ULF waves in the magnetosheath

R. E. Denton

Physics and Astronomy Department, Dartmouth College, Hanover, New Hampshire

Contents

Abstract

1. Introduction

The magnetosheath is the region of interaction between the solar wind plasma and the Earth's magnetic field. The magnetosheath exhibits large inhomogeneity due to the stress of the solar wind dynamic pressure. Since this pressure is pushing nearly continuously on the magnetopause, the structure of the magnetosheath is in the roughest approximation time stationary. This makes it an ideal region for studying the effects of such inhomogeneity. Inhomogeneity has a crucial effect on the generation and propagation of ultra low frequency (ULF) waves. In turn, ULF waves have significant feedback on the macroscopic plasma.

The purpose of this paper is to review what we know about magnetosheath ULF waves. Our presentation is not totally comprehensive, but rather expresses our view of major issues in ULF wave studies as presented at the 1999 IAGA meeting [Denton, 1999]. Two recent reviews of a similar nature have been given by Schwartz et al. [1996] and Song and Russell [1997]. An outline of our paper is as follows: In section 2, we discuss methods of mode identification. In section 3, we discuss some important properties of the magnetosheath which relate to the generation and propagation of ULF waves. In section 4, we discuss ULF waves in the magnetosheath when the upstream conditions are quasi-parallel, and in section 5, we discuss ULF waves in the magnetosheath when the upstream conditions are quasi-perpendicular. Finally, we have a summary in section 6.

2. Methods of Mode Identification

Since the mode properties can be strongly modified by the kinetic nature of a plasma, it is best to use kinetic theory when making comparisons with observation for the purpose of mode identification [Denton et al., 1995a; Krauss-Varban et al., 1994]. At frequency f F_cp, where F_cp is the proton cyclotron frequency, up to four distinct modes can propagate in a relatively isotropic plasma: the three waves corresponding to the normal modes of MHD theory and the mirror mode. The mirror mode has zero phase velocity in a homogeneous plasma (though it can acquire a finite phase velocity when there is inhomogeneity [Johnson and Cheng, 1997]). The three modes with finite phase velocity are the magnetosonic/fast/whistler mode, the Alfvén/ion-cyclotron mode, and the ion-acoustic/slow/sound mode. The first term listed (i.e., "magnetosonic,'' "Alfvén,'' and "ion acoustic'') represents our preferred notation [Denton et al., 1995a] and the other terms have been used by other authors [for example, Krauss-Varban et al., 1994]. The terms "fast'' and "slow'' here are appropriate descriptions of the phase speed of the respective waves at low parallel beta b_||p 8 pp_||p/B₀² in CGS units, where p_||p is the proton pressure parallel to B, and B is the magnetic field. At high beta, what we call the "slow'' mode sometimes has the largest phase velocity [Denton et al., 1995a; Krauss-Varban et al., 1994]. Our use of the terms "slow'' and "fast'' here agrees with the nomenclature of Krauss-Varban et al. [1994], which was designed to use the same term to refer to the wave with similar fluctuations (transport ratios), regardless of phase speed. On the other hand, Gary and Winske [1992] and Lacombe et al. [1992, 1995] have retained the use of "slow'' and "fast'' to refer explicitly to phase speed. (It is easy to see why we would prefer not to use these terms.)

The linear modes are defined on dispersion surfaces as a function of the wave vector k. One can distinguish whether the modes are approximately quasi-parallel ( k approximately parallel to B ) or quasi-perp ( k approximately perpendicular to B ) [Denton et al., 1995a]. Both the magnetosonic/fast/whistler and Alfvén/ion-cyclotron modes are Alfvén-like for parallel propagation. In that case, the magnetosonic/fast/whistler mode is right hand polarized while the Alfvén/ion-cyclotron mode is left hand polarized. Both of these waves become more and more linearly polarized as k turns away from B. As discussed by Schwartz et al. [1996], identification of wave modes is hampered by a number of factors. Most of the theory is based on linear homogeneous theory, whereas the observed modes are observed in an inhomogeneous medium and are often significantly nonlinear. Perhaps the greatest problem is that there can be a mixture of different modes. Denton et al. [1998] found that in a number of cases, the identification of the wave mode was not certain.

Methods of mode identification use transport ratios, phase angle relations, and polarization information (see review by Schwartz et al. [1996] for an extensive list of transport ratios with references). Gary and Winske [1992] introduced the term "transport ratios'' to denote dimensionless ratios of the squares of fluctuating field and plasma quantities. One of the most commonly used transport ratios is the magnetic compressibility, the ratio of parallel to total magnetic fluctuations

(1)

where the angular bracket indicates an average (often calculated using the power spectrum at a particular frequency). This is expected to be large for the quasi-perpendicular magnetosonic (fast) mode and mirror mode, but small for the Alfvén mode. A quantity functionally equivalent to C_B was used by Anderson and Fuselier [1993] to distinguish Alfvén (ion cyclotron) waves from the mirror mode.

Two other useful transport ratios are the compressibility C_p

(2)

where dn_p and n_p0 are the fluctuating and equilibrium (slow time scale) proton density, respectively, and B₀ is the equilibrium magnetic field, and the Alfvén ratio R_Ap

(3)

where d v_p and V_A are the fluctuating proton velocity and equilibrium Alfvén speed B₀ / 4 pm_p n_p in CGS units, where m_p is the proton mass. Figure 1 is a dramatic demonstration of the effectiveness of these transport ratios for mode identification. Figure 1 shows the transport ratios C_p and R_Ap obtained for waves observed near the magnetopause (crosses). These waves were thought to be either the mirror mode or the ion acoustic (slow) mode based on the relative phase in dn_p and dB_|| (not shown). Based on the transport ratios in Figure 1, it is clear that these waves should be identified as the mirror mode.

A second important determining factor for wave identification is based on the phase difference between various fluctuating quantities. For the magnetosheath data of Figure 1, dn_p and dB_|| were shown to be 180 ^o out of phase. Such a phase relation exists for the quasi-perpendicular mirror and ion acoustic (slow) modes, but dn_p and dB_|| should be in phase for the quasi-perpendicular magnetosonic (fast) mode.

Polarization information can be very useful for determining the wave mode. In the Earth's ion foreshock (the region just outside the bowshock where ions reflected off the bowshock are observed), Alfvén-like waves are often observed. These may be left or right hand polarized (the latter is the quasi-parallel magnetosonic mode in our nomenclature), where the handedness indicates the direction of rotation of fluctuating quantities about the equilibrium magnetic field. In order to determine polarization, it is most beneficial to have multi-spacecraft observations. Russell et al. [1987] used simultaneous observations by the ISEE 2 and AMPTE/UKS spacecraft to the determine polarization of foreshock waves. Blanco-Cano and Schwartz [1997], using single spacecraft data, measured a number of transport ratios to identify these waves; unfortunately these transport ratios did not enable them to distinguish the waves. Their identification was based mainly on a determination of polarization which depended on minimum variance analysis (to determine the direction of k ) and properties of the cross-helicity which enabled them to eliminate the sign ambiguity (  ) [Blanco-Cano and Schwartz, 1997]. Using the minimum variance direction for magnetic fluctuations is a common method to infer the direction of k (based on Faraday's law), but can be misleading if there is a mixture of modes (see [Denton et al., 1996]). Use of multi-spacecraft data is therefore highly desirable for determining wave polarization.

3. Properties of the Magnetosheath

The particular properties of the magnetosheath play a large role in the generation, propagation, and modification of magnetosheath ULF waves. Whether the upstream conditions are "quasi-perpendicular'' or "quasi-parallel'' depends on the direction of the interplanetary magnetic field (IMF) when the solar wind plasma reaches the bowshock. (The use of "quasi-perpendicular'' and "quasi-parallel'' here should not be confused with their use to describe the relative orientation of k and B in "quasi-perpendicular'' and "quasi-parallel'' wave propagation.) By upstream conditions, we mean then that if we were to follow the convecting plasma backward in time, the IMF would be "quasi-perpendicular'' or "quasi-parallel'' at the time that the plasma crossed the bowshock. The plasma convects through the magnetosheath to its present position maintaining some general characteristics resulting from that orientation. The plasma with quasi-perpendicular upstream conditions (when the IMF is roughly aligned with the bowshock, or perpendicular to the bowshock normal) exhibits the most regular structure. The value of B₀ typically increases from the bowshock to the magnetopause. Sometimes, particularly for low magnetic shear [Phan et al., 1994], the density n_p0 decreases near the magnetopause; this region of decrease is sometimes called the plasma depletion layer. Field lines in the magnetosheath drape around the magnetopause leading to field line curvature.

When the upstream conditions are quasi-perpendicular, the plasma typically exhibits temperature anisotropy T _p / T_{| p} > 1, where T _p and T_||p are the proton temperatures respectively perpendicular and parallel to B [Phan et al., 1994]. The region close to the bowshock exhibits a large anisotropy due to the fact that ions entering the magnetosheath through the bowshock roughly have their large bulk flow (solar wind) velocity converted into a (perpendicular) gyrovelocity [Sckopke et al., 1990]. Other effects leading to temperature anisotropy are compression of flux tubes as they press up against the magnetopause and their lengthening as they drape around the magnetopause (see Figure 2) [Denton et al., 1994c]. How these effects lead to the development of temperature anisotropy can be easily seen from the double adiabatic equations [Chew et al., 1956], which can be expressed as T _p A^-1 and T_||p L^-2, where A and L are the area and length of a flux tube, respectively [Denton et al., 1994c]. (While double adiabatic theory does not by itself adequately describe temperature evolution in space plasmas, a modified form of the theory including energy exchange due to ion cyclotron waves has been relatively successful [Denton et al., 1994c, 1995b].) Temperature anisotropy which develops when the upstream conditions are quasi-perpendicular leads to the growth of ion cyclotron and mirror waves [Anderson et al., 1994].

When the upstream conditions are quasi-parallel, (so that the IMF is roughly aligned with the bowshock normal), the plasma typically has large plasma beta and is very turbulent. The high beta conditions arise from the fact that the shocked solar wind plasma is compressed, leading to large increase in plasma pressure, but the quasi-parallel magnetic field is not (this is precisely true only when the IMF is exactly quasi-parallel). When the upstream conditions are quasi-parallel, the magnetic field exhibits large amplitude fluctuations which accompany the fluctuations in thermal plasma pressure, the latter of which lead to the dominant force density in the high beta magnetosheath. The direction of the magnetic field is then ill-defined, as are the separate values of T _p and T_||p. A spacecraft within the magnetosheath may observe alternating periods of time for which the magnetosheath exhibits quasi-perpendicular or quasi-parallel-like upstream conditions, as illustrated in Figure 3, where the periods of large b_||p 10 represent quasi-parallel upstream conditions. Another diagnostic for quasi-parallel upstream conditions is the presence of elevated fluxes of energetic He²⁺ [Fuselier et al., 1991].

4. Waves for Quasi-Parallel Upstream Conditions

Typically, broad band turbulent waves are observed when the upstream conditions are quasi-parallel, with power peaking in the Pc3-4 range (period from 10-150 s) [Engebretson et al., 1991, and references therein; see their Plate 4 for an example of broad band turbulence]. These waves are thought to be caused, at least in part, by the ion foreshock waves mentioned in Section 2 (see papers in [Engebretson et al., 1994], particularly [Krauss-Varban, 1994]). They are also generally thought to be the source of the toroidal Alfvén wave (with magnetic fluctuation in the azimuthal direction) harmonics observed in the magnetosphere [Anderson, 1993, and references therein], though the path the wave power takes to get to the magnetosphere is still a matter of debate (Mark Engebretson, private communication, 1999).

A statistical survey by Anderson and Fuselier [1993] showed that Alfvén/ion cyclotron and mirror waves could be observed when the upstream conditions are quasi-parallel, though the most likely situation was to observe broadband waves. Even when there is no explicit evidence for the existence of ion cyclotron waves amid the broad band turbulence, there is indirect evidence that ion cyclotron waves are present (anisotropy-beta correlation; see Section 5.2) [Fuselier et al., 1994].

Little has been done theoretically to describe the high beta waves. A recent paper applies an approach based on magnetohydrodynamics (MHD) [Song et al., 1998], though it may be difficult to justify the use of MHD and the assumption that the equilibrium magnetic field is steady.

5. Waves for Quasi-Perpendicular Upstream Conditions

When the upstream conditions are quasi-perpendicular, the magnetosheath exhibits more regularity in macroscopic structure and in the ULF waves observed. We consider the plasma as it convects from the bowshock to the magnetopause and the characteristic waves of each region. One should keep in mind that not all the waves described here may be present at any one time.

5.1. Within the Bowshock

Since the bowshock is itself a manifestation of the quasi-perpendicular magnetosonic (fast) mode reflecting off the magnetopause, it is not too surprising that Lacombe et al. [1992] identified this wave within the bowshock structure. They also identified both quasi-parallel and quasi-perpendicular Alfvén waves; these may be due to fluctuations at the bowshock.

5.2. Outer Magnetosheath (Just Downstream From the Bowshock)

A large proton temperature anisotropy T _p T_||p develops just downstream of the bowshock [Sckopke et al., 1990, and references therein] due to the conversion of solar wind bulk flow energy into energy associated with the (perpendicular) gyromotion. An anisotropic plasma can be unstable to the ion cyclotron or mirror instabilities [Gary, 1993]. The instability of the plasma increases with increasing beta b_||p and temperature ratio T _p / T_{| p}. At low b_||p, a large value of T _p / T_{| p} is required for instability, while at high b_||p, a plasma can be unstable with a low value of T _p / T_{| p}. Whether the ion cyclotron or mirror mode is dominant depends on the values of b_||p and T _p / T_{| p}. Generally the ion cyclotron mode is favored for low b_||p and large T _p / T_{| p}, while the mirror mode is favored for high b_||p and low T _p / T_{| p} [Denton et al., 1994a; Gary et al., 1993]. While T _p increases steeply across the quasi-perpendicular bowshock, does not. The result is that T _p / T_{| p} is large and b_||p T_||p relatively low just downstream of the bowshock so that ion cyclotron waves naturally grow.

Figure 4 demonstrates the growth of ion cyclotron waves in the post bowshock region. There are two bowshock crossings in Figure 4; we concentrate on the first one at 0655 UT. Following this crossing, T _p has become very large, while T_||p has increased, but not nearly as much. Consequently T _p / T_{| p} is very large. Ion cyclotron waves have polarization which varies from left hand polarized for parallel (  k B ) propagation to nearly linearly polarized for highly oblique waves [Denton et al, 1993]. The growth of transverse wave power with more power in the left hand polarized waves P_L than in right hand polarized waves P_R, which occurs at about 0657 UT is indicative of the presence of ion cyclotron waves.

Sckopke et al. [1990] observed a "double humped,'' or bifurcated structure in wave power as a function of frequency. Brinca et al. [1990] interpreted the bifurcated spectra as being due to the combination of a core and beam component of protons, but it is possible that the bifurcated spectra result from the presence of He²⁺ as discussed in Section 5.4.3.

At the same time that the ion cyclotron waves grow large in Figure 4 (0657 UT), there is a transfer of energy from T _p to T_||p so that T _p / T_{| p} is greatly reduced. The process by which this occurs is called pitch angle scattering [Kennel and Petschek, 1966]. Figure 5 shows that the values of T _p / T_{| p} observed by the AMPTE/CCE spacecraft in the magnetosheath line up roughly along a curve which was first expressed [Anderson et al., 1994] as

(4)

and that this curve is not far above the marginal stability condition for ion cyclotron waves [Anderson et al., 1994; Denton et al., 1994c; Gary et al., 1993, 1994]. While the value of T _p / T_{| p} may lie under this curve [Denton et al., 1995b; Phan et al., 1994], it is rare that the value of (4) is significantly exceeded; certainly it is not exceeded greatly for any period of time exceeding the growth time of ion cyclotron waves. Thus it appears that ion cyclotron waves regulate the temperature ratio.

While it seems clear that the transverse waves observed in Figure 4 are caused by the ion cyclotron instability, Alfvén waves are sometimes observed in the outer magnetosheath when T _p / T_{| p} is low [Denton et al., 1998]. These waves could have resulted from fluctuations at the bowshock, or might have been generated by ion cyclotron waves upstream of their observation.

Lacombe et al. [1992] identified both Alfvén (ion cyclotron) waves and mirror mode waves (see Section 5.3) in the outer magnetosheath.

5.3. Middle Magnetosheath

Due to the increase in T_||p caused by the ion cyclotron waves in the outer magnetosheath (Figure 4), the value of b_||p T_||p increases. As a result of the increased value of b_||p and decreased value of T _p / T_{| p}, the plasma conditions become more favorable to the growth of the mirror mode. The mirror mode has been identified in the magnetosheath by a number of authors [Anderson et al., 1994; Fazakerley and Southwood, 1994; Hubert, 1994; Hubert et al., 1989; Lacombe et al., 1995; Tsurutani et al., 1982]. While in Figure 4, the ion cyclotron mode appears to remain dominant downstream of the bowshock (we never observe in Figure 4 a magnetopause crossing; we may always be in the outer magnetosheath), the normal situation seems to be that the mirror mode has the dominant wave power throughout most of the magnetosheath. Figure 6 shows out of phase fluctuations of B and electron density N_e which were identified as the mirror mode [Anderson et al., 1994].

Alfvén (ion cyclotron) waves are also sometimes observed in the middle magnetosheath. Some evidence suggests that the ion cyclotron waves may be the dominant cause of temperature anisotropy regulation even when the mirror mode is the dominant wave [McKean et al., 1992, 1994]; however, except for very low b_||p, the mirror mode marginal stability criterion is similar to (4) indicating that the mirror mode could also possibly play a role.

Lacombe et al. [1995] claims to identify the He²⁺ cutoff mode (see also [Denton et al., 1994a] for pictures of the dispersion surface) which exists due to the presence of the heavy ion.

5.4. Inner Magnetosheath (Close to Magnetopause)

Figure 7 shows a density enhancement observed by the ISEE 1 spacecraft in front of the magnetopause on September 5, 1978. Based on such observations, Song et al. [1990b, 1992a] hypothesized that the enhancement was due to an ion acoustic (slow) mode shock in front of the magnetopause. Song et al. [1992b, 1994] went on to identify ion acoustic (slow) waves in the region of the magnetosheath close to the magnetopause. The observed waves had magnetic fluctuations out of phase with density fluctuations. The waves could thus be the mirror mode (Figure 6) or the ion acoustic mode. The identification as the ion acoustic mode was based on the fact that the observed waves had a finite upstream phase velocity in the rest frame of the plasma. (Recall that the mirror mode has zero frequency in a homogeneous plasma.)

Whether or not density enhancements like that in Figure 7 are related to a standing ion acoustic (slow mode) front or shock [Song et al., 1990b, 1992a] is still a matter of debate; however, the weight of evidence is that the waves observed by Song et al. [1994] are the mirror mode, not the ion acoustic mode. The linear ion acoustic mode is strongly damped, as is well known, but it was argued that nonlinear effects might allow the mode to persist [Song et al., 1994]. Denton et al. [1995a] showed that the values of the transport ratios strongly indicated the mirror mode (see Figure 1). The problem remained, however, to explain the finite phase velocity of the waves. Omidi and Winske [1995] showed using a one dimensional hybrid code simulation of the magnetosheath that mirror modes convecting from the bowshock pile up at the magnetopause; they are unable to penetrate to the low beta magnetosphere (see Figure 8).

Subsequently, Johnson and Cheng [1997] solved for the mirror eigenmodes in a model magnetosheath and found that due to the inhomogeneity, the mirror mode acquires a finite phase velocity near the magnetopause. (Their theory did not include coupling to the ion acoustic mode; it is possible that there is coupling between the two modes.) Finally, Lin et al. [1998] examined additional phase relations between field components that indicated that the waves of Song et al. [1994] were really the mirror mode. (The linear theory of Lin et al. [1998] is at best of doubtful relevance to the mirror mode phase relations they use, but the mirror mode phase relations are verified using hybrid code simulations. We are forced, however, to accept their linear fluid theory for the ion acoustic mode phase relations.)

5.4.2. Quasi-Parallel Mirror Mode.

In addition to identifying the ordinary quasi-perpendicular mirror mode (  k approximately B ), Denton et al. [1995a] identified the quasi-parallel mirror mode (  k approximately B ). Denton et al. [1998] reexamined the identification of these waves and concluded that "the quasi-parallel mirror mode may be observed in the inner magnetosheath, but that identification is not certain.'' The technique of Lin et al. [1998] was used to examine event number 7 of Denton et al. [1998] for a third time (J. K. Chao, private communication, 1998). There was mixed evidence for the mirror mode and the Alfvén wave. It appears that both of these modes may be present simultaneously. This makes the identification of the quasi-parallel mirror mode very uncertain.

5.4.3. Ion Cyclotron Waves.

As mentioned earlier, the magnetic field generally increases toward the magnetopause. In addition, a region of depleted density n_p, called the depletion layer, may be present adjacent to the magnetopause. If there is such a decrease in n_p, there is usually also a decrease in the parallel temperature T_||p. All these factors lead to a decrease in b_||p as the magnetopause is approached, and the decrease in T_||p leads to an increase in T _p / T_{| p}. The combination of low b_||p and large T _p / T_{| p} is conducive to the growth of ion cyclotron modes in the depletion layer, as discussed in Section 5.2. Fairfield [1976] first identified ion cyclotron waves in this region. More recent observations have been made by Song et al. [1990a], Anderson and Fuselier [1993] and Anderson et al. [1994] ( Song et al. did not regard the transverse waves they observed as ion cyclotron waves).

Figure 9 shows magnetic power spectra measured by the AMPTE/CCE spacecraft and magnetic field and density data measured by CCE and AMPTE/IRM after a magnetopause crossing at ~1300 UT observed by CCE. At that time, the AMPTE/IRM spacecraft was upstream in the solar wind. The IRM density and magnetic field data shows that the decreased density and increased magnetic field measured by CCE from 1300-1340 UT cannot be explained by upstream temporal variations; CCE is therefore in the plasma depletion layer at that time. To the left in Figure 9, the value of b_||p is lower (due to lower proton density and T_||p (not shown) and larger B₀ ). At the lowest values of b_||p, there is a gap in the transverse power spectra at about 0.7 Hz; the gap is close to the He ²⁺ (alpha particle) gyrofrequency F_a. Moving from lower to higher b_||p, Figure 9 reveals a progression from bifurcated transverse spectra above and below F_a (B), to continuous transverse spectra extending across F_a (C), to transverse spectra below F_a (L), to the simultaneous presence of low frequency transverse power and parallel power assumed to be associated with the mirror mode (LM), to just parallel power (M) [Anderson et al., 1994]. (There is no stop He²⁺ stop band due to the high temperature of the He²⁺ ; see [Denton et al., 1994a].)

The structure of the wave spectra displayed in Figure 9 was accounted for by Denton et al. [1994c]. Their work was based on a simple model of the magnetosheath which assumed 4% He²⁺ and incorporated the anisotropy-beta relation (4); a Vlasov dispersion solver was used to solve for the real and imaginary parts of the wave frequency. Figure 10 shows the main results of their model. Figure 10a shows that the ion cyclotron instability splits into two branches at low parallel beta b_||p, one driven by the temperature anisotropy of the protons (marked "p'') and one driven by the temperature anisotropy of the He²⁺ (alpha particles) (marked " a ''). These two modes merge at high b_||p. Figure 10b shows the normalized growth rate for these two modes and also for the mirror mode (which has zero real frequency, so it does not appear in Figure 10a). The letters "B,'' "C,'' "L,'' "LM,'' and "M'' in Figure 10a stand for bifurcated, continuous, low frequency, low frequency and mirror, and mirror mode spectra, respectively, as described above in reference to Figure 9. Anderson et al. [1994] used a collection of 102 magnetosheath intervals observed by the AMPTE/CCE spacecraft and sorted the observed spectra into these types. The letters ("B,'' "C'' etc.) in Figure 10a are placed at a value of b_||p corresponding to the average value of observed b_||p for each spectral type.

It is clear that the theoretical curves in Figure 10a indicate bifurcated spectra (distinct proton and alpha particle branches), continuous spectra (with frequency extending above w_r / W_p = 0.25 ), and low frequency ( w_r / W_p 0.25 ) spectra at the respective b_||p values indicated by the letters "B,'' "C,'' and "L'' and "LM.'' Furthermore, the growth rate of the mirror mode becomes comparable than that of the ion cyclotron waves at a value of b_||p corresponding to the "LM'' (low frequency and mirror) spectra, and becomes greater than that of the ion cyclotron waves at a value of b_||p corresponding to the "M'' (mirror) spectra, Note the remarkable similarity between the frequency spread of transverse power in Figure 9 and the spread of ion cyclotron real frequency in Figure 10. Based on the detailed agreement between the observations and model, we regard the identification of these ion cyclotron and mirror waves as quite solid.

5.5. Magnetopause Current Layer

Broadband transverse waves are observed in the magnetopause current layer (region of large magnetic shear), especially during periods of southward IMF leading to large magnetic shear at the magnetopause [Rezeau et al., 1989, 1993; Song et al., 1993]; see also [Anderson and Fuselier, 1993]. All of these authors assume that the broadband waves are associated with reconnection. Rezeau et al. [1989] describe the waves as Alfvénic, while Song et al. [1993] describe the waves with peak power as ion cyclotron waves. Song et al. [1993] states also that the wave power extends up to the electron gyrofrequency. This high frequency turbulence is also highly correlated with the magnetic shear [Zhu et al., 1996] and is now thought to be associated with whistler waves resulting from reconnection [Mandt et al., 1994; Shay et al., 1999].

Johnson and Cheng [1997] describe these waves as kinetic Alfvén waves resulting from mode conversion of compressional (mirror) modes convecting toward the magnetopause. The mode conversion occurs in the region of magnetic shear due to finite Larmour radius effects. They argue that particle transport resulting from these waves can be quite substantial. While there are appealing features to this theory, it seems to us that more work needs to be done to verify observationally that such mode conversion is actually occurring (some recent progress in this direction has been made [Park et al., 1999]).

6. Summary

There are four basic ultra-low-frequency (ULF) modes, the Alfvén/ion cyclotron mode, the magnetosonic/fast/whistler mode, the ion acoustic/slow/sound mode, and the mirror mode (Section 2). These can in principle be identified with the help of transport ratios, phase relationships, and polarization information. In many cases, however, a unique identification is difficult to make. Problems are that the theories are usually based on the linear homogeneous assumption, and that there may be a superposition of observed modes.

Whether the upstream conditions are quasi-parallel or quasi-perpendicular depends on the orientation of the interplanetary magnetic field (IMF) at the bowshock (quasi-parallel indicates that the IMF is roughly parallel to the shock normal; see Section 3). When the upstream conditions are quasi-parallel, the magnetosheath plasma usually has a large value of beta, and is characterized by a broad band turbulent spectrum of waves with little ordering by the ill-defined (for high beta) ambient magnetic field (Section 4). The observed wave power is generally thought to be transmitted, with some modification, through the magnetosheath to the magnetosphere from the foreshock.

When the upstream conditions are quasi-perpendicular, the dominant waves (Section 5) appear to be caused by temperature anisotropy ( T _p > T_{| p} ), which is in turn initially caused by reflection at the bowshock and then driven by the compression and stretching of convecting flux tubes. In the middle magnetosheath, the mirror mode is usually the dominant mode. There can also be ion cyclotron waves, especially near the bowshock and in the plasma depletion layer (if there is one) near the magnetopause. Mirror modes observed near the magnetopause develop a finite upstream phase velocity as they are unable to penetrate the low beta magnetospheric plasma. Broadband Alfvénic waves are observed in the magnetopause current layer which are associated with reconnection or possibly with kinetic Alfvén waves.

Inhomogeneity plays a crucial role in the generation and evolution of all these waves. For instance, temperature anisotropy (which drives the ion cyclotron and mirror waves) is caused by the presence of the bowshock and the compression and lengthening of flux tubes as they convect across the magnetosheath. Further examples are the modification of the mirror mode near the magnetopause due to the decreasing beta and the generation of waves in the magnetopause current layer due to large magnetic shear. In the quasi-parallel magnetosheath, the broad-band turbulence is in part generated by foreshock waves which come about due to the presence of the bowshock.

The waves also appear to have an appreciable feedback to the macroscopic plasma. The most certain effect we know about is the regulation of the temperature ratio T _p/T_{| p} by ion cyclotron waves. The energy exchange caused by the waves (from T _p to T_||p ) has an important effect on the evolution of the separate T _p and T_||p. Based on the effect of the waves, an anisotropic ( T _p T_||p ) fluid model has been developed which appears to do a good job of describing the temperature evolution in the magnetosheath [Denton et al., 1994c, 1995b], and this model has been used in fluid simulations of the magnetosheath [Denton and Lyon, 1996]. Whether the whistler waves observed in the reconnection region are a cause or an effect is still under study, but it is clear now that the whistler dynamics which gives rise to the waves plays a crucial role in fast collisionless reconnection [Shay et al., 1999]. Possibly mode conversion of compressional (mirror) waves to kinetic Alfvén waves leads to enhanced transport of particles across the magnetopause [Johnson and Cheng, 1997].

Acknowledgments

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