in the Magnetosphere

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 89, NO. A7, PAGES , JULY 1, 1984 Relations Between Polarization and the Structure of ULF Waves in the Magnetosphere DAVID J. SOUTHWOOD 1 AND MARGARET G. KIVELSON 2 Institute of Geophysics and Planetary Physics, University of California, Los Angeles Large-scale low-frequency ULF signals in the terrestrial magnetosphere are expected to have the structure of standing waves along the ambient magnetic field and to propagate across the field. By making simple assumptions regarding the wave form, we show that wave polarization in a plane perpendicular to the magnetic field B may be interpreted in terms of the signal structure across B. Two cases are distinguished, corresponding to a pure Alfvbn mode (transverse) wave and a purely compressional wave. Examining published ULF data, we find that many compressional signals appear to have transverse polarization more appropriate to the Alfv6n mode. We conclude that the compressional signals are commonly coupled to Alfvbnic disturbances, but there is evidence of purely Alfv6nic signals at times. INTRODUCTION The use of three-dimensional matrix techniques [Means, 1972; Samson, 1972; Arthur et al., 1976; McPherron, 1979] for magnetospheric wave studies is now fairly standard. In particular, there has been interest in their application to ULF signals as the references indicate. Olson and Samson [1979] and Samson [1982] have extended the use of such techniques by generalizing the notion of polarization state to allow for the nonplanar nature of ULF geomagnetic signals originating in the terrestrial magnetosphere. Olson and Samson ] tested Hughes and Southwood's [1976] theoretical model of the magnetic field pattern at the earth's surface generated by driven field line resonance in space [Southwood, 1974; Chen and Hasegawa, 1974]. In a similar spirit, Samson [1982] generated and then tested a simple model for the large-scale pattern of Pi 2 ULF signals, the pulsation type intimately associated with magnetospheric substorm onsets. As yet, little use has been made of the techniques introduced by Samson in the analysis of ULF data obtained in space, although it is planned (R. L. McPherron, private communication, 1983). This is partly explained by the absence of published theoretical predictions concerning polarization states. Such is the gap between theory and experiment that some published ULF three-dimensional spectral matrix analysis has been interpreted using the assumption that the wave is planar. The origins of the technique in optics [Born and Wolf, 1964] make this understandable, but it is misleading; the scale size of ULF signals is such that it is unreasonable to start from the notion of plane waves. A recent review of ULF wave theory is given by Southwood and Hughes [1983]. Field line resonance theory and its subsequent developments form the most developed paradigm for ULF signals. The theory has had much success, especially with ground-based data sets. However, as Southwood and Hughes [1983] make clear, there are good reasons for believing that other mechanisms are also important in the ULF band. Other excitation mechanisms carry with them different Also with Department of Physics, Imperial College of Science and Technology, London. 2 Also with Department of Earth and Space Sciences, University of California, Los Angeles. Copyright 1984 by the American Geophysical Union. Paper number 4A /84/004A expectations concerning relative phase and amplitude distributions among Cartesian components, i.e., different expectations concerning polarization states. By and large, theoretical studies of other excitation mechanisms, such as drift instabilities or other internally driven instabilities (see, e.g., Hasegawa [1969], Southwood et al. [1969], Southwood [1973, 1976], Lin and Parks [1978, 1982], and Walker et al ]), have not concentrated on polarization expectations. However, spacecraft data, in particular from synchronous orbit region, leave us with a knowledge of the signal polarization. What we propose here is a synthesis of some very simple theoretical ideas and constraints with the existing experimental knowledge. Our aim is to outline polarization states worthy of further analysis and to indicate how one may interpret polarization data. Our perhaps unexpected conclusion is that the polarization expected for localized Alfv6n (or transverse) mode signals may have much relevance to many of the compressional signals observed in geosynchronous vicinity and beyond. MHD WAVES At high enough ULF frequency, the plane wave approximation is a good assumption in the absence of any contrary information (e.g., a nearby localized source). Spectral matrix analysis yields a plane in which the major perturbation lies. The wave propagation vector is normal to the plane. Provided the polarization is elliptical, the propagation direction (but not its sense) is determined. However, much below the ion gyrofrequency, the expected polarization of the two wave modes that can occur in a uniform cold plasma is linear rather than elliptical (see, e.g., Dungey [1968] and Southwood and Hughes [1983]). The same consideration applies in compressible magnetohydrodynamic (MHD) waves where the three modes (fast, slow, and transverse) have distinct linear polarization if they are planar. Linear signal polarizations are reported somewhat rarely in the magnetosphere, and thus assumptions such as signal planarity or plasma uniformity need be questioned. Let us here examine planarity and let us start by noting that two of the MHD waves share the special feature of being field guided. The transverse mode is strictly guided (i.e., group velocity is along B), the slow only approximately so. A consequence of the guidance is that complicated wave amplitude and phase structure can be sustained perpendicular to B even far from the source along flux tubes that connect to the source without affecting the harmonic nature of the signal. To see

2 5524 SOUTHWOOD AND KIVELSON' ULF STRUCTURE AND POLARIZATION y We illustrate these results in Figures 1 and 2. Figure 1 shows by means of contours a schematic variation of amplitude and phase with the coordinates x and y. No particular significance is claimed for the chosen pattern. Phase is shown varying linearly with y. A more complicated amplitude pattern is shown. The contours show a general decrease, say, with x but also a falling away in amplitude with y on each side of a maximum in the center of the diagram. Gradients of b and a are shown at two points. Two points, A and B, are marked and possible forms of polarization derived from (6) at these points are shown in Figure 2. At A the phase and amplitude gradients are at right angles (as in (4) and (5)), while this is not so at B. For convenience we have written oh'(y) = o Fig. 1. Schematic variation of phase tp and amplitude a. Contours of phase are dotted; contours of amplitude are continuous. a' (ln a)= O why this is so, consider the Alfv6n wave dispersion relation in a uniform magnetic field. For a wave of frequency co and wave vector k with components kll and k_ along and across the background field, B = œb, kll 2A2 (1) where A is the Alfv6n velocity. As only kll is involved, the variation perpendicular to the background field B has no impact on the frequency. However, what is significant for our study here is that the polarization does depend strongly on the form of variation across the field. The wave magnetic field lies in the (x, y) plane. As v. b = o (2) b can be written in terms of a stream function, ½t, as b = [,8½r l_ c y 8½r ] ', 0 (3) Now say the phase of b varies only with y, and the amplitude with x. Then we can write where a and p are real. Hence ½ r = a(x) ei*(y) (4) b ic '(y) _ (5) by (d/dx)(ln a) The derivatives of b and a are real. The wave magnetic polarization is thus fully determined by wave structure perpendicular to B, and in this case b,, and by are in quadrature. Thus the signal is elliptically polarized with major axis in the x or y direction. The sign and size of the ellipticity are functions of the scale in x and the wavelength in y. The magnetic vector will always tend to align perpendicular to the direction in which the signal varies most rapidly in amplitude or phase. The amplitude and phase variation specified by (4) is a special case. The most general case is given by specifying y as the direction in which phase varies locally perpendicular to B and by allowing the amplitude a to depend on both x and y. Then one has -- (ln a) = 7 and thus at point A, 7-0. The polarization ellipses shown in Figure 2 correspond to various conditions on c,, and 7. In Figure 2a, as for points such as A in Figure 1, 7 = 0. It has also been assumed that 101 > Il. Thus the ellipse major axis is aligned with the y axis. If the relation between the gradient scales of phase and logarithmic amplitude were reversed {ll > 101), the ellipse would be oriented with major axis aligning with the amplitude gradient, i.e., the x axis. Circular polarization corresponds to the special case = c. The consequence of phase and amplitude gradients having a component in common (i.e., not being at right angles) is immediately evident in Figure 2b; the ellipse major axis is tilted with respect to the coordinate axes. The ellipticity itself is a function of the relative size of 101, Il, and 171. If is very small, the signal adopts linear polarization aligned perpendicular to the gradient of a. In the other extreme where phase variation completely dominates the gradient, linear polarization is also expected, but aligned perpendicular to the phase gradient. Two intermediate cases are illustrated in Figures 2b and 2c. In Figure 2b, > I1, dominant variation is in amplitude, and the ellipse major axis is tilted to align almost at right angles to the local gradient in amplitude. In Figure 2c, I/1 > 171. The polarization is more circular. If 101 > I1, (a) by by bx {b) b i p' + (c¾c3y)(ln a) - (6) by (a/ax)(ln a) If there is some phase variation across B, the signal is still elliptically polarized. However, in this general case, the major axis is tilted at an angle with respect to the (x, y) axes. (c) Fig. 2. (a) Polarization at. point A in Figure 1 if 101 > I l (see text for details). (b) Polarization at point B in Figure 1 if I/ > I 1-(c) Polarization at point B if 101 I l > 171.

3 SOUTHWOOD AND KIVELSON' ULF STRUCTURE AND POLARIZATION 5525 then the major axis is nearly perpendicular to the local gradient in amplitude (roughly in the x direction). The slight variation of amplitude in the direction of phase variation causes the tilting of the ellipse major and minor axes with respect to x and y axes. The Alfv n mode is distinguished by carrying current parallel to B. Evidently from (3) and Amp re's law, V2½T = --tt0j (7) Transient sources of field-aligned current can excite Alfv n waves [Southwood and Hughes, 1983]. The current j can be thought of as the source of the signal. Any phase variation in b and ½ must be present also in j. Conversely, when source mechanisms for Jz have no spatial phase variation, no phase variation is imposed in the signal (or = 0), and a linearly polarized magnetic perturbation is produced. In fact, purely linearly polarized signals are very rarely reported, as was noted earlier. Both fast and slow signals have zero parallel current (see, e.g., Dungey [1968] and Southwood and Hughes [1983])' thus in a straight field, B, a compressional signal has - (8) y x and so the transverse field components take the form (bx, b) = ( ½c k,2x ' ½c.',2y / (9) Now let us assume, much as we did before, that then, from (9), one has ½c = a(x, y)e bx ( / x)(ln a) - = by ic)' + ( / y)(ln a) Hence the transverse components of a compressional (fast or slow) mode are also elliptically polarized if there is both perpendicular amplitude and phase variation. However, in this case, the major axis tends to align with the direction of the direction of maximum spatial (including both phase and amplitude) variation of ½c. In particular, for waves with small phase variation, the wave major axis aligns parallel to the maximum wave amplitude variation. This is exactly opposite to the Alfv n wave case above. Should phase and amplitude variation be at right angles (cf.(4)), then the major and minor ellipse axes align with the (x, y) axes. It is apparent above that the transverse ellipticity of a compressional wave is controlled very differently from the ellipticity of a transverse signal. Although we introduce an important reservation below, a priori the transverse component of a compressional signal is not hard to characterize, for the compressional modes have another magnetic field component, b:. As equation (9) shows that 2½ c x 2 V.b=0 y2 Now let us say one has ½c varying as a(x, z) i*(y' ), i.e., phase and amplitude variation are at right angles in the (x, y) plane. One then has x 2 -- k, r3yj + i a z c3y 2 c3z (11) If the phase variation is fairly smooth (wavelength not a strong function of y), then c (12) c y >> 7 c y If (12) holds, b / z shares the phase of ½c, and thus the phase relationship between b and ½c depends on the signal phase variation along B. For a wave with a component of phase propagation along B, r3b /r3z is in quadrature with b, and if (12) holds, then b is in quadrature with ½c. It follows from (9) that b is in (or 180 ø out of) phase with by and in quadrature with b. It is far more likely, however, that a low-frequency ULF signal does not propagate along B. The equatorial Alfv n speed is typically,- 103 km/s, as is the ion thermal speed in the outer magnetosphere. Hence even a wave with a period as short as 30 s has wavelength of,- 5 earth radii, a scale comparable with the magnetospheric scale size. As long as reflection at the ionosphere is good and damping in the intervening medium is weak, there will be little phase variation along B and waves will have standing structure along B. Thus in a compressional signal for which (12) holds, one expects b to be in phase with b /c z and thus with ½c. Hence from (9) and (11), b is in phase (or 180 ø out of phase) with b and in quadrature with by. The magnetic polarization is thus still describable with an ellipse, but the normal to the ellipse is tilted in the x, z plane as illustrated in Figure 3. Now a potentially important difference between a compressional signal and the transverse Alfven wave is that the compressional wave may not be guided, and thus the signal vari- ation perpendicular to B may not be arbitrary. Consider the fast mode in a uniform cold plasma. The dispersion relation, involving co, kll, k, and ky, is 02 = k2a 2 = kll 2A2 + (k, 2-3- ky 2)A2 and as a result, any harmonic variation in time at frequency co must only be associated with harmonic variation in x, y, and z. Consider a situation where the signal phase varies in the y direction, but say amplitude varies with x and z' ½½ would take the form ½c = a(x, z)e i*(y) However, if the signal is to have frequency co, a(x, z) and p(y) are necessarily constrained to take forms such as c)(y) = kyy + c a(x, z) = ao sin (kxx + d) sin (kllz + e) where a0, c, d, and e are constants and k, ky, and kll are related by the dispersion relation. Here k and kll are real. The dispersion relation takes on a particularly significant form for magnetospheric application when ky 2 > co2/a2 for then k is imaginary, and the wave has a surface wave form (see, e.g., Uberoi [1982]), where ½c = a0 sin ( k II z + c)e ikyy e - k = (ky 2-1- kll 2 _ co2/a2)1/2 The wave polarization produced by such a compressional signal which may have co2,, kll2a 2 (i.e., frequency as low as a standing Alfv n wave) is closely akin to the variation in the

4 5526 SOUTHWOOD AND KIVELSON' ULF STRUCTURE AND POLARIZATION Fig. 3. b z bx Three-dimensional sketch illustrating the orientation of a standing compressional mode polarization ellipse. field line resonance signal far from resonance (Southwood [1974] and Chen and Hasegawa [1974]' see also Southwood and Hughes [1983]). Substitution in (10) shows that the transverse polarization is elliptical with the semimajor axis along y and with sense determined by the sense of propagation in y and the sign of the gradient in x. The compressional component bz is in phase with + b,, as in Figure 3. COUPLING OF COMPRESSIONAL AND ALFV N MODES In the second section of this paper we treated the transverse polarization of a transverse mode wave and of a compressional mode wave separately and contrasted the results. Evidently, the transverse components of any wave form a twodimensional field. There is a well-known theorem of vector field theory that any field can be split uniquely into a solenoidal and an irrotational part (the Helmholtz theorem' see, e.g., Morse and Feshbach [1953]). Conditions (2) and (8) show that the transverse wave field is solenoidal and the transverse components of a compressional mode signal are irrotational, respectively' thus the two cases we have treated cover all possibilities. However, any given signal that is observed may not be purely transverse or compressional. In particular, there are many theoretical reasons for expecting coupling between Alfv6n and compressional modes. Inhomogeneity couples the Alfv6n and fast modes in a cold plasma [Dungey, 1968]. Hot plasma effects commonly lead to coupling (see, e.g., Lin and Parks [-1978-], Southwood [1976, 1977-], and Walker et al. [1982]). The coupling expected between compressional and transverse modes makes any interpretation of compressional wave signal polarization data ambiguous. There is no way of establishing the degree of coupling by use of magnetic polarization data alone. However, as we show in our later discussion, further information can be used to clarify the situation. Indeed, on the basis of circumstantial evidence associated with observed compressional signal types, we shall conclude that compressional signals commonly are strongly coupled with Alfv n signals. [1970], using the same instrument, and many studies have followed. Polarization of pulsations seen on the synchronous orbit ATS 6 spacecraft has been studied by Tonegawa [1982]. In Figure 4 we show the polarization reported by Tonegawa for a transverse signal largely polarized in the azimuthal direction. The y coordinate is east-west perpendicular to B, z is along B, and x is perpendicular to B in the meridian [Tonegawa, 1982]. The signal's largest amplitude is in the y component, z has the smallest amplitude; the signal is effectively transverse. The discussion of previous sections leads one to conclude that the most rapid variation of wave phase and/or amplitude is in a direction roughly aligned with the meridian (x), as required by (5) or (6). The small ellipticity suggests that the scales of variation of amplitude and phase are very different, but no argument is put forward in the previous section for deducing which is dominant. Other considerations must be brought in order to decide. A powerful argument that the signals have phase varying in azimuth (slowly) and amplitude varying in the meridian (rapidly) follows from observations of Takahashi and McPherron [1982]. They showed that spectra of the transverse signals vary slowly as ATS 6 moves through local time and indeed that multiple harmonics are generally present. It is suggested that the signals are Alfv6n waves with standing structure along local magnetospheric flux tubes. Because Alfv6n wave eigenfrequencies vary strongly in the meridian but there is clear fairly narrow spectral structure detected on the spacecraft, one concludes that the amplitude of a signal at any given frequency must be localized in the meridional coordinate (x); thus phase variation is largely azimuthal, and east-west wavelengths are large. This notion in turn fits well with the fact that ATS 6 sees signals for extended periods; the signals have a large azimuthal extent. All in all, the simplest polarization interpretation fits well with all other known features of the waves. Figure 5 is also based on the work of Tonegawa [1982] and shows a polarization plot of a compressional ULF wave seen on ATS 6, typical of a class seen predominantly in the afternoon hours; x, y, z coordinates are defined as before. The signal is highly elliptical in the plane transverse to B, and the ellipse aligns with the x coordinate. In the meridian the polarization is also elliptical. The ellipse is strongly tilted; z has a small phase lead over x that is much less than z /2. If the signal is purely compressional (no jz), then the transverse polarization leads one to the conclusion that the prime signal variation is in the meridian. As the z and x components are closer to being in phase than quadrature, one would conclude from our description in the previous section that if there is standing structure along B, then the variation in the meridian is pri- X UT Z EXAMPLES OF MAGNETOSPHERIC WAVES Synchronous orbit has provided data for very productive studies of ULF waves. As early as 1969, Curnrnrnings et al. [1969], using the University of California, Los Angeles (UCLA), magnetometer data, reported the regular occurrence of purely transverse oscillations on the ATS 1 spacecraft, using the UCLA magnetometer data. Large-amplitude compressional oscillations were reported by Barfield and Coleman LH RH TRANSVER: PLANE MERIDIAN PLANE Fig. 4. Polarization of a typical example of an azimuthally polarized transverse wave recorded at geosynchronous orbit [after Tonegawa, 1982]. The plane of the polarization ellipse is tilted at an acute angle to the (bx, by) plane. The dotted lines are in the plane of the ellipse and indicate its major and minor axes. ß

5 SOUTHWOOD AND KIVELSON: ULF STRUCTURE AND POLARIZATION 5527 RH x TRANSVERSE UT Z :::::::::.-<... PLANE LH MERIDIAN PLANE Fig. 5. Polarization of a typical example of a compressional meridionally polarized wave recorded in the afternoon hours at geosynchronous orbit [after Tonegawa, 1982]. marily in amplitude rather than phase. The polarization is in fact not inconsistent with the signal being a compressional meridional (poloidal) oscillation with very small east-west wave number. There are two strong arguments against the latter conclusion. First, east-west phase measurements on signals similar to the Tonegawa example were made by Hughes and coworkers [Hughes et al., 1978, 1979]. These signals have low coherence lengths and thus a fortiori short wavelengths. Such signals must admit large phase variation east-west. As Hughes et al. [1978] report very high coherence and zero phase difference in meridional components during the period where spacecraft were separated radially, it seems reasonable to assume the phase variation east-west is the dominant signal variation. If the same is assumed for the Tonegawa example, the transverse polarization of the signal is more or less perpendicular to the direction of phase variation, i.e., the orientation is appropriate to a transverse mode signal. Hence we conclude that there must be strong coupling between Alfv6n and compressional modes. There is a further argument to bolster the view that the compressional signals analyzed by Tonegawa [1982] have a large coupled transverse mode component. Let us assume locally b c bo(z)e ik- 'r Hence from V ß b = 0 it follows that dboz ikz.b0+- -z =0 If we accept that the signal has standing structure along B, then dboz bll dz LRe where L is the magnetospheric L parameter, and R e is an earth radius. The polarization ellipse shows that bll b x Now let the angle between the vector k and the major axis of the transverse polarization ellipse be. We then have 1 Icos << 1 k LRe i.e., the phase variation must be at a large angle to the perpendicular magnetic field component. We thus claim that the afternoon sector meridionally polarized Pc 4 pulsations have a large Alfv6n mode component. A,<: major implication that follows from our earlier discussion is that large field-aligned current components are present in the signals. The late afternoon compressional signals reported at synchronous orbit are not the only examples of compressional signals reported in the literature where there seems a case for believing substantial transverse mode signals are also present. One very interesting case where evidence is very strong concerns magnetotail vortices [Hones et al., 1978; Saunders et al., 1983, and references therein]. Saunders et al. [1983] find the polarization of a vortex event to be linear transverse to B and elliptical in a plane containing B. The phase difference between the perpendicular and parallel magnetic perturbations is,-, 120 ø. However, using energetic particle data, Saunders et al. [1983] can assess the wavelength and the direction of phase propagation perpendicular to B. A figure from Saunders et al.'s paper, reproduced in Figure 6, shows a schematic of what was deduced. The ambient magnetic field is perpendicular to the plane of the diagram. The direction of wave propagation is at right angles to the plane in which the wave is polarized. The two spacecraft ISEE 1 and 2, from which the field and plasma measurements were obtained, are separated by,-,450 km in a direction roughly at right angles to the predicted phase variation. Identical signals are seen at the two spacecraft, as would be expected. The theory for purely compressional waves would predict that the major variation perpendicular to B was in the direction of the transverse field perturbation. Because the polarization is linear, one would predict also that the variation is entirely in phase or amplitude, but not in both. The wavelength deduced by Saunders et al. is,-, 5 x 103 km. No significant amplitude or phase change is detected at right angles to the apparent phase propagation direction between the two spacecraft. Thus the major variation perpendicular to B is not in the direction of the transverse field perturbation, and one concludes that strong compressional-alfv6n mode coupling is occurring in this case also. Another class of compressional signal seen at synchronous orbit has been documented by Kremser et al. [1981]. The transverse polarization is elliptical with major axis in the meridian. The meridional component is in phase with the dominant compressional component. Thus the polarization is unlike that of the magnetotail vortices. Similar events have been reported by Barfield et al. [1972], Hedgecock [1976], and Barfield and McPherron [1978]. Walker et al. [1982] study one event in detail and in addition identify it in ionospheric electric field data recorded by the STARE radar. The STARE data show that the east-west wavelength is short (,-, 1 Re at the equatorial plane). The signal does not seem to be extremely localized in latitude, and thus once again the major transverse field component is at right angles to the major sl atial variation across B (the east-west phase variation). Once again we have a case of a compressional signal exhibiting the transverse polarization of the Alfv6n mode. Once again the signal must contain field-aligned current and be due to a coupling of compressional and Alfv6n waves. Walker et al. [1982] also invoked coupled modes to interpret the waves but did not comment on the relevance of wave polarization to their interpretation. CONCLUDING REMARKS We have outlined features of the expected polarization states of ULF magnetic signals observed on spacecraft in the magnetosphere. ULF signals are believed to be hydromagnetic

6 5528 SOUTHWOOD AND KIVELSON: ULF STRUCTURE AND POLARIZATION //\ X MVA (NORTHWARD) EE 2 \ / o DIRECTION YHVA (SUNWARD) / I P PAGATION -- T NSVERSE WAVE OSCILLATI m l TlON (NOT O SCALE) /. DIRECTION Fig 6. Traverse wave schematic of December 11, 1977, vortex event. Although the satellites arc separated km per ndicular to B, no phase discrete is sccn between the satellites because their separation vector, R, is almost parallel to the direction of transvcr wave polarization. or MHD waves, waves which are linearly polarized if they are plane waves and propagate in a uniform field. However, the magnetosphere is nonuniform on expected MHD wave scales, and it is not appropriate to assume observed oscillations are plane waves. Fairly complicated three-dimensional polarizations are recorded in ULF magnetic signals, which also emphasizes the nonplanar nature of the signal. We have pointed out that very general considerations lead one to some simple expectations concerning wave polarization. We considered two classes of signal, transverse Alfv6n and compressional. In either case, polarization perpendicular to B is a function of the variation across the field. However, the major axis of the noncompressional signal ellipse tends to align at right angles to the direction of maximum signal gradient, while the major axis of the ellipse traced by the transverse projection of the purely compressional signal tends to align along the direction of maximum signal gradient. Examination of commonly observed classes of ULF signal revealed that the transverse waves seen at synchronous orbit conformed:well w th our: notions of transverse polarization. However, the :polari.zat;aan,.- ed for. ver!al different: types of ULF CømpreSsiønal signal taken in Cønjlunctiøn With Othe r evidence is inconsistent with the expectations advanced for purely compressional signals. We believe in each such case that there is strong coupling between A!fv6n oscillations and compressional components Theoretically ' such coupling is ex- pected an d can be:achieved byl høt Plasm a ffe t s or ta rough inhomogeneity. Our major conclusion is that a signal with polarization appropriate to the Alfv6n mode contributes sig- nificantly to all ULF signals we have examined, whether the signal be purely transverse (Alfv6n) or contain compressional components. Future interpretations of polarization analysis should recognize this feature of magnetospheric waves. Acknowledgments. We are grateful to R. L. McPherron for suggesting that a paper on this topic would be useful and to C. T. Russell for disagreeing. This work was supported by the National Science Foundation Division of Atmospheric Sciences under grant AMT The Editor thanks the two referees for their assistance in evaluating this paper. REFERENCES Arthur, C. W., R. L. McPherron, and J. D. Means, A comparative study of three techniques for using the spectral matrix in wave analysis, Radio Sci., 11, 833, Barfield, J. N., and P. J. Coleman, Jr., Storm-related wave phenomena observed at the synchronous, equatorial orbit, J. Geophys. Res., 75, 1943, Barfield, J. N., and R. L. McPherron, Storm time Pc 5 magnetic pulsations observed at synchronous orbit and their correlation with the partial ring current, J. Geophys. Res., 83, 739, Barfield, J. N., R. L. McPherron, P. J. Coleman, Jr., and D. J. South- Wood, Storm-associated Pc 5 micropulsation events observed in the synchronous equatorial orbit, J. Geophys. Res., 77, 143, Born, M., and E. Wolf, Principles of Optics, pp , Pergamon, New York, Chen, L., and A. Hasegawa, A theory of long-period magnetic pulsa- tions, 1, Steady state excitation of field line resonance, J. Geophys. Res., 79, 1024, Cummings, W. D., R. J. O'Sullivan, and P. J. Coleman, Jr., Standing Alfv6n waves in the magnetosphere, J. Geophys. Res., 74, 778, Dungey, J. W., Hydromagnetic waves, in Physics of Geomagnetic Phe-

7 SOUTHWOOD AND KIVELSON.' ULF STRUCTURE AND POLARIZATION 5529 nomena, edited by S. Matsushita and W. H. Campbell, p. 913, Academic, New York, Hasegawa, A., Drift mirror instability in the magnetosphere, Phys. Fluids, 13, 2642, Hedgecock, P. C., Giant Pc5 pulsations in the outer magnetosphere: A survey of HEOS-1 data, Planet. Space Sci., 24, 921, Hones, E. W., Jr., G. Paschmann, S. J. Bame, J. R. Asbridge, N. Sckopke, and K. Schindler, Vortices in the magnetospheric plasma flow, Geophys. Res. Lett., 5, 1059, Hughes, W. J., and D. J. Southwood, An illustration of modification of geomagnetic pulsation structure by the ionosphere, J. Geophys. Res., 81, 3241, Hughes, W. J., R. L. McPherron, and J. N. Barfield, Geomagnetic pulsations observed simultaneously on three geostationary satellites, J. Geophys. Res., 83, 1190, Hughes, W. J., R. L. McPherron, J. N. Barfield, and B. N. Mauk, A compressional Pc 4 pulsation observed by three satellites in geostationary orbit near local midnight, Planet. Space Sci., 27, 821, Kremser, G., A. Korth, J. A. Fejer, B. Wilken, A. V. Gurevich, and E. Amata, Observations of quasi-periodic flux variations of energetic ions and electrons associated with Pc 5 geomagnetic pulsations, J. Geophys. Res., 86, 3345, Lin, C. S., and G. K. Parks, The coupling of Alfv6n and compressional waves, J. Geophys. Res., 83, 2628, Lin, C. S., and G. K. Parks, Modulation of energetic particle fluxes by a mixed mode of transverse and compressional waves, J. Geophys. Res., 87, 5102, McPherron, R. L., Dynamic cross correlation studies of wave particle interactions in ULF phenomena, Ann. Telecornrnun., 34, 1, Means, J. D., Use of the three-dimensional covariance matrix in analyzing the polarization properties of plane waves, J. Geophys. Res., 77, 5551, Morse, P.M., and H. Feshbach, Methods of Theoretical Physics, pp. 53 and 153, McGraw-Hill, New York, Olson, J. V., and J. C. Samson, On the detection of the polarization states of Pc micropulsations, Geophys. Res. Lett., 6, 413, Samson, J. C., Three-dimensional polarization characteristics of high- latitude Pc 5 geomagnetic micropulsations, J. Geophys. Res., 77, 6145, Samson, J. C., Pi 2 pulsations: High-latitude results, Planet. Space Sci., 30, 1239, Saunders, M. A., D. J. Southwood, T. A. Fritz, and E. W. Hones, Jr., Hydromagnetic vortices, 1, The 11th December 1977 event, Planet. Space Sci., 31, 1099, Southwood, D. J., The behaviour of ULF waves and particles in the magnetosphere, Planet. Space Sci., 21, 53, Southwood, D. J., Some features of field line resonances in the magnetosphere, Planet. Space Sci., 22, 483, Southwood, D. J., A general approach to low-frequency instability in the ring current plasma, J. Geophys. Res., 81, 3340, Southwood, D. J., Localised compressional hydromagnetic waves in the magnetospheric ring current, Planet. Space Sci., 25, 549, Southwood, D. J., and W. J. Hughes, Theory of hydromagnetic waves in the magnetosphere, Space Sci. Rev., 35, 301, Southwood, D. J., J. W. Dungey, and R. J. Etherington, Bounce resonant interaction between pulsations and trapped particles, Planet. Space Sci., 17, 349, Takahashi, K., and R. L. McPherron, Harmonic structure of Pc 3-4 pulsations, J. Geophys. Res., 87, 1504, Tonegawa, Y., Compressional Pc 4 pulsations observed at synchronous orbit, Mere. Natl. Inst. Polar Res. Spec. Issue Jpn., 22, 17, Uberoi, C., A note on the existence of Alfv6n surface waves, Sol. Phys., 78, 351, Walker, A.D. M., R. A. Greenwald, A. Korth, and G. Kremser, STARE and GEOS 2 observations of a storm time Pc 5 ULF pulsation, J. Geophys. Res., 87, 9135, M. G. Kivelson and D. J. Southwood, Institute of Geophysics and Planetary Physics, University of California, Los Angeles, CA (Received November 29, 1983; revised March 14, 1984; accepted March 15, 1984.)