Low-Frequency Waves in Space Plasmas

By Andreas Keiling, Dong-Hun Lee and Valery Nakariakov

Low-frequency waves in space plasmas have been studied for several decades, and our knowledge gain has been incremental with several paradigm-changing leaps forward. In our solar system, such waves occur in the ionospheres and magnetospheres of planets, and around our Moon. They occur in the solar wind, and more recently, they have been confirmed in the Sun’s atmosphere as well. The goal of wave research is to understand their generation, their propagation, and their interaction with the surrounding plasma. Low-frequency Waves in Space Plasmas presents a concise and authoritative up-to-date look on where wave research stands: What have we learned in the last decade? What are unanswered questions? 

While in the past waves in different astrophysical plasmas have been largely treated in separate books, the unique feature of this monograph is that it covers waves in many plasma regions, including:

• Waves in geospace, including ionosphere and magnetosphere
• Waves in planetary magnetospheres
• Waves at the Moon
• Waves in the solar wind
• Waves in the solar atmosphere 

Because of the breadth of topics covered, this volume should appeal to a broad community of space scientists and students, and it should also be of interest to astronomers/astrophysicists who are studying space plasmas beyond our Solar System.

• Language: English
• Publisher: Wiley
• Release date: Feb 29, 2016
• ISBN: 9781119055037

Book preview

Section I

Ionosphere

1

Energetic Particle-Driven ULF Waves in the Ionosphere

T. K. Yeoman,¹ M. K. James,¹ D. Yu. Klimushkin,² and P. N. Mager²

¹Department of Physics and Astronomy, University of Leicester, Leicester, UK

²Institute of Solar-Terrestrial Physics SB RAS, Irkutsk, Russia

1.1. INTRODUCTION

Ionospheric radar systems have proved to be a powerful tool for the investigation of magnetospheric ULF waves. Because of their multipoint remote sensing capability, they are suitable for tracking waves with periods in the Pc3–5 bands (frequencies of 100–2 mHz). The high spatial resolutions (typically 15–45 km) they produce of the wave ionospheric electric field have provided direct information as to the ionospheric boundary conditions determined by the ionospheric Pedersen conductivity, rather than being sensitive to the ionospheric Hall currents which provide the magnetic field signature most commonly measured by ground magnetometer systems. Magnetospheric ULF waves are generally classified into one of two types, depending on whether their polarization is predominantly toroidal or poloidal. Toroidal waves are those in which the magnetic field oscillates in the azimuthal direction and are characterized by low effective azimuthal wave numbers (m), or equivalently by large azimuthal scale sizes. Conversely, poloidal waves oscillate with a magnetic field in the meridional direction with high m numbers (a smaller azimuthal scale size). Both toroidal and poloidal ULFwaves propagate as Alfvén standing waves between the two conjugate endpoints of the magnetic field at the Earth’s ionosphere. Low-m (toroidal) waves are generally thought to have their energy source external to the magnetosphere. High-m (poloidal) events usually have a different generation mechanism to the low-m events, where the energy source is thought to be from energetic particle populations within the magnetosphere, which may be transferred from the particles into the wave within the collisionless magnetosphere via wave–particle interactions. The energetic particle populations generating high-m waves enter the inner dipolar magnetosphere from the magnetotail, whereupon they gradient-curvature drift around the planet, forming part of the global ring current.

Both toroidal and poloidal ULF waves are changed as they pass from the magnetosphere through the ionosphere, where they undergo rotation and attenuation. It is assumed that on passage through the conducting, vertically stratified ionosphere above the insulating atmosphere, the Alfvén wave will rotate 90°. Thereupon the azimuthal magnetic field component in the magnetosphere is detected on the ground as a north–south magnetic field perturbation [Hughes and Southwood, 1976]. The attenuation that occurs is proportional to , where |k| is the field-perpendicular value of the wavenumber and z is the E-region height. The greater the attenuation is, the smaller is the field-perpendicular scale size of the wave.

Consequently high-m poloidal waves become much more attenuated in ground magnetometer data than low-m toroidal waves. For this reason ionospheric radar systems have been effective in the study of high-m poloidal waves driven by energetic particle populations within the magnetosphere, and it is this class of ULF waves that will be discussed in this chapter. These ULF waves are implicated in the energization (e.g., O’Brien et al. [2003]) and decay (e.g., Baddeley et al. [2004]) of radiation belt particles, which is an area of considerable current research interest. The frequency, polarization, and azimuthal structure of the waves are key elements in controlling this energy exchange [Elkington, 2006], and hence ionospheric observations of high-m ULF waves have an important role to play in furthering our understanding of the wave characteristics, and their role in radiation belt physics.

In order for a high-m, poloidal wave to be generated, two conditions must be satisfied. First, there must be a source of free energy for wave growth within the particle population, and second, the spatial and temporal evolution of the waves and the particles must match via a resonance condition, such that the free energy has an opportunity to transfer from the particles to the waves. The usual free energy condition is one that requires that the particle distribution function, f, increases with particle energy, W,

(1.1)

(e.g., Southwood and Hughes [1983], Mann and Chisham [2000]), where L is the L-shell under consideration. Thus instability can occur if there is a sufficiently large spatial gradient in the distribution, or if a population inversion occurs at some point in the distribution , usually referred to as a non-Maxwellian or bump-on-tail distribution [Southwood et al., 1969].

The resonance condition, which is also required to be met for effective energy transfer from the particles to the wave, is given by

(1.2)

where ωwave, ωb, and ωd are the angular frequencies of the wave, the proton bounce, and the proton azimuthal drift, respectively [Southwood et al., 1969]. In drift-bounce resonance N is an integer (usually ). Where the particle bounce is not required for the resonance condition, Equation (1.2) reduces to the , drift resonance case,

(1.3)

An early confirmation of these ideas came from Hughes et al. [1978], who were able to use the ATS6 geostationary spacecraft to measure both the wave field and a population inversion in the driving particle population for a wave attributed to the drift-bounce mechanism. More recently, convincing evidence of a drift-bounce resonance wave and its driving particle population were presented by Liu et al. [2013], based on THEMIS particle and field data. However, to this day such datasets have proved to be rare and elusive, and a variety of techniques have had to be harnessed to progress our understanding of wave–particle interactions in the magnetosphere.

While many of the characteristics of high-m ULF waves can be explained by the drift resonance conditions defined in Equations (1.2) and (1.3), these equations do not offer an explanation of the latitudinal phase structure. The latitudinal phase structure is likely determined by the particle distributions driving the waves, and ionospheric observations have revealed a wide variety of such structures.

Mager and Klimushkin [2008] and Mager et al. [2009] have suggested the possible role of the radial structure of a cloud of injected energetic particles driving a high-m wave in determining the latitudinal phase structure of the wave. Mager et al. [2009] considered waves of form eimϕ where ϕ is the azimuthal angle. Assuming the local field line eigenfrequency is ω(x) where x is the radial coordinate, and that the wave source is a local inhomogeneity resulting from particle injection drifting at speed ωd(x), producing a nonsteady current j(t), Mager et al. [2009] showed that the wave phase is then given by

(1.4)

An example of the phase evolution determined by Mager et al. [2009] is illustrated in the plane in Figure 1.1. If the particle drift velocity grows with the radial coordinate, x, then the particle cloud is stretched into a spiral in the equatorial plane. Near the source the phase follows the source closely. The variation of the particle drift with x may then result in an inwards phase motion (a negative wavevector kx), which will manifest itself as an equatorward phase motion in the ionosphere. This equatorward phase motion would reverse to poleward (a positive wavevector kx) at a later time further from the source as the natural frequency of the field lines becomes important. This transition is marked in Figure 1.1 by the line . A particle drift velocity decreasing with radial coordinate would show poleward phase propagation throughout. Such features in the latitudinal phase structure of high-m waves have been observed and are discussed in later sections. The wave features predicted by such a moving source are not in conflict with the drift and drift-bounce mechanisms outlined above, as any wave event generated by a moving particle cloud source may be enhanced and sustained by these energy sources.

Graph of the radial coordinate x versus angle ϕ presenting lines of constant phase for a wave of westward-drifting protons depicting increase in drift velocity, with solid line as kx=0 and dashed line as source.

Figure 1.1 Lines of constant phase for a wave driven by a localized cloud of westward-drifting protons whose drift velocity increases with the radial coordinate x. From Mager et al. [2009].

1.2. EARLY RADAR OBSERVATIONS

The first opportunities for ionospheric observations of high-m ULF waves in the ionosphere came with the development of coherent scatter radars. Early oscillations associated with ULF waves were reported in the 1960s (e.g., Keys [1965]), but the development of very high frequency (VHF) coherent scatter radars such as the Scandinavian Twin Auroral Radar Experiment (STARE; Greenwald et al. [1978]) and the Sweden and Britain Radar experiment (SABRE; Nielsen et al. [1983]) provided major new datasets that transformed our knowledge of these phenomena. Early results from the STARE system [Walker et al., 1979] focused on low-m waves where ground-based magnetometer data were also available, and provided important confirmation of the field line resonance theory of Southwood [1974] and Chen and Hasegawa [1974], showing a clear ampliude maximum coincident with a poleward phase change in latitude. However observations of high-m ULF waves followed shortly after, and a new class of ULF waves, termed storm-time Pc5 waves were discovered [Allan et al., 1982, 1983a, b; Walker et al., 1982]. These waves were identified as compressional waves of high m number ( to –80) with periods in the Pc5 range (200–400 s), predominantly observed in the dusk sector of the ionosphere during disturbed magnetic conditions. The ionospheric wave electric fields were small and linearly polarized, with similar magnitudes in the north–south and east–west components. In contrast to the low-m wave observations of Walker et al. [1979], little phase variation in latitude was observed. The waves were attributed to the drift-resonance source mechanism described by Equation (1.3), with the responsible particle population being westward-drifting protons of energy 20–80 keV, and were the first radar observations of waves not attributed to a driving mechanism external to the Earth’s magnetosphere.

At a similar time another population of waves with unusual latitudinal phase variation were observed by the SABRE radar [Waldock et al., 1983], an example of which is reproduced here in Figure 1.2. In this case an equatorward phase propagation was seen, and again the wave events were associated with the dusk sector. Subsequent analysis of the occurrence statistics of these waves by Tian et al. [1991] led to the conclusion that they were associated with the plasmapause, as they occurred at a local time when the plasmapause lay within the radar field of view. However, similar observations from the higher latitude Bistatic Auroral Radar System (BARS; McNamara et al. [1983]) eliminated that possibility [Grant et al., 1992]. These higher latitude waves exhibited equatorward phase propagation like the SABRE observations, but at latitudes significantly higher than the expected plasmapause position. Analysis of their azimuthal structure revealed azimuthal wavenumbers with magnitudes in the range 45–60, suggesting a similar generation mechanism to the STARE storm-time Pc5 events. Invoking a similar drift resonance generation mechanism then suggested that somewhat lower energy protons ( ) were involved than those driving the STARE observations, with the BARS observations being at higher latitudes. Further analysis of the SABRE results [Yeoman et al., 1992] provided a detailed analysis of the meridional and longitudinal phase propagation of the events. Figure 1.3 presents an example of the spatial structure of the east–west and north–south horizontal velocity components of a wave event observed by the combined fields-of-view of the two overlapping SABRE radars. The Fourier phase of the peak Fourier component (a frequency of 1.7 mHz) for a wave event observed between 1530 and 1600 UT on day 48, 1985 is presented on a geographic grid. The spatial variation of the Fourier phase reveals a westwards phase propagation in geographic latitude in both the north–south and east–west velocity components, corresponding to an effective azimuthal wavenumber, m, of magnitude between 30 and 40. An equatorward propagation is seen in latitude, and this phase change often exceeded . Such signatures in the radar data were demonstrated to often have no significant corresponding signature in ground magnetometer data. Yeoman et al. [1992] suggested that the same drift resonance mechanism proposed by Grant et al. [1992] could also be a source for these lower latitude equatorward propagating Pc5 observations, but with particles of similar energies to the earlier STARE storm-time Pc5 results being invoked.

Equatorward-moving bands observed in a SABRE range–time–intensity plot, with range from 495 to 1230 km and threshold 15 dB.

Figure 1.2 Equatorward-moving bands observed in a SABRE range–time–intensity plot. From Tian et al. [1991].

Two graphs presenting the spatial variation of the peak Fourier component at 1.7 mHz frequency of the SABRE East–West (left) and North–South (right) horizontal velocity component for day 48, 1985; 1530 UT.

Figure 1.3 Spatial variation of the peak Fourier component at 1.7 mHz frequency of the SABRE East–West and North–South horizontal velocity component for day 48, 1985; 30 minutes of data are processed starting at 1530 UT. From Yeoman et al. [1992].

1.3. SUPERDARN OBSERVATIONS

More recent ionospheric observations of high-m ULF waves have taken advantage of the Super Dual Auroral Radar Network (SuperDARN). SuperDARN is a global array of high-frequency (HF) radars. The use of HF frequencies allows radio propagation beyond the horizon, greatly extending the capabilities of the systems compared to the VHF radar systems used in the studies described in Section 1.2. Full details of SuperDARN are given in Greenwald et al. [1995] and Chisham et al. [2007]. Whilst the radars’ design is focused on measuring the global ionospheric convection pattern at a 1 or 2 min cadence, lower frequency ULF waves may be investigated with the standard data products, and a variety of novel scan modes and operations have been devised to allow the study of higher frequency wave regimes. For example, the addition of a second receive channel to some SuperDARN radars allows for so-called stereo operations [Lester et al., 2004], where a single or a small number of beams can be sampled on channel B of the radar receivers independently of the main 16 beam scan sampled simultaneously in channel A, in order to improve the temporal resolution of the radars.

The first results on the observation of high-m ULF waves with SuperDARN were performed by Fenrich et al. [1995]. They noted many common characteristics between low and high-m waves, including the wave frequencies and their local time occurrence statistics. High-m waves were noted to generally have an equatorward phase propagation, in contrast to the poleward-propagating low-m events, but their similarities to the low-m waves led to the conclusion that wave–particle interactions could not provide the sole explanation for their occurrence characteristics, although they were likely to be involved in the amplification of the observed wave signatures. These ideas were developed by Fenrich and Samson [1997], where a possible explanation for the equatorward phase propagation was included. It was suggested that the latitudinal phase could be reversed in cases where the wave growth via wave–particle interactions exceeded the wave dissipation through the ionosphere, such that the overall Poynting flux was directed outward from the resonance location rather than inward, toward the resonance location.

Following these early SuperDARN studies, the use of active radar techniques, where high-power radiowave transmissions are used to generate backscatter in the SuperDARN radar fields of view, were extensively used over the next few years for the investigation of high-m ULF waves, and these were summarized in Yeoman et al. [2006]. More recent results from SuperDARN have provided a wealth of new information on the wave events observed with equatorward phase propagation, as discussed above and in Section 1.2. Yeoman et al. [2008] presented data for a high-m wave with an equatorward phase propagation, a period of 300 s and , that was observed at very high latitude over Svalbard during an interval when the open-closed field line boundary had retreated poleward of the high-latitude location. A drift–resonance source in 15 keV protons was inferred, with the high-latitude location shown to preclude the trapping of protons with population inversions at higher energies but to be able to sustain such populations at these lower energies on occasion.

Yeoman et al. [2010] presented a case study of another event observed by the SuperDARN radars at Hankasalmi, Finland, and Þykkvibær, Iceland. The event was associated with a substorm expansion phase, which was detected with the FUV instrument [Mende et al., 2000a, b] on the IMAGE spacecraft. Figure 1.4 shows the fields-of-view and data coverage from the SuperDARN radar channel A data, along with three images from the FUV instrument, all in magnetic latitude–magnetic local time coordinates during substorm onset at 2337 UT on 21 March 2002. For this event, the substorm onset occurred within the radar fields of view, with the auroral signature then expanding poleward and westward over the radars. ULF wave observations during the interval are sampled on channel B. These are presented in Figure 1.5, with the Hankasalmi data from a meridional beam (beam 9) presented in Figure 1.5a and the Þykkvibær data in Figure 1.5b. Figure 1.5a clearly shows the equatorward phase propagation of the observed wave. Figure 1.5b shows little phase evolution in the poleward- and westward-oriented beam 5 data from Þykkvibær. Analysis of the wave characteristics showed that this resulted from the combination of the equatorward propagation seen in Figure 1.5a ( per degree of latitude), and an eastward longitudinal phase propagation corresponding to an azimuthal wave number of . Yeoman et al. [2010] interpreted these data as implying a wave source in drifting 33 keV particles, with the eastward propagation implying that electrons were the source, rather than protons. Free energy should be available on occasion in the electron populations when the conditions in Equations (1.1) and (1.3) are met for electrons, although in the case of electrons the much more rapid electron bounce period would preclude solutions for conditions other than in Equation (1.2). The equatorward propagation of the observed wave was explained in terms of a development of the Alfvén ship wave theory elaborated by Mager and Klimushkin [2008] and Mager et al. [2009].

Image described by caption.

Figure 1.4 Fields-of-view and data coverage from channel A of the SuperDARN radars at (a) Hankasalmi, Finland, and (b) Þykkvibær, Iceland in magnetic latitude–magnetic local time coordinates during substorm onset at 2337 UT. Red (negative) velocities are away from the radar and blue (positive) velocities are toward the radar. The radial dashed lines are separated by 1 hr local time, with local midnight being marked by the vertical dashed line. The dashed circles indicate magnetic latitude at separations. (c–e) present IMAGE WIC auroral data in the same coordinate system for three times during the substorm expansion phase. From Yeoman et al. [2010].

Image described by caption and surrounding text.

Figure 1.5 SuperDARN radar velocity measurements from (a) Hankasalmi beam 9 and (b) Þykkvibær beam 5. The ionospheric velocities are color-coded as in Figure 1.4. From Yeoman et al. [2010].

The case study reported above suggested that both westward-drifting protons and eastward-drifting electrons could drive high-m waves. The relatively modest m value of 13 was suggested to be a result of the close proximity of the wave observations to the substorm onset, where higher energy particles might be available for wave growth. Both these predictions were subsequently tested in a statistical study of similar wave types undertaken by James et al. [2013]. In this study 83 similar wave events that were associated with substorm expansion phase onsets identified from IMAGE were analyzed, and their frequencies, latitudinal and longitudinal phase evolution, and proximity to the location of the substorm determined. Figure 1.6 summarizes the findings of the paper. The x-axis of Figure 1.6 shows the longitudinal separation of the substorm onsets and the wave observations. The y-axis illustrates the driving particle energies derived from the wave characteristics, assuming a simple expression for particle drift [Yeoman and Wright, 2001] and using Equation (1.3). Westward-drifting particles are inferred for waves west of the substorm onset, and eastward-drifting particles for waves east of the substorm. In both cases, the energy of the particles decreases as the longitudinal separation increases, with the reduced longitudinal drift speed of the lower energy particles implying an increased azimuthal wave number in Equation (1.3). This situation is illustrated schematically in Figure 1.7. Earlier spacecraft observations of similar high- m wave events presented by Takahashi et al. [1990] also saw westward azimuthal phase propagation in the dusk sector and eastward phase propagation in the dawn sector, although the waves were not directly correlated with substorm onset locations. In this case the eastward propagation was interpreted as being the result of the Doppler shift imposed by the eastward drift in the dawn sector, with westward phase propagation being the case in both sectors in the plasma rest frame. In the case of Takahashi et al. [1990] considerably larger phase shifts and higher wave frequencies were seen in the westward-propagating (dusk) events (where the drift added to the proposed wave phase evolution) than in the eastward propagating (dawn) events (where the drift subtracted from the proposed wave phase evolution). The events in James et al. [2013] were very symmetric in both frequency and phase propagation speed to the east and west of the substorm, and are interpreted as a genuine eastward and westward wave propagation in the plasma rest frame.

Image described by caption and surrounding text.

Figure 1.6 (a) Calculated particle energies for each of the 83 wave events analyzed in James et al. [2013] plotted against the azimuthal separation between the waves and their associated substorm positions. (b) Same data as in (a) but now placed into magnetic longitude bins.

Image described by caption.

Figure 1.7 Schematic illustration of the interpretation of the wave events analyzed in James et al. [2013]: clouds of protons and electrons generate waves to the west and to the east of the substorm onset (SO), respectively. In each case the nonsteady currents j(t) that Mager and Klimushkin [2008] proposed as a mechanism for wave generation are also illustrated. From James et al. [2013].

1.4. DOPPLER SOUNDER OBSERVATIONS

Opportunities for the study of high-m ULF waves in the ionosphere are not restricted to ionospheric radar systems. HF Doppler sounders offer one such alternative technique. In a Doppler sounder, use is made of the direct reflection of a radio wave from the ionosphere, rather than a scattering process. While a multipoint investigation of the spatial structure of the ULF wave is more difficult with such a system, it does have the advantage of excellent spatial resolution of for an F region reflection. Such systems are also simple and inexpensive, and thus can offer continuous operations in a mode suitable for ULF wave investigations, enabling statistical studies to be built up. Baddeley et al. [2005a] studied a population of 27 high-m ULF waves from a the DOppler Pulsation Experiment (DOPE), a Doppler sounder located at Tromsø, Norway, at an invariant latitude approximately corresponding to geostationary orbit (an L-shell of 6.3). Direct measurement of the m -number of the waves from two azimuthally separated HF Doppler propagation paths revealed waves with m typically being −100 to −200, representing some of the smallest scale waves ever observed in the ionosphere. Figure 1.8 presents an example of such a wave event, which is clearly visible as a Doppler shift of peak-to-peak amplitude imposed on the HF radio signal, but which is completely shielded from the ground-based magnetometer traces from nearby magnetometers. Considering typical observed population inversions at these latitudes as had been reported by Baddeley et al. [2004], Baddeley et al. [2005a] concluded that the solution to the resonance Equation (1.2) indicated that for waves with moderately large azimuthal m numbers a drift-bounce resonance was statistically the more likely. For waves with larger m numbers, both the drift (Equation (1.3)) and drift-bounce (Equation (1.2)) resonance interactions were possible. When considered alongside the MLT location of the waves in this study, this indicated that a drift-bounce resonance was more likely in the pre-noon sector but both drift and drift-bounce resonance interactions were equally likely in the post-noon and dusk sectors. Recent spacecraft observations by Takahashi et al. [2013] have confirmed that both fundamental (drift resonance) and second harmonic (drift-bounce resonance) type-waves with no corresponding ground magnetic signatures are seen in space, which is supportive of these conclusions.

Image described by caption and surrounding text.

Figure 1.8 DOPE trace from the Ramfjordmoen–Seljelvnes propagation path along with x and y component magnetic field traces from three nearby magnetometers. This wave event is classified as uncorrelated as there is no magnetic ground signature. From Baddeley et al. [2005a].

The DOPE system was further exploited by Baddeley et al. [2005b], who were able to assemble a database of 130 high-m wave events from DOPE. Combining the small number of events where near-conjugate and simultaneous particle data were available from the Polar spacecraft TIMAS [Shelley et al., 1995] and CAMMICE [Wilken et al., 1992] instruments, and a database of similar observations from these latitudes from 2.5 years of observations from these instruments, they were able to demonstrate a statistically significant relationship between wave observations in the ionosphere and population inversions in the in situ particle data. For two case studies, they were also able to demonstrate an approximate agreement between the free energy available within the particle distribution functions for wave growth, and the energy deposited from the wave into the ionosphere in the form of Joule heating.

1.5. OBSERVATIONS FROM ALTERNATIVE INSTRUMENTATION

As outlined above, observations from VHF radars (Section 1.2), HF radars (Section 1.3), and HF Doppler sounders (Section 1.4) have made strong contributions to our understanding of the ionospheric signatures of high-m ULF waves, and undoubtedly they will continue to do so. This is by no means an exclusive set of instrumentation, however, and other experimental techniques have contributed to the field of study. Incoherent scatter radars have provided invaluable detail on the response of the ionosphere to ULF wave activity (e.g., see Pilipenko et al. [2014a] and references therein). Few results for high-m ULF waves exist in the literature, but Buchert et al. [1999] provided observations of Pc5 pulsations with the EISCAT radar showing westward propagation with an m value of −30. The wave was seen to modulate the ionospheric conductivities by a factor of two, as a result of the periodic modulation of hot electron precipitation, and the diffusion rate for these electrons was estimated. Incoherent scatter radar operations are often incompatible with the high cadence data required for ULF wave studies, but technical advances are making them increasingly viable instruments in this area.

Riometers also provide information on ULF wave activity, as any modulation of the precipitating electron fluxes, as discussed above, will modulate the ionospheric absorption of HF radio wave signals, and hence modulate the cosmic noise absorption (CNA) measured by riometers. Spanswick et al. [2005] provided statistics of riometer detection of large-scale, low- m ULF waves. The ability of imaging riometer systems to provide the spatial resolution required for the detection of high-m ULF waves was demonstrated by Beharrell et al. [2010]. Here riometer observations of the modulation of CNA data revealed ULF signatures which showed eastward phase propagation, with an azimuthal wavenumber of up to . Figure 1.9 shows a 2D image of the relative phase of some typical wave observations in each imaging riometer beam for an event presented by Beharrell et al. [2010]. The small azimuthal scale size of the event is clearly illustrated, and highly structured phase behavior in latitude was also commonly observed. The mechanism proposed for the generation of these signatures by Beharrell et al. [2010] was a multi-stage one, where seeding of the wave came via a large-scale, low-m ULF wave, which then was able to generate a population inversion in the proton distribution function. This unstable particle population then generated a high-m wave, which in turn modulated the hot electron precipitation and hence modulated the CNA. The eastward phase propagation was attributed to the drift of these hot electrons. Further observations including in situ data will be required to confirm these ideas.

Image described by caption and surrounding text.

Figure 1.9 A phase map of a high-m ULF wave event observed in imaging riometer data. From Beharrell et al. [2010].

The aurora are also well known to show modulation at ULF auroral frequencies. Rae et al. [2012] demonstrated a very close correlation between ULF magnetic perturbations and auroral intensity, at both low- and high-m numbers. The high spatial resolution of ground-based all-sky camera data therefore has a great potential for future investigations of high-m ULF waves.

ULF waves have also been demonstrated to modulate other measureable ionospheric parameters. Pilipenko et al. [2014b] have recently demonstrated that the measurements of Total Electron Content (TEC) derived from Global Positioning System (GPS) spacecraft may also be modulated by ULF wave activity. In the published literature thus far, only large-scale ULF wave modulations have been reported, but there remains great scope for further exploitation of this technique for high-m waves.

1.6. SUMMARY

Ionospheric radar observations have provided a wealth of information on the characteristics of ULF waves, and have provided a unique window for the observation of waves with small azimuthal scale sizes associated with wave growth through wave–particle interactions with ring current particles. A number of alternative techniques are available for exploring the ionospheric signatures of such wave events, as discussed in Section 1.5, which are relatively underexploited, and have the potential to provide important new observations. Combining these ionospheric techniques with spacecraft observations such as those from the ongoing van Allen probe mission will provide new opportunities for combined ionospheric electric field observations and in situ observations of both the wave fields and the driving particle populations to address many of the remaining mysteries in the structure, modes and excitation of these wave types.

ACKNOWLEDGMENTS

The work by T.K.Y. is supported by STFC grant ST/H002480/1 and NERC grant NE/K011766/1. M.K.J. was supported by a NERC studentship and STFC grant ST/H002480/1. The work by D.K. was supported by project Ultra-low-frequency waves in the solar wind, ionospheric, and magnetospheric plasma (program No 9 of the Presidium of the Russian Academy of Sciences Experimental and theoretical studies of the objects of the solar system and stars’ planetary systems). The work by P.M. was supported by RFBR grant 14-05-00588.

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2

ULF Waves and Transients in the Topside Ionosphere

V. A.Pilipenko¹ and B.Heilig²

¹Space Research Institute, Moscow, Russia

²Geological and Geophysical Institute of Hungary, Tihany, Hungary

2.1. INTRODUCTION

Like seismic waves from the Earth’s interior that provide us with information on the crust structure and processes inside the planet, electromagnetic waves provide information about the dynamics of the near-Earth environment. Yet space physicists nowadays can extract only a small portion of this information because the processes of wave excitation, propagation, and conversion in the near-Earth plasma are much less known than those in seismology. Our knowledge of space wave physics in the ultra-low-frequency (ULF) band—from fractions of Hz to several Hz—comes for the most part from electromagnetic observations either in the near-equatorial magnetospheric domain with geosynchronous spacecraft or in the lower ionosphere with radar facilities and ground magnetometers. The topside ionosphere, which is the key space physics region where the energy from the magnetosphere flows toward the upper atmosphere, has remained mostly unexplored.

Low Earth orbit (LEO) satellites with precise high-rate sensors onboard have advanced the prospect of our examining the different kinds of ULF waves in the topside ionosphere. The sensitivity of modern LEO satellite magnetometers and electric field sensors, such as MAGSAT, DE-1, Ørsted, FAST, ST5, C/NOFS, Chibis-M, CHAMP, and SWARM, has become sufficient to detect in situ ULF waves and transients in the topside ionosphere (e.g., typical amplitudes of ULF signals are about 0.002% of the background geomagnetic field). A real breakthrough in the ULF wave studies was achieved in 2000 thanks to the CHAMP satellite mission, which has provided 10 years of high-quality data.

The LEO observations cover the ULF range from Pc1/Pi1 waves (fractions of Hz) to Pc3 waves ( mHz). Because of the fast motion of a spacecraft, lower frequency Pc4–5 waves ( mHz) cannot be detected by LEO satellites. Although Pi2 waves also have low frequencies ( mHz), their large spatial scales at low latitudes makes it possible for low-orbiting spacecraft to detect their presence.

LEO satellite observations therefore play an important role in ULF wave physics. They have enabled us to bridge the gap between magnetospheric and ground observations, especially in studying the interactions of ULF waves with the ionosphere. Based on these observations, we already know that some existing theoretical views have to be revised. We now have sufficient physical information from LEO statellites about the various types of ULF waves (Pc3, Pi1–2, Pc1–2) in the topside ionosphere that has made it possible to study the ULF transient response of the upper ionosphere to atmospheric thunderstorm activity. In this chapter, we update our earlier review (Pilipenko et al., 2011) to include many more recent observations on the behavior of these wave categories. We also review such evidence from these observations that may help settle some of the unsolved problems of ULF wave physics.

2.2. ULF WAVE OBSERVATIONS IN LEO MISSIONS

A number of studies have made important contributions on the types of ULF waves detected by LEO space missions, and we outline here some of the key results. However, we do not consider observations at auroral latitudes, above the auroral oval, because for this region the typical types of ULF wave modes are small-scale kinetic and inertial Alfvén waves. Such wave activity is related to fascinating, but specific, physical processes of the wave–particle interaction that contributes to auroral electron acceleration [Chaston et al., 1999; Lysak and Andre, 2001].

In the magnetosphere, the wave electric (e) and magnetic (b) fields can belong to one of two modes:

Alfvén mode, a carrier of nonsteady field-aligned currents, where the disturbed magnetic field is perpendicular to B0, and the longitudinal component is vanishing , or

fast magnetosonic (FMS) mode, a carrier of magnetic field compression, where the field-aligned component of the current vanishes . The field-aligned (compressional) magnetic component is typical for FMS mode and produces plasma compression: .

The topside ionosphere is a difficult region for ULF wave analysis. In this region, as observed by LEO missions, there is a complicated mixture of incident, reflected, and mutually converted MHD waves. Beside the varying wave phenomena, the spatial structures (field-aligned currents, plasma bubbles, etc.) sampled over time by fast-moving satellites appear as fluctuations. The LEO satellites’ orbital speed is around 7.5 km/s, which has other consequences for ULF detection. In only 10 min a LEO satellite covers . In fact it covers so many different regions that most of the signals cannot be considered stationary, and this precludes use of Fourier spectral analysis. Depending on the phase structure of the wave phenomena, strong Doppler shifts may even arise.

The pre-processing of LEO magnetic data typically is done in two steps. First, data are transformed into mean field-aligned (MFA) coordinate system with three components: the compressional (parallel), azimuthal (pointing East), and the poloidal (pointing earthward) components. Second, the mean field model is subtracted from the compressional component (the mean transverse components are zero by definition), and the residuals are analyzed. More advanced approaches use high-resolution field models to remove signals associated with crustal field anomalies, as well as external fields. The latest magnetic field models have a spatial resolution enabling the removal of crustal anomalies with a few hundred km wavelength corresponding to Pc3, Pi2 wave frequencies when sampled by a fast-moving satellite. Sutcliffe and Lühr [2003] have demonstrated how the removal of the magnetic signature of crustal field anomalies influences the detectability of Pi2 waves.

2.2.1. Pc1 Waves

Pc1 waves ( Hz) are thought to be highly effective in depleting relativistic electrons from the outer radiation belt and protons from the ring current. Therefore these waves have been prioritized in wave studies. As far as we know today, Pc1 pulsations consist of packets of electromagnetic ion cyclotron (EMIC) waves that are excited as a result of the cyclotron instability of energetic protons with an anisotropic temperature distribution [e.g., see Kangas et al., 1998]. It is furthermore thought that this EMIC instability is convective; that is, the region of instability at the top of a field line works as an amplifier of running along the field line Alfvén waves. Wave packets are thought to oscillate between the conjugate ionospheres and to intensify at each passage through the equatorial region of the magnetosphere (the bouncing wave packet model), though current research is casting doubt to the reliability of this model [Mursula, 2007].

Pc1 observations in the ionosphere were first reported during the MAGSAT (altitude ~500 km) era [Iyemori and Hayashi, 1989]. Pc1 waves can be ducted within the ionosphere and appear on the ground over a much wider region than in space [Kim et al., 2010]; therefore a good conjunction between space and ground magnetometers is not necessary. As a result the ratio between the amplitude of the Pc1 waves observed by MAGSAT and that on the ground varied widely, ~5–100.

The availability of 10 years of CHAMP data enabled Park et al. [2013] to examine a global climatology of Pc1 pulsations. Diurnal variation of Pc1 occurrences showed a primary maximum early in the morning and a secondary maximum during pre-midnight hours. Annual variations in the occurrence rate showed a clear preference for the local summer. The solar cycle dependence revealed the occurrence rate maximum at the declining phase (2004–2005), though neither magnetic activity nor solar wind velocity controlled the Pc1 occurrences significantly. The Pc1 occurrence rate peaked at subauroral latitudes, with the steep cutoff toward higher latitudes. An interesting, but still unexplained, feature noted is that the global distribution of Pc1 exhibits the highest occurrence rate in the longitude sector of the South Atlantic Anomaly.

The multi-probe LEO missions have contributed new data that has helped with the problem of understanding space-time uncertainty. A successful attempt to identify EMIC waves on the LEO mission ST5 (altitude ) was made by Engebretson et al. [2008]. On this mission, the three probes were located in almost identical orbits in a pearls-on-a-string configuration with distances between them from first thousands to hundreds of km. The ST5 probes crossed the same spatial region with a delay of . All EMIC wave packets detected by the two ST5 probes were observed as crossing the same latitude, which indicated their narrow localization in latitude with a characteristic scale of and transverse dimension .

Interestingly, EMIC emissions were never detected with comparable amplitudes by all three ST5 probes. Moreover, when at the moment of registration of the Pc1 wave packet the satellite orbit passed in the vicinity of a ground station, a prolonged emission at the same frequency was observed on the ground. In order to reconcile these observational facts, it could be assumed that the EMIC instability develops in the magnetosphere as a series of irregular bursts of instability (like toasting popcorn). That is to say, EMIC waves are excited not in continuous emission but in the form of relatively short strongly localized wave bursts distributed randomly in time and space in a finite magnetospheric region. That may explain why by a LEO satellite only short bursts of EMIC waves can be observed, whereas at ground stations a prolonged emission collected from a large area is registered. Thus the EMIC instability of the ring current may work not as a convective amplifier of oscillating wave packets but as a generator of wave bursts (absolute instability). Nevertheless, the toasting popcorn hypothesis is still mere speculation.

The traditional theory of EMIC wave generation was developed by the assumption that, during the field-aligned wave propagation, the packet wave vector remains parallel to the external magnetic field , since only these waves can interact efficiently with resonant protons. The critical transverse scale, on controlling the condition of quasi-parallel propagation , is determined by the value (where Ω is the ion gyrofrequency) [Leonovich et al., 1985]. The small scale of EMIC waves detected by ST5 in fact corresponds to quasi-perpendicular propagation, . EMIC waves can be narrowly localized by wave-trapping them in a local waveguide. In fact the radial distribution structure of the magnetospheric plasma is so irregular that local waveguides not related directly to the plasmapause have been suggested to exist for EMIC waves. A waveguide for EMIC waves can be formed by the joint action of the transverse wave dispersion and plasma inhomogeneity. The dispersion of the Alfvén wave may indeed be due to (1) a finite gyrofrequency , (2) a finite Larmor radius of ions , and (3) electron inertia, characterized by inertial electron length [Dmitrienko et al., 1992]. The waveguide character of EMIC waves was noted to be clearly evidenced by the polarization features of the wave structures in the topside ionosphere [Engebretson et al., 2008; Pilipenko et al., 2012]. For a typical EMIC wave packet, the polarization ellipticity (i.e., rotation) of the transverse wave component changed its polarity in the region of maximum amplitude. This polarization reversal suggests a standing-mode structure of EMIC waves in the transverse direction, as is characteristic of waveguide trapping. Comparisons of ST5 observations with inferences based on waveguide theory [Leonovich et al., 1985; Dmitrienko et al., 1992], however, had alleged that none of those mechanisms could explain adequately the observed transverse scale of EMIC trapped modes in the topside ionosphere [Pilipenko et al., 2012]. Given that elliptical polarization and changing wave ellipse rotation do not follow from the existing theoretical models of the magnetospheric waveguide for EMIC waves, the theoretical models used to explain this effect may need to be refined. Thus the instability regime and the mechanism of spatial structure formation of EMIC waves remain open questions.

2.2.2. Pi1 Wave Bursts

Pi1 bursts in the 0.1–1 Hz band are considered to be a sign of auroral intensification. However, Lessard et al. [2006] suggested that Pi1 wave bursts could be not just a marker but even a driver of auroral activations. Typically, auroral electron acceleration is produced by the mechanism of a steady field-aligned magnetospheric electric field , resulting in a nearly monoenergetic beam of electrons. Additionally, Alfvénic waves are also presently considered to energize the auroral electrons in the topside ionosphere, above an auroral arc.

Using a good conjunction of ground stations, geosynchronous GOES footprint, and the track of the low-orbiting FAST spacecraft (apogee/perigee ), Lessard et al. [2006] found that Pi1 waves propagate past GOES in a compressional mode earthward and couple to transverse waves at LEO altitudes. Subsequently Cluster and Polar missions have confirmed that Pi1 pulsations are associated with plasma fast flows from deep within the magnetotail. The implication is that fast flows trigger the compressional wave energy that couples to the shear mode waves. These Alfvén waves drive the Alfvénic aurora in what is observed as the brightening of an existing arc. With relation to the FAST-GOES observations, there is yet, in particular, a question as to the presence of a conversion mechanism of magnetospheric compressional wave energy into Alfvén waves in a frequency band that is much higher than typical eigenfrequencies of field line Alfvén oscillations. A possible mechanism responsible for the resonant mode conversion of a fast mode wave packet into Alfvénic wave packet due to the finite frequency effect was proposed by Pilipenko et al. [2008]. So far, only few events were noted, so this suggestion awaits further validation.

2.2.3. Pc2 Waves

Pc2 waves ( mHz) are rare type of pulsations observed on the ground. Surprisingly, they are found to be almost always present in the topside ionosphere and magnetosphere, as shown by low-orbiting CHAMP and magnetospheric THEMIS spacecraft data analysis [Yagova et al., 2015]. These Pc2 pulsations have occurred at CHAMP mostly just inside the plasmapause . The amplitudes of compressional and transverse components were comparable. The mechanism behind these signals is not yet known. The responsible wave mode is thought to be a mode of the waveguide formed at the plasmapause, and partly converted into Alfvén waves. It is, of course, possible that these waves were generated by the ion cyclotron instability of energetic oxygen ions.

2.2.4. Pc3 Waves

Dayside Pc3 (20–70 mHz) waves are typical dayside ULF wave activity observed during quiet and moderate geomagnetic activity nearly every day. A part of dayside Pc3 waves at low latitudes can leak to the nightside. These waves are commonly considered as a magnetospheric and ground image of upstream waves beyond the bow shock. Under a favorable interplanetary magnetic field (IMF) orientation, most of the dayside bow shock is confined to a quasi-parallel shock wave (IMF is normal to the bow shock surface). The protons of the solar wind can then be energized and reflected back from the bow shock to generate EMIC waves in the foreshock region. This conjecture is supported by the linear statistical relationship between wave frequency f and IMF magnitude BIMF, and strong control of Pc3 wave activity by the IMF cone angle θxB. The more complete discussion of this dependence can be found in [Takahashi et al., 1984].

Pc3 waves in the near-equatorial regions of the magnetosphere have been suggested as the mechanism of inward transport of upstream wave energy into the inner magnetosphere via compressional fast mode (e.g., see Yumoto et al. [1985]; Kim and Takahashi [1999]; Takahashi et al. [1994]). Because fast waves are reflected from regions with high Alfvén velocity VA, they are thought to be localized only in the near-equatorial plane of the magnetosphere, and that they can reach the ionosphere only as an evanescent mode. Therefore, traditionally, it has been assumed that Pc3 waves on the ground are mainly produced by Alfvén waves, which can reach the bottom ionosphere without reflection. Alfvén field line oscillations can be resonantly excited by the compressional fast wave mode in a latitudinally localized resonance region, where the frequency of an external source f matches the eigenfrequency of a magnetic shell, .

Heilig et al. [2007] and Ndiitwani and Sutcliffe [2009] found the compressional power to be unexpectedly large in LEO measurements. In magnetic field measurements from CHAMP satellite, Pc3 waves were seen instead to be clearly in the magnetic field-aligned component, whereas on the ground their signatures were in the H component. The coherence between ground and satellite wave signatures was high over wide latitude and longitude ranges. Observations of Pc3 pulsations by the scalar magnetometer on the Ørsted satellite (altitude ~ 650–900 km) also showed dominance of the compressional component [Jadhav et al., 2001]. Pc3 wave packets were almost simultaneous at Ørsted and at ground magnetic stations. In nighttime events, the Pc3 packets had about the same amplitude on the ground and in space, but during the daytime, Pc3 amplitudes at the satellite were larger than on the ground, especially at lower latitudes.

Heilig et al. [2007] performed a statistical analysis of the compressional Pc3 waves in the topside ionosphere recorded onboard CHAMP (Figure 2.1). The observations revealed a clear latitudinal distribution of the Pc3 amplitudes: the average dayside compressional power had a peak near the geomagnetic equator and at high latitudes, and minima showed up at latitude in both hemispheres. The latitudinal characteristic was rather symmetrical about the dip-equator, and peak values at high latitudes and at the equator had similar magnitudes. The additional nighttime maximum at low latitudes and high-latitude maxima on the dayside and nightside were likely produced by the contribution of spatial structures sampled by the fast moving satellite, namely the equatorial spread F phenomenon and field-aligned currents.

Image described by caption.

Figure 2.1 MLT-magnetic latitude distribution of the compressional power in the mHz band near March equinox (about 4 month of data per year centered at March equinox) based on all observations between 2001–2007 by CHAMP. The wave power has been corrected for solar wind speed variation.

These authors showed that besides the upstream wave-related activity with BIMF-dependent frequency, a typical Pc3 pulsation observed at LEO contains a field line resonance contribution with latitude dependent frequency. A case study on a conjunction event between CHAMP and the ground SEGMA network clearly detected the field line Alfvén resonance [Vellante et al., 2004]. These authors succeeded in locating the characteristic signatures of the Alfvén resonance in the spatial structure of Pc3 wave. The behavior of the azimuthal magnetic component showed a specific amplitude-phase structure: the reversal of polarization sense through the resonant shell and π/2 rotation of the polarization ellipse upon transmission through the ionosphere.

Ndiitwani and Sutcliffe [2009] evaluated a similar Pc3 event and found a negative Doppler frequency shift during a poleward section of CHAMP’s orbit. Ndiitwani and Sutcliffe [2010] reported on two Pc3 events observed by CHAMP with L-dependent Doppler-shifted frequency. These results and especially the results of the statistical survey of Heilig et al. [2013] confirmed the occurrence of the flight direction dependent Doppler shift. Figure 2.2 shows the power spectrum of toroidal Alfvén waves as a function of latitude averaged from four months of daytime (07–15 MLT) observations made by CHAMP along poleward orbit segments around the March equinox in 2003. As compared with simultaneous field line resonances detected along the MM100 ground magnetometer array with latitude dependent frequency (dashed line), CHAMP recorded Alfvén waves that were Doppler shifted to lower frequencies (dotted line). No significant dependence