The possible relationship between the auroral breakup and the interchange instability of the ring current

Planet.

Space Sci. 1967. Vol. 15, pp. 1225 to 1237.

Pergmon

Press Ltd.

Printed

in Northern

Ireland

THE POSSIBLE RELATIONSHIP BETWEEN THE AURORAL BREAKUP AND THE INTERCHANGE INSTABILITY OF THE RING CURRENT DANIEL W. SWIFT Geophysical Institute, University of Alaska, College, Alaska (Received 16 December 1966) Abstract-Morphological evidence is presented suggesting that the aurora1 breakup may be the result of an instability on the boundary of the ring current belt. This suggestion is examined quantitatively by studying the consequences of a dispersion relation which includes the effects of wave particle interactions and the depolarizing effects of a finitely conducting ionosphere in a dipole magnetic field. Assuming reasonable ionospheric and magnetospheric parameters, it is shown that qualitative agreement can be obtained between predicted growth rates and wavelengths and those observed by the all-sky camera. Connections between the auroral breakup and the polar magnetic substorm and the structure of the magnetospheric tail are suggested. INTRODUCTION

In this paper, the possibility that the aurora1 breakup is a manifestation of an instability on the boundary of the ring current will be examined. First, some features of aurora1 morphology which are suggestive of a close relationship between the aurora1 breakup and a ring current instability will be presented. Next some of the features of the instability problem will be discussed. This will be followed by the development of a dispersion relation based upon the formulation given by Chang et al. (l) Finally, the consequences of the dispersion relation will be discussed in terms of the aurora1 data. 1. AURORAL

MORPHOLOGY

Essentially, the breakup marks the beginning of an aurora1 substorm as described by Akasofu,(2) in which previously quiet aurora1 forms around the midnight sector will suddenly brighten and then tend to explode westward, northward and eastward. Following the breakup, bright rapidly moving aurora1 forms may be seen over the whole darkened portion of the aurora1 zone in both the northern and southern hemispheres. Gradually, the activity subsides and the parallel aurora1 arcs tend to reform. This process may be repeated every few hours or more often. The breakup also marks the beginning of the magnetic substorm and of the aurora1 absorption event. To illustrate the concept of the breakup more clearly, Fig. 1 shows a sequence of 9 all-sky camera photographs taken at College, Alaska on the night of January 7-8, 1965. During the ten minutes prior to 0007, the aurora1 arcs were virtually motionless, with a broad diffuse arc to the south of the zenith and some other arcs on the northern horizon. Then as shown in the frame of minute 0007, a secondary arc developed just north of the most prominent arc. The frames for minutes 0008 and 0009 show the development and kinking of this secondary arc. The frames of minutes 0010, 0011 and 0012 show the continued development of the aurora1 forms. Then, in frame 0013 the poleward motion becomes more pronounced and in frame 0014 the aurora1 arc brightens to the point where even the details on the inside of the camera box are illuminated by scattered light from the 1225 1

DANIEL

1226

W. SWIFT

aurora. Finally, in the frame 0015, it can be seen that the arc has expanded from the zenith to cover the whole northern sky. Among the significant features to notice in the example shown in Fig. 1 is that the breakup arc initially developed without any particular movement and without any noticeable change in other parts of the sky, and that the later motions were characterized by an expansion primarily in the poleward direction. The magnetic field variations during the time shown in Fig. 1 are also of interest and

II

22

23

00 l%YWMT

01

02

03

FIG.~. A MAGNETIC RECORD FOR COLLEGE, ALASKAON THE NIGHT OF JANUARY 7-8 (1965). Notice that before the breakup, the magnetometer trace is relatively quiet, but a sharp negative bay sets in simultaneously with the aurora1 breakup. are shown in Fig. 2. The important feature of this magnetogram is that the magnetic effects of the auroral breakup appear to follow rather than precede the breakup. The same is also true of the overhead absorption of radio waves as measured with the riometer. From Fig. 2, it can also be seen that the first spike on the H trace occurred coincident with the flash brightening of the aurora (frame 0014 of Fig. l), but that the main part of the magnetic bay did not occur until after the poleward expansion of the breakup. The example shown here is rather typical of the aurora1 breakup, and will be used as a model in further discussion. The fact that the aurora1 breakup initiated just south of College (64.7’ geomagnetic latitude) and resulted in a predominantly poleward expansion suggests that the breakup was the result of an internal process in the magnetosphere, because the poleward motion when mapped along the geomagnetic field lines into the equatorial plane implies an outward motion. The fact that there is no evident precursor to the events starting at minute 0007 and that there is no apparent disturbance in other parts of the sky suggests that the breakup

Foci. 1. A

SEQUENCE OF ALL-SKY CAMERA PHOTOGRAPHS SHOWING THE DEVELOPMENT AURORALBREAK-UP AT COLLEGEON THE NIGHTOFJANUARY 7X3(1965).

OF AN

Geomagnetic north is to the right of each frame. The exposure time is 8 sec. Notice the flash brightening in frame 0014 accompanied by the rapid poleward motion. Compare this with the magnetic data in Fig. 2. 1226

RING

CURRENT

INSTABILITY

1227

initiated on the magnetic field lines passing through the diffuse arc on the frame 0007 shown in Fig. 1. Detailed comparisons by Heppner et al. w between the occurrence of aurora1 zone magnetic bays and magnetic bays in the magnetospheric tail show a close relationship between the two events. A comparison of the onset time of the two events shows that the terrestrial event consistently happens first. If there is indeed a causal relationship between the two events, then the analysis of Heppner et al.t3) again implies that the aurora1 breakup initiates a reaction deep within the magnetosphere that results in an outward motion into the magnetospheric tail. Studies of magnetic storms by Akasofu and Chapman(4) indicate a close morphological relationship between the growth of the ring current and polar magnetic substorms. Further, the study of Akasofu and Chapmant5) indicates that the ring current contains more than sufficient energy for an aurora1 substorm. Theyt4) also comment that the occurrence of aurora1 substorms and the growth of the ring current have no simple relationship to the pressure of the solar wind against the magnetosphere. This assertion is further supported by the analysis of Wilcox et al. w of the Imp. 1 data on the ionized solar wind and interplanetary magnetic field. Scatter plots of the solar wind number density and momentum flux versus K, showed no consistent relationships. Further, comparisons between the southward directed interplanetary magnetic field strength and the averaged value of K, showed a linear relationship, but the standard deviation of K, was several times the average so this relationship is of questionable significance. In summary, the above discussion suggests that the aurora1 breakup is (1) related to the ring current, (2) the result of an internal process taking place within 10 earth radii, and (3) results in an outward motion into the tail of the magnetosphere. A simple explanation of these facts is that the aurora1 breakup is the result of an interchange or flute instability which results in the jetting of part of the ring current plasma into the tail of the magnetosphere. The rest of this paper is directed toward a more detailed examination of this hypothesis. 2. INTERCHANGE

INSTABILITY

It is well known that a confined plasma is unstable if there exist sufficiently sharp gradients in the plasma energy density. Sharp gradients on the outer boundary of the ring current may be the result of the rather definite magnetospheric boundary on the sunward side of the magnetosphere. Beyond this, no attempt will be made to account for the existence of a potentially unstable ring current boundary on the night side of the ring current belt. This section of the paper will be confined to a detailed discussion of the consequences of a number of assumed ring current boundary configurations. The fact that radiation belts in the magnetosphere may be unstable against the flute or interchange instability is not new. Golda) concluded that if the particle density decreased faster than r-2o’3, where r is the geocentric distance, the radiation belt would be unstable. He also concluded that an interchange could take place in a very long time scale if the energy density decreased faster than r-4. Sonnerup and Laird c8)have also studied the interchange instability under a variety of conditions; however, neither of these authors has considered explicitly the time constants of the motion and the effects of the finitely conducting ionosphere. Perhaps the best formulation of the interchange or flute instability in the dipole field has been given by Chang et al. (l) Their formulation includes the effect of the ionosphere in addition to containing the microscopic effects of wave-particle interaction. However, they did not consider in any detail the growth rates. There is also an extensive body of

1228

DANIEL W. SWIFT

literature resulting from the research effort on controlled thermonuclear fusion on the flute instab~ty for a variety of magnetic field geometries. There appears to have been no specific consideration of the stability of the ring current against interchange, although many of the features of radiation belt calculations are applicable. The ring current is believed to consist primarily of protons and the particles associated with it may form the bulk of the particles present in the magnetosphere at geocentric distances of greater than 4 Earth radii. In this paper, growth rates of the instab~i~y will be calculated assuming a finitely conducting ionosphere and a zero conductivity ionosphere. The growth rates will be computed as a function of the wavelength of the flute perturbation so that the effects of wave-particle interactions will be considered in some detail. Equation 46 of reference 1 will be used as a starting point, It is given by

where the potential function associated with the pe~urbation

is given by

where 8 is the azimuthal variable measured about the geomagnetic dipole axis, and r is the geocentric radius measured in the equatorial plane. The integrations are carried out over the length of the field line from the ionosphere in one hemisphere to the ionosphere in the conjugate hemisphere and back again, ol, and o, are the Pederson and Hall conductivities, respectively. They include terms to allow for both the polarization current in the magnetosphere and the conduction currents in the ionosphere, The terms M&D, and Me@, represent the perturbation charge densities of the ions and electrons in the magnetosphere. The quantity is found by solution of the guiding center Vlasov equation and is given in Ref. 9 as -

O-45& - 3E3@Z

(2)

where i and e denote the contributions due to the ions and electrons respectively. In the above expressions the flat pitch angle dist~bution has been assumed and the zero order dist~bution function is of the form where E is the particle energy and r is the geocentric distance in the equatorial plane (rE in Refs. 1 and 9). Thus, any quantity expressed as a function of r is understood to be evaluated in the geomagnetic equatorial plane. Another important change in notation in (1) is that p sin 1 is used to replace the cylindrical coordinate r of Ref. 1. IIere p stands for the geocentric radius and il the coIatitude in a spherical coordinate system. Also, the symbol I will be used as the azimuthal wave number rather than m in order to avoid confusion with the symbol used for the particle masses. The derivation of 1 and 2 assumes that the field lines are equipotentials and the first and second adiabatic invariants are valid.

RING

CURRENT

1229

INSTABILITY

Since this paper concerns possible instabilities of a ring current, the effect of the radiation belt electrons will not be considered because the energy of the electrons is believed to be a small fraction of the ring current proton energy. * Accordingly, the ion dist~b~tion function will be written in the form (34 h = n(r)g(E) + W) - 44 NE) where n(r) is the equatorial number density of energetic protons, and N(r) is the total density of protons, including the cold component. The assumed electron distribution function can then be written in the form fe = NrN(E)

(3b)

By substituting (3) into (2), it is possible to obtain an explicit expression for the right hand -

sihe of (1).

I--

Mi(r) + M,(r) = s

r fr n(r) + 1.05 n(r) :

* Eg(E) dE 3clE - W) IS 0 o--eBr2

m

s0

&(E)dEj /

E2

O---

3clE eBr2

/ i

(4) As a result, it can be seen that the right band side depends only on the number of energetic protons present. The left hand side can be split into two parts by writing the conductivity in the form ice c2 %t

=

zc

+

cr,

(54

and c2t =

(72

(5b)

where a, and a2 are the usual Pederson and Hall conductivities which are significant only in the thin ionospheric shell. The first term in (5a) is due to the frequency-dependent polarization current which is important in the regions above the ionosphere, and V, is the Alfven velocity. Upon substituting (5a, b) into (1) and making use of the approximation

that -4T% >l, w

(1) becomes

where use has been made of the fact that a@/& is independent of s. In evaluating the ionospheric contribution to 1, the magnetic field lines entering the ionospheric shell were * Recently Frankllo’ has suggested that low energy electrons of about 1 keV energy may contribute a substantial part to the main phase decrease associated with the ring current. This will not substantially aIter the conclusion of this paper.

DANIEL

1230

W. SWIFT

assumed to be nearly vertical so that

I&).= 2

Ll =

s

or dh = 2 XI

(7b)

s

a2 dh = ;r;,

(7c)

The coefficients of the first terms are given by, Br=

gee =

c= ds ” s o Va2Bp2 sin2 L

(84

Bp2 sin2 12

ds vlZ= (8~)

where the limits of integration are from the equator (S = 0) to the ionosphere (S = si). The terms in (7) were evaluated by assuming that r/p, > 1 where pe is the radius of the ionospheric shell. The integrals are over the thickness of the conducting region of the ionosphere. The same expression can be derived by mapping the ionospheric potentials and currents from the ionospheric shell into the magnetospheric equatorial plane. The terms for g,,, g,, and g, can be evaluated by performing the integrations over a l/2

line iz = sin-l

5

0r

and writing the derivative with respect to u as

a

au =

00til a --__ a 2

1

Bp(1 + 3 cos= A)l’= ap

P

an )

Because the term for Va2 = B2/4n-Nm, the expressions for g,,, g,. and g,, all contain a factor of the type N sin l3 A(1 + 3 cos2 A>B,(a = 0, -l), this function is quite sharply peaked in the neighborhood of A = 742. Consequently, for many reasonable distributions of N(S), the integrals appearing in (8) can be usefully approximated by setting N(S) = N(s = 0) = constant. The total ion number density evaluated only at the equator appears in the approximate expressions for g,, g, and g,, : g,, N 0.34 4qN(r)(l

to(:))

47wmc2 g, N 0.34 7 [ 8*35N(r)+r;N](l

gee N 0.34 yN(r)(l

++))

+0(t))

RING CURRENT

INSTABILITY

1231

With the above expressions substituted back into (6) and multiplying B2(1*36rrrmc2N) the following dispersion relation is obtained

through

by

where

Cl,, B2 v1’2= 0.68 rmc2N Here y1 represents the time constant for the decay of plasma motions in the radial direction. If the various constants in (11) are lumped together and C is expressed in mks units, the decay time constant can be written as Yr = o-9 x 10s -$

(lla) e where r, is in units of earth radii. For r, = 6, Xc, = 1 mho and N = 1 cm-3, then Y = 0.32, representing a decay time of 3 sec. Because (10) is a differential equation, there exists no simple means of determining the complex eigenvalues w = 0, + icoi. However, it is useful to examine the local approximation where the azimuthal wavelength is assumed to be small compared to distances over which the parameters vary significantly.

d’% dr = 0. It is also useful

In this approximation,

to define the azimuthal wave number, k, by k, = I/r. Now if &2 is assumed to be independent of r, (10) reduces to al

_

-6’7 ke2 ntr) mr2co

ah n

ar

N(r)

a

-

ooE2 FE g(E)

+ 1.05

>S

0

m Eg(E) dE _ 3 3ck,E so CC-eBr

w--

3ck, dE eBr

Here since only the Pedersen conductivity enters into this equation, the subscripts on C, and Y have been dropped and the subscript 1 is understood. This equation can now be used to determine o = o(k,). First, it is useful to examine the dispersion relation in the hydromagnetic limit, in which the phase velocity of the perturbation wave w/k, is much 3cE greater than the guiding center drift speed of the particle, eBr . Also, let n vary as r-p, then --co2 + ivo = - mqi

(E) (7.05 -p)

(13)

1232

DANIEL

W. SWIFT

This simple dispersion relation has 2 roots:

w%=l

. b tir: 34~” -

4v2N

2

(14)

where y2 =

z2 ; (E) (7.05 - p)

(15)

and (E) is the average particle energy. Since the negative imaginary part of w corresponds to growing waves, it can be seen that only if p > 7.05 will there be growing waves. This is in agreement with the analysis of Chang et al. VJ) From this, it follows that in the hydromagnetic limit the condition for instability is independent of the ionospheric conductivity so that for p > 7.05 the ring current boundary is likely to be unstable. It can be seen, however, that the effect of the ionosphere is to greatly retard the growth rate of any instability and that in the limit that YS> r” wcz -i-

Y2

(16)

V

It is also worth pointing out that in this limit, the growth rate is independent of the cold plasma density, N. But if N becomes s&iciently large, or 4y2 is much larger than ye, the growth rate is proportional to W1i2. In order to consider in more detail the effects of wave-particle interactions, it is necessary to specify the energy distribution function for the particles, g(E). Since there is no specific information on the particle energy distribution, Const g(E) = [(E - E,J2 +

s

(17) K212

02

and the constant is chosen such that

g(E) dE = 1. This particular choice of the dis-

tribution function permits evaluation o;! the integrals appearing in (12) in closed form. The roots of the more general dispersion relation for finite k, can be obtained by an iteration procedure on (12). For most values of k, the iteration routine converged in a very few iterations. The physical consequences of (12) can be rather well illustrated by the example shown in Fig. 3. In this example, r = 6 earth radii, N = IZ= 1-Ocm-9, K = 5 keV and E, = 0 giving an average particle energy of 3.18 keV. The choice of N = 1 is based upon the whistler meas~ements of Angerami and Carpenter. W) The choice of n = 1 results in a @= 8rrn (Q/B2 ‘U O-1. Figure 3 gives the growth rate of the fluting instability as a function of the wave length of the perturbation as measured in the equatorial plane. Curves are shown for various values of p = 3 In @3 In r when the ionosphere was assumed to be nonconducting and when the ionosphere was assumed to have a height-integrated conductivity of 1 n&o. The growth rate in the hydromagnetic Iimit is also indicated on the right hand end of the curves. It is interesting to note that as the wavelength of the pe~urbation decreases, the growth rate increases, goes through a maximum and then decreases very rapidly. The rapid decrease in the growth rate occurs when the frequency of the over-stable wave (Re(w)) becomes comparable with the growth rate (-1m(o)). Perhaps the most important feature of Fig. 3 is that when the depolarizing effects of the

RING

CURRENT

1233

INSTABILITY

ionosphere are negligible, the ring current boundary may be unstable even though the Another feature of the E = 0 curves is hydromagnetic theory would indicate stability. that the growth rate increases with decreasing wavelength until the wavelength becomes comparable with the average proton gyroradius (70 km in this example). This effect was discussed by Lehnert. (r2,13) The short wavelength cutoffs occur when the wave frequency, wr, becomes comparable to wi. The stabilizing effect results from the fact that the electric field drift reverses before the wave amplitudes have a chance to grow by a factor of e.

ww IO’

FIG.~. GROWTH Assuim~~ rn~

104

IO’

A(KM)

Id

RATES OF THE INTERCHANGE INSTABILITY AS A FUNCTIONOF WAVELENGTH,& THE EOUAT~RIAI. NUMBER DENSITY OF PARTICLES FALLS OFF AS r--p WHERE r Is THE GEOCENTRIC DISTANCE.

labeled X = 0 were calculated with the assumption that the ionosphere has zero conductivity. The curve calculated with I: = 1 assumed that the ionosphere has a conductivity of 1 mho. The ring current boundary was assumed to be at about 6 Earth radii. The average particle energy assumed was 3.2 keV.

The curves

It turns out that in the I; = 0 cases more important finite ion-gyroradius stabilizing effects were demonstrated by Roberts and Taylor. (14) Thus the growth rates shown here for wavelengths comparable to 70 km are not significant. The physical reason that an instability can occur when p < 7.05 and Y = 0 is that in the long wavelength limit the boundary can exhibit a stable oscillation. As the wavelength is decreased, there will be more and more particles drifting at the same rate or faster than the phase velocity of the wave. The wave becomes unstable as a result of a resonance effect when the majority of particles drift faster than the wave, and the particles are able to feed energy into the wave. When the ionosphere is assumed to have a height-integrated Pederson conductivity of 2 = 1 mho, the damping time constant as given in (1 la) for hs = 1 and r, = 6 is v = 0.32

1234

DANIEL W. SWIFT

se&. This is larger than any of the growth rates shown in Fig. 3. It is not at all surprising that the growth rates are considerably less than the I; = 0 cases, but the important feature is that the ring current boundary tends to be stable for p < 7.05, as predicted by the asymptotic equations. Another important feature is that the modes are stabilized at longer wavelengths than would be the case if the ionosphere were nonconducting. In this case, it also turns out that the cutoff occurs when the oscillation frequency becomes greater than the growth rate. Other numerical computations indicate that when the ionospheric conductibity is further increased, the growth rates of the instability are decreased in proportion to the conductivity increase. Further, the short wavelength cutoff of the modes occurs at proportionately longer wavelengths. An increase in the cold plasma density, N, decreases the growth rates in the limit of low ionospheric conductivity by N-l12, but does not seriously affect the growth rate in the hcgh conductivity limit. Raising the particle energy increases the growth rate. When the ionosphere is highly conducting, the cutoff wavelength is insensitive to the particle energy. Increasing the geocentric radius, I, results in a decrease in the growth rate in the limit of low ionospheric conductivity, but an increase in the growth rate in the limit of high ionospheric conductivity. It is important to compare the time scales appearing in Fig. 3 with the mirror frequency and the time an Alfven wave takes to propagate over the length of the field line. The mirror period using the formulas of Hamlin et al. (15)turns out to be approximately 100 sec. This is quite comparable with the growth times and frequencies under discussion. Consequently, the results presented here are strictly valid only in the limit of pitch angles near 90”, because the perturbations are capable of breaking down the longitudinal invariant. The effect of this breakdown would be the transfer of energy between the perturbation and the longitudinal motion. With the model chosen here, the time taken by the Alfven wave to propagate between the equatorial plane and the ionosphere is about 7 sec. This is still somewhat shorter than the time constants under discussion here so that the field lines should remain as approximate equipotentials. The Alfven propagation time increases as r4N1i2 so that for disturbances at greater geocentric distances or larger values of N the propagation time could well become comparable with the growth times. Under these conditions, the field lines would no longer be equipotentials; but even more serious, if there exists a mode which can grow at a rate fast compared to the Alfven propagation time, the instability amplitude could e-fold many times before the ionosphere would have a significant depolarizing effect. In other words, for disturbances which have high characteristic frequencies, the inductive reactance of the field line may become large compared to the ionospheric resistance. One dithculty with the local approximation discussed here is that the assumption that the parameters N, IZand C (mapped into the magnetosphere from the ionosphere) do not change much in the radial direction over the distance of a wavelength. This appears to contradict the rather well-defined arc structure shown in Fig. 1. Figure 1 indicates that a sharp boundary approximation would be more suitable. Indeed, a dispersion relation appropriate to the sharp boundary can be derived from (10). Although the derivation will not be given here, the dispersion relation can be written in a form similar to (12), with the term containing a Inn/& being replaced by a term proportional to (nr - n,)k, where n1 and n2 are the ion plasma number densities on either side of the boundary. Again, it is possible to obtain a variety of growth rates by varying n, and n2 and the other parameters. However, because of the factor ko, it turns out that there is no short wavelength cutoff, unless (nl - n2) is made some function of k,. The sharp boundary approximation would

RING CURRENT

INSTABILITY

1235

tend to break down as soon as the wavelengths become comparable to the thickness of the boundary region. A more satisfactory discussion of this problem will have to wait until a solution of (10) can be obtained for a boundary region of finite thickness. DISCUSSION

AND CONCLUSIONS

is now of interest to compare the results of the calculations with the events shown in Fig. 1 and with other examples of the aurora1 breakup. A study indicates that the breakup can be separated into three phases. The first is the quiet phase, before there is any indication of the impending breakup. The second may be termed the brightening phase, in which an arc appears and brightens as shown in the frames of minutes 0007 to 0012 of Fig. 1. During this phase, the arc appears to remain stationary, but ripples and waves appear in the arc. This phase lasts the order of 5 min. The third and expansive phase occurs when the arc moves rapidly poleward as shown in the frames of minutes 0013 to 0015. During this phase, the greater part of the poleward motion may occur within a minute or two. According to the model discussed in the last section, the first phase would be ascribed to the period of time when the ring current belt is stable against the interchange instability, during which the ionosphere plays an effective role in inhibiting the development of the instability. Since the breakup arcs often develop in the neighborhood of other aurora1 forms, the ring current boundary may be tied to a rather highly conducting region of the ionosphere. In this case, for any instability to develop, the boundary configuration must develop to the point where it is unstable in the long wavelength limit. In the model discussed in the last section, p must be greater than 7.05. The second phase of the breakup could be ascribed to the time when the growth of the instability is constrained by the depolarizing effects of the ionosphere. Here the growth rates shown in thep = 7.1, X = 1 curve of Fig. 3, match the time scales shown in Fig. 1 rather well. The third and rapid expansive phase would then correspond to the development of the instability, with the depolarizing effects of the ionosphere significantly reduced below those associated with phase 2. The onset of phase 3 may be caused by the increased resistivity of the field lines due to the acoustic wave instability resulting from longitudinal currents flowing between the magnetosphere and ionosphere, as discussed by Swift.(16) Another point of comparison with the aurora1 data is the wavelength of the perturbations associated with the breakup. The dominant wavelength should correspond to the modes with the fastest growth rate. Thus the maxima of the curves shown in Fig. 3 should give an indication of the dominant wavelengths. In the case of the multiple time scales associated with phases 2 and 3, the wavelength associated with phase 2 should also be dominant during much of phase 3 because those waves would possess the most energy at the start of phase 3. In the example shown in Fig. 1, the wavelengths are shorter than is consistent with the S = 1 curves shown in Fig. 3. In addition, the breakup phenomenon develops over a distance at least as wide as the field of view of an all-sky camera. Consequently, we must be able to understand the development of perturbations with a wavelength of the order of 2 x 104 km as measured in the equatorial plane. These wavelengths are about a factor of 10 longer than would be indicated by the p = 7.1, C = 1 curve of Fig. 3. From the preceding discussion, it can be seen that a longer wavelength cutoff would result if the ionospheric conductivity were increased. Increasing the ionospheric conductivity results in a slower growth rate, but this can be offset by increasing the value ofp and the particle energy. It

1236

DANIEL W. SWIFT

It turns out that the wavelength of 2 x lo4 km and growth time of 5 minutes can be accounted for by assumingp = 8.1, E = 10 mho, (E) = 13 keV, n = 1 cm3 and N = 1 or 5 cm-3. We are still left with the problem of accounting for the existence of the breakup arc whose width, when projected into the equatorial plane, is a small fraction of the 2 x 104 km wavelength discussed above. In order to develop a consistent picture of the breakup, it is suggested that the outward moving plasma associated with the long wavelength perturbation develops a “front” which is associated with the appearance of the breakup arc, This front may then contain a rather sharp change in the ring current plasma density and the shorter wavelength perturbations seen on the arc could be the result of a more localized flute instability. In this case, the sharp boundary approximation to (10) may be valid. The short wave perturbations have a wavelength that is approximately the thickness of the breakup arc; and they are not more than a factor of 10 longer than the gyroradius of a 3 keV proton. Thus, the wavelength of the ripples on the breakup arc may be determined by the point where the sharp boundary approximation breaks down: that is, all modes with large wavelengths have slower growth rates and all modes of shorter wavelengths are cut off by the same mechanism that was discussed in the local approximation. A more complete discussion of the interchange instability in the magnetosphere will await a more complete solution to (10). However, with the appro~mations used here, it has been possible to account for some of the observed features of the amoral breakup. Unfortunately, with our present knowledge of the ring current belt, a wide variety of assumptions can be made as to its structure so that one is able to account for a wide range of growth times and wavelengths. The ionospheric conductivities discussed here are somewhat high for nighttime conditions, but again, if allowance is made for enhanced ionization due to particle precipitation, a wide range of effective ionospheric conductivi~es can be assumed. The calculations reported here, therefore, serve merely to establish the plausibility of a connection between the aurora1 breakup and an interchange instability of the ring current belt. The model proposed may be able to account for the polar magnetic substorm that follows the aurora1 breakup. Since the instability results in a jetting of particles into the outer magnetosphere, a large asymmetry in the ring current will develop due to the depletion of particles on the night side of the ring current. Polarization electric fields will quickly build up due to the differential particle drifts. It is suggested that the polar electrojet is driven by these ring current electric fields and part of the ring current circuit is completed through the ionosphere. The radiation belt asymmetry assumed by Fejero’) to calculate aurora1 zone ionospheric currents may be qualitatively similar to the type of asymmet~ that may result from an aurora1 breakup. Finally, the aurora1 breakup model presented here suggests an explanation for the formation of the extended magnetospheric tail, The plasma responsible for the formation of the neutral sheet may be injected into the magnetospheric tail by repeated aurora1 substorms. In other words, the neutral sheet plasma may have originally been part of the ring current plasma which was injected into the tail during an aurora1 substorm. If particle losses from the neutral sheet region are slow, a substantial amount of energy may be accumulated there over a time scale long compared to the aurora1 substorm cycle. Acknowledgements-This

work was performed under NSF Grants G-25193 and GP-5540.

RING

CURRENT

INSTABILITY

1237

REFERENCES 1. D. B. CHANG, L. D. PEARLSTEIN and M. N. ROSENBLUTH, J.geophys. Res. 70,3085 (1965). 2. S.-I. AKASORI, Planet. Space Sci. 12,273 (1964). 3. J. P. HEPPNER,M. SUGIURA,B. G. LEDLEY,T. L. SKILLMANand M. J. CAMPBELL, Trans. Amgeophys. Un. 47. 160 (1966). 4. S.-I. A~A~~FU and S. CHAPMAN,J. geophys. Res. 68, 3155 (1963). 5. S.-I. AKAWFU and S. CHAPMAN(cd. S. Matsushita and W. H. Campbell). Academic Press, New York (1966). 6. J. M. WILCOX and K. H. SCHA~ERN, Trans. Am. geophys. WI. 47, 152 (1966). 7. T. GOLD. J.peo~hvs. Res. 64. 1219 (1959). 8. B. U. O.'.&NE‘R~P and M. j. LAIR;, J. geophys. Res. 68, 131 (1963). 9. D. B. CHANG, L. D. PEARLSIEM and M. N. ROSENBLUTH, J. geophys. Res. 71, 351 (1966). 10. L. A. FRANK, J.geophys. Res. 71,4631 (1966). 11. J. J. ANGERAMIand D. L. CARPEK~R, J. geophys. Res. 71,711 (1966). 12. B. LEHNERT,Phys. Fluids, 4, 847 (1961). 13. B. LEHNEKT,Phys. Fluids, 5,432 (1962). 14. K. V. ROBERTSand J. B. TAYLOR, Phys. Rec. Letters 8, 197 (1962). 15. D. A. HAMLM, R. KARPLUS, R. C. VIK and K. M. WATSON, J.geophys. Res. 66, 1 (1961). 16. D. W. SWIFT, J. geophys. Res. 70,306l (1965). 17. J. A. FUR, J.geophys. Res. 69, 123 (1964). Peaio.r~+Cornacrro npeAmwumewuM Mopf$onorwIecKwM AaIIIIHM, pacnaA, nonnpmIx CKflHIl~MOXeT6blTbpe3yJIbTaTOM HeyCTO~YIIBOCT~IIarpaIIii~enORCaKOJIb~eBOrOTOK3. TaKoc npeAnoJIomcHKe no;lBepraeTcfz KOJIWIeCTBeHHOMy aHanmy IIyTeM KayqeIim nOCJIeACTBIIfiCOOTIIOUIeHIlR AkICIIepCKIi,ImjlwiaIoIqero 3@$cKTb1 n3anMoAeikrBm BO;IHODI,IX ‘IPCTLIU, B TPKRW 3@jE!KTLJ KOIICWIO~ IIpOnOJAMOCTl4 IlOI?OC@phl I3 ~HIlOJIbHOM YKa3bmaeTcK. 9~0 npri IicJwim np~e~.w~b~x IroIiocQepHua 14 MBrHWTHOM IIOJIC. M’drHklTOC@2pIIbIX MC!mny

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