetic energy density, also
the ring current energy density, and therefore, the main phase depression.
Energetic protons resonate with electromagnetic ion-cyclotron waves
when their motions parallel to the magnetic field Doppler-shift the wave frequency
to the proton cyclotron frequency. This instability is believed to control the
populations of energetic protons, Ep >100 KeV1' ) As we shall see, energetic
protons are likely to be unstable throughout the entire magnetosphere. Recently, in
applying the above instability theory to lower energy (10-100 KeV) ring current
protons, Cornwall, Coroniti and Th ne(13)protons, Cornwall, Coroniti and Thorne have stressed the fact that the ion
3cyclotron instability only affects protons whose energy exceeds a threshold
which depends upon the magnetic field strength B and plasma number density
N. The threshold energy E is given by a relation of the formC
E EM f( w,A) (2)
where f(u;WA) denotes a weak dependence on wave frequency and pitch angle
anisotropy AR For the exact form, of f(w,A), see Kennel and Petschek!1 2 )
Ec is primarily controlled by the magnetic energy per particle
EM = B2/8'rrN (3)
which has a strong spatial variation throughout the magnetosphere. EM is
smallest ( hence permitting lower energy particles to participate in the instability)
near the geomagnetic equatorial plane and in regions where the electron density
is large or, where the magnetic field strength is small, namely inside the
plasmapause or at large radial distance in the auroral zone.
If, for simplicity, the arbitrary assumption is made that the pitch angle
anisotropy is roughly constant, f(A) ; 1, throughout the magnetosphere, several
pronounced properties of the ring current are readily explained. Figure 1 shows
schematically how the threshold energy for instability varies with geocentric
distance along the geomagnetic equatorial plane. It is immediately clear that
high energy particles, E >100 KeV, are susceptible to the cyclotron instability
at all locations in the magnetosphere. However, due to wave energy loss processes,
4the resonant interaction will be self-sustaining only if the particle flux also
exceeds a critical value!1 1 2) The cyclotron instability therefore limits the
storm-time injection of high energy particles (E >100 KeV) to their stably
trapped flux levels. The resulting total energy content (E > 100 KeV) in high
energy electrons and protons is consequently limited to values which are insuf-
ficient to produce the observed main phase geomagnetic field depression. This
(14,15,16)
conclusion agrees with observations of high energy radiation belt fluxes 
One can therefore theoretically and experimentally rule out high energy particles
as important members of the ring current.
At lower energies, between 10 and 100 KeV, Figure 1 predicts two
regions of cyclotron instability separated by a stable zone just.outside the plasmapause.
The two unstable regions have recently been associated with the location of the
ionospheric SAR arc observed at midlatitudes and proton precipitation emissions
observed at auroral latitudes.(17)
This simple description of the location and maximum energy of the ring
current particles agrees well with the few direct observations of the particles
responsible for the main phase depression during moderate geomagnetic storms 8)
A strong coincidence between the inner edge of .the proton ring current and the
plasmapause(19) has been noted during all phases of one geomagnetic storm( 2 0 )
and interpreted in terms of the above cyclotron instability. 2) Furthermore,
Figure 1 predicts that the energy of individual particles comprising the stable
5symmetric ring current are less at larger radial distance. Such a softening of
the ring current energy spectrum has been observed! 7 ) Finally, the dominant
energy of precipitating particles should also decrease with increasing covariant
latitude; a trend which is becoming increasingly apparent'from recent auroral
zone observations. ' )
In summcliy, figure 1 tells us where the intense 10--100 KeV proton
ring current is allowed to exist and why it is that the observed ring current
protons have the energy they do. (Higher energy protons, E > 100 KeV, are
always stable in the ring current region.) Furthermore, by assigning an average
ratio p between the plasma kinetic and magnetic energy densities in the ring current
one can approximately relate the main phase magnetic depression to the location
of the boundaries of the region of cyclotron stability:
AB )D (4)B ( 3 )a (4)0 pp
The fudge factor a depends weakly on the pitch angle anisotropy of the plasma
and lies between 1/2 to 1/4 for typical ring current conditions. Notice that AB
is primarily controlled by the location of the plasmapause L since the auroral
pp
zone is generally much further from the Earth. For a moderate magnetic storm
[AB - 50y and L - 3] predicts p -1/5 to 1/10 which agrees well with the
inner edge observations of Frank( 7 )
It is clear that magnetic storms, which involve large magnetic field
depressions, require either that the plasmapause move inward or that P increase
6in the stable trapping zone. Significant inward penetration of the plasmapause
has indeed been observed 2 3 2 4 ) it is currently popular to associate injection
into the stable trapping zone with magnetospheric substorms, which periodically
squirt plasma Earthwards from the geomagnetic tail. In support of this we note
that substorms are very frequent during the buildup phase of geomagnetic storms.
A unified theory of the ring current and piismapause may be possible, since the
large electric fields associated with substorms, according to current thinking(25,26)
also determine the position of the plasmapause.
Future models which utilize the enhanced substorm inward convection
of the plasma must include the effect of rapid particle loss by strong pitch angle
diffusion throughout the auroral zone (2 7 ) , which is interpreted here as the unstable
region between the ring current and tail. In order to build up a strong ring current
the time scale for transport across this unstable zone must become less than the
scattering loss time. Because electrons are more rapidly removed by pitch angle
(27)
scattering ( , the convecting protons should form the most important constituent
of the ring current in agreement with the observations of Frank(7 ) Also,since the
convection time scale depends on the electric field across the magnetosphere tail,
the above injection model places a lower limit on the substorm electric field needed
to produce a storm. Once the particles are convected into the zone of stability
they are able to complete drift orbits around the Earth and thus contribute to the
symmetric ring current depression. The only apparent means of removing this stably
7trapped belt of particles is by charge exchange interactions( 2 8 ) or by waiting
for the outward expansion of the plasmapause to erode the ring current along
its inner edge 1 3 '17) Both of these processes require about two days,which is
the characteristic decay period of the main phase depression.
Below are listed a-few questions whose answers are necessary to
for-nulate a qusntita,'ive theory of geomragnetic sormrrs which relates main phase
depression to solar wind parameters.
(a) For given solar wind conditions, what is the maximum electric
field associated with substorms? What is the substorm repetition rate?
(b) For a given substorm amplitude and repetition rate, what is the
plasmapause location? Rough estimates are possible here already.
(c) What shuts off substorms, stopping further proton injection,
allowing the plasmapause to expand outward, and thereby initiating the recovery
phase? Does a strong ring current moderate the substorm repetition rate, or is.
the recovery phase related to a relaxation of the solar wind?
(d) What process limits the proton energy density in the stable trapping
region?
Such questions should not be interpreted as a sign of our ignorance; rather the
mere fact that they can be asked so specifically indicates the considerable progress
which has been made recently. Hopefully this will encourage renewed attacks
on this, the oldest geophysical problem after the aurora.
Richard M. Thorne
Charles F. Kennel
References
1. A. J Dessler and E. N. Parker, J. Geophys. Res. 64, 2239 (1959).
2. N. Sckopke, J. Geophys. Res. 71, 3125 (1966).
3. E. N. Parker, Physics of Geoma.netic Phenomena, edited by Matsushita
and Campbell (Academic Press, New York, 1967).
4. R. L. Carovillno and J. J. Maquire, Physics of -he Magnetosphere, edited
by Carovillaino, MvcClay and Radoski Springer Veriag, New York; 1968).
5. S. Olbert, G. L. Siscoe and V. M. Vasyliunas, J. Geophys. Res. 73, 1115
(1968).
6. G. L. Siscoe, J. Geophys. Res. 75, 5340 (1970).
7. L. A. Frank, J. Geophys. Res. 72, 3753 (1967).
8. D. W. Swift, Planetary Space Sci. 15, 1225 (1967).
9. C. S. Liu, J. Geophys. Res. 75, 3789 (1970).
10.' F. V. Coroniti and C. F. Kennel, J. Geophys. Res. 75, 1863 (1970).
11. J. M. Cornwall, J. Geophys. Res. 71, 2185 (1966).
12. C. F. Kennel and H. E. Petschek, J. Geophys. Res. 71, 1, (1966).
13. J. M. Cornwall, F. V. Coroniti and R. M. Thorne, J. Geophys. Res. 75,
4699 (1970).
14. L. R. Davis and J. M. Williamson, Space Research ll, (North Holland
Pub. Co. Amsterdam, 1963).
15. J. A. Van Allen, Rev. Geophys. 7, 233 (1969).
16. S. N. Vernov, E. V. Gorchakov, S. N. I<uznetsov, Y. I. Logachev,
E. N. Sosnovets and V. G. Stolpovsky, Rev. Geophys. 7, 257 (1969).
17. J. M. Cornwall, F. V. Coroniti and R. M. Thorne, J. Geophys. Res. (1970).
(in press 1971) -
18o L. A. Frank, J. Geophys. Res. 75, 1263 (1970).
19. H. A. Taylor, H. C. Brinton and M. W. Pharo III, J. Geophys. Res. 73,
961 (1968),
20. C. T. Russell and R. M. Thorne, Cosmic Electrodynamics 1, 67 (1970).
21. G. T. Romnick and R. D. Sharp, J. Geophys. Res. 72, 4791 (1967).
22. R. D. Shcarp, D. L. Carr, and R. G. Johnson, J. Geophys. Res. 74,
4618; (i 969).
23. D. L. Carpenter, J. Geophys. Res. 72, 2969 (1967).
24. C. R. Chappell, K. K. Harris and G. W. Sharp, J. Geophys. Res. 75,
50 (1970).
25. A. Nishida, J. Geophys. Res. 71, 5669 (1966).
26. N. M. Brice, J. Geophys. Res. 72, 5193 (1967).
27. C. F. Kennel, Rev. Geophys. 7, 379 (1969).
28. R. L. Swisher and L. A. Frank, J. Geophys. Res. 73, 5665 (1968).
FIGURE CAPTION
The threshold energy for unstable cyclotron resonance Er = B2/8rrN is
schematically plotted against radial distance along the equatorial plane. The
curve is drawn for moderately disturbed conditions and the hatched area indicates
stability.
1000
Plasmopouse
100 .
@ i 
-
z Proton
Sav-Are .,i~i......,.,............. . ,..,@
I 2 3 4 5 6 7 8 9 10
L VALUE
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~?!~ii!ii~iiiiE~i~iiiiii?~ii~:i~i~iii~iiiiiiiiiiii:ii?!~i~i i~ii~iiii~ii~iii!~:~iiii~iiii:!i:ii!!~.................:...........ii:!iE~ii~~il~i
HH H~i~i~iiiiiiiiiiH~H~!i~H~H~ H~H~iH! HH H ~i iiiiiiiiiiH HH HHH~H~ !!!HH !!H!!!iii~HH~......:.......................................i..ii....................!HH .....
.
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Locating the magnetospheric ring current

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