We use Van Allen Probes (Radiation Belt Storm Probes A and B, henceforth
RBSP-A and RBSP-B) and GOES-13 and GOES-15 (henceforth G-13 and G-15) multipoint
magnetic field, electric field, plasma, and energetic particle observations
to study the spatial, temporal, and spectral characteristics of
compressional Pc5 pulsations observed during the recovery phase of a strong
geomagnetic storm on 1 January 2016. From ∼ 19:00 to 23:02 UT, successive magnetospheric compressions enhanced the peak-to-peak
amplitudes of Pc5 waves with 4.5–6.0 mHz frequencies from 0–2 to 10–15 nT at
both RBSP-A and RBSP-B, particularly in the prenoon magnetosphere. Poloidal Pc4
pulsations with frequencies of ∼ 22–29 mHz were present in the
radial Bx component. The frequencies of these Pc4 pulsations diminished with
increasing radial distance, as expected for resonant Alfvén waves
standing along field lines. The GOES spacecraft observed Pc5 pulsations with
similar frequencies to those seen by the RBSP but Pc4 pulsations with lower
frequencies.
Both RBSP-A and RBSP-B observed frequency doubling in the compressional
component of the magnetic field during the Pc5 waves, indicating a
meridional sloshing of the equatorial node over a combined range in ZSM
from 0.25 to -0.08 Re, suggesting that the amplitude of this meridional
oscillation was ∼ 0.16 Re about an equatorial node whose mean
position was near ZSM=∼0.08 Re. RBSP-A and RBSP-B HOPE (Helium Oxygen Proton Electron)
and MagEIS (Magnetic Electron Ion Spectrometer) observations provide the first evidence for a corresponding
frequency doubling in the plasma density and the flux of energetic electrons,
respectively. Energetic electron fluxes oscillated out of phase with the
magnetic field strength with no phase shift at any energy. In the absence of
any significant solar wind trigger or phase shift with energy, we interpret
the compressional Pc5 pulsations in terms of the mirror-mode instability.
Introduction
Ultralow frequency (ULF) pulsations – with periods of 100 s or greater, with high azimuthal wave
numbers (m), with magnetic field perturbations in the radial direction, and
with electric field perturbations in the azimuthal direction – within the Earth's
magnetosphere are typically poloidal waves (Sugiura and Wilson, 1964).
According to Elkington et al. (2003), energetic particles with drift
frequencies of 6.7–22 and 1.7–6.7 mHz can readily interact with
corresponding high-m poloidal Pc4 and Pc5 pulsations. Because the atmosphere
and ionosphere screen these high-m waves from the ground, they can only be
studied with the help of satellite observations. Past studies of Pc4 and Pc5
pulsations with significant compressional components employed observations
from locations at or near geosynchronous orbit (e.g., Dai et al., 2013).
Higbie et al. (1982) and Nagano and Araki (1983) showed that long-lasting
compressional Pc5 pulsations occur most frequently in the dayside
magnetosphere during the recovery phase of magnetic storms. Storm-time Pc5
pulsations occur in the afternoon sector between 12:00 and 18:00 LT (local time)
following injections of ring current particles (Kokubun, 1985).
A number of studies have examined compressional Pc5 waves outside
geostationary orbit. According to these studies, compressional Pc5 waves
were observed in the dawn (Hedgecock, 1976), dusk (Constantinescu et al.,
2009), and noon (Takahashi et al., 1985) sectors. Zhu and Kivelson (1991)
reported that intense compressional waves are a persistent feature on both
flanks of the magnetosphere. Compressional Pc5 pulsations occur within
∼ 20∘ latitude of the magnetic equator (Vaivads et
al., 2001). They have wavelengths of several radii (Walker et al., 1982) and
often exhibit harmonics. Elkington et al. (2003) noted that poloidal and
compressional modes are far more effective for the radial transport of
energetic particles than the toroidal mode. Two methods are used to identify
the harmonic mode of a poloidal oscillation. The first compares the phase
difference between the radial component of the magnetic field and the
azimuthal component of the electric field (Takahashi et al., 2011). The
second compares observed wave frequencies with the eigenfrequencies
predicted by theory (Cummings, 1969). The multisatellite study of Takahashi
et al. (1987a) showed that a compressional Pc5 wave had an antisymmetric
standing structure.
Compressional Pc5 pulsations have been ascribed to numerous excitation
mechanisms. They can be produced by internal and external processes. It is
supposed that the solar wind is the main external source for pulsations
produced by the Kelvin–Helmholtz (KH) instability at the magnetopause or the
inner edge of the low-latitude boundary layer (e.g., Guo et al., 2010).
Observations indicating enhanced rates of Pc5 occurrence during periods of
greater solar wind velocity support this model (e.g., Engebretson et al.,
1998). Transient variations in the dynamic pressure of the solar wind or
foreshock (e.g., Wang et al., 2018; Shen et al., 2018) that cause abrupt
changes in the magnetic field strength in the magnetosphere and sudden
impulses in the ionosphere (e.g., Zhang et al., 2010; Sarris et al., 2010)
provide another possible trigger for Pc5 pulsations. External pressure
impulses can cause compressional oscillations of the magnetosphere with
discrete eigenfrequencies, known as global modes or cavity/waveguide modes
(Samson et al., 1992). Periodic solar wind dynamic pressure variations
directly drive some compressional magnetospheric magnetic field oscillations
(e.g., Kepko and Spence, 2003; Motoba et al., 2003). Takahashi and Ukhorskiy (2008) considered solar wind pressure variations as the main external driver
of Pc5 pulsations observed at geosynchronous orbit in the dayside
magnetosphere.
Internal generation mechanisms for compressional Pc5 pulsations include the
drift-bounce resonant instability which occurs for particles with resonance
drift and bounce periods (Southwood et al., 1969) and the drift-mirror
instability in the presence of strong temperature anisotropies (Chen and
Hasegawa, 1991). In high β plasmas (β is the plasma pressure
divided by the magnetic pressure), these mechanisms favor antisymmetric
waves (Cheng and Lin, 1987).
One possible generation mechanism for compressional Pc5 pulsations at
geosynchronous orbit is a drift-mirror instability of ring current particles
(e.g., Lanzerotti et al., 1969). While the observed anticorrelated magnetic
field strength and ion flux oscillations are expected for a drift-mirror
wave (Kremser et al., 1981), the instability criterion is generally not
satisfied (Pokhotelov et al., 1986). One possible reason for the lack of
consistency between theory and observation might be because the real
geometry of the magnetosphere is not taken into account (Cheng and Lin,
1987). Compressional pulsations are often accompanied by pulsations in
particle fluxes (Kremser et al., 1981; Liu at al., 2016). Particle
observations can provide useful information on the spatial and wave
structure of ULF pulsations. Lin et al. (1976) explained flux oscillations
as the adiabatic motion of particles in a magnetohydrodynamic wave. Kivelson
and Southwood (1985) studied charged particle behavior in compressional ULF
waves and showed that “a mirror effect” is the dominant cause for particle
flux modulations. Finite gyroradius effects enable detection of gradients in
particle flux associated with waves (e.g., Korotova et al., 2013).
We use multipoint magnetic field, plasma, and energetic particle
observations from RBSP-A and RBSP-B (Radiation Belt Storm Probes) and G-13 and G-15 (GOES) to study the spatial,
temporal, and spectral characteristics of compressional Pc5 pulsations
observed deep within the magnetosphere during the recovery phase of the
strong magnetic storm which began on 31 December 2015. We investigate the
type of pulsation (compressional versus transverse), their harmonic mode,
and their latitudinal nodal structure. We focus on the properties of double-frequency pulsations that occurred in the vicinity of the geomagnetic
equator. We demonstrate that the energetic particles respond directly to the
compressional Pc5 pulsations and also exhibit a double-frequency
oscillation. We search for possible solar wind triggers and test two
possible generation mechanisms: drift-bounce resonance and mirror
instability. The paper is organized as follows. Section 2 describes
the instruments and resources. Section 3 presents the solar wind and interplanetary magnetic field (IMF)
conditions. Section 4 provides an analysis of these waves and their
generation mechanisms.
Resources
The Van Allen Probes mission can be used to study the geospace response to a
fluctuating solar wind. The mission began in August 2012 with a twin
spacecraft launch into similar 10∘ inclination orbits with perigee
altitudes slightly greater than 600 km and apogee altitudes just beyond
30 000 km (Mauk et al., 2012). The spacecraft carry instruments that measure
electromagnetic fields, ultralow frequency waves, and charged particle populations deep within
the magnetosphere. This paper employs observations of the most abundant ion
components as well as electrons, over the 0.001–50 keV energy range, of the
core plasma populations from the HOPE instrument; populations of 20–4000 keV
ions and electrons from the MagEIS instrument (Blake et al., 2013) in the
Energetic Particle, Composition, and Thermal Plasma (ECT) suite (Spence et al.,
2013); and fluxes of ions over the energy range from ∼20 to ∼1 MeV and electrons over the energy range from ∼25 to ∼1 MeV
(RBSPICE, Radiation Belt Storm Probes Ion Composition Experiment) (Mitchell et al., 2013) in conjunction with observations from the
magnetometer in the Electric and Magnetic Field Instrument Suite and
Integrated Science (EMFISIS) suite (Kletzing et al., 2013) and the Electric
Field and Waves (EFW) instrument (Wygant et al., 2013). We examine electric
and magnetic field measurements with 11 and 4 s time resolutions,
respectively, and differential particle flux observations with
∼11 s (spin period) time resolution. The data are provided by
NASA GSFC's CDAWeb (Coordinated Data Analysis Web) in the MGSE (modified GSE, with GSE meaning geocentric solar ecliptic) coordinate system. We use
magnetic field data from G-13 and G-15 with 0.5 s time resolution (Singer et
al., 1996). Finally, we employ Wind (spacecraft) solar wind magnetic field and 3DP plasma
data with 3 s time resolution (Lepping et al., 1995; Lin et al., 1995).
Bz component of the magnetic field observed at Wind and
geomagnetic activity indices (Dst and AE) obtained from the OMNI database
(upper panels) from 12:00 UT on 30 December to 00:00 UT 2 January 2016. The
bottom panels show Wind observations of the magnetic field components, total
magnetic field strength, cone angle, pressure, plasma density, and velocity
from 16:00 UT on 1 January 2016 to 00:00 UT on 2 January 2016. Shading
highlights intervals when magnetospheric spacecraft observed Pc5
compressional pulsations.
Orbits, solar wind, and geomagnetic conditions
Figure 1 presents the Bz component of the interplanetary magnetic field
observed at Wind, and geomagnetic activity indices (Dst and AE) obtained from
the OMNI database (upper panels; (http://omniweb.gsfc.nasa.gov, last access: 30 April 2020), from 12:00 UT on 30 December to 00:00 UT on
2 January 2016. The bottom panels show Wind observations of the magnetic
field components, total magnetic field strength, cone angle, pressure,
plasma density, and velocity from 16:00 UT on 1 January 2016 to 00:00 UT on
2 January 2016 during which time the spacecraft moved from GSM (X, Y, Z) = (194.7, 20.1, -12.5) Re to (194.8, 23.6, -7.4) Re (where GSM represents the geocentric solar magnetospheric system and Re represents Earth radius). The pulsation events
to be studied here occurred late on 1 January 2016, following a prolonged
period of strongly southward IMF orientation and geomagnetic activity. A
substantial increase in the solar wind dynamic pressure early on 31 December was followed by a strong southward IMF that persisted from 19:00 UT on
31 December 2015 until 09:00 UT on 1 January 2016. A strong electrojet
with AE index greater than 2100 nT at 12:36 UT on 31 December 2015 was
followed by two moderate substorms that enhanced AE at ∼ 14:00
and 18:45 UT on 1 January 2016. The Dst index responded by reaching a value
as low as -110 nT at 00:30 UT on 1 January 2016. Shading highlights the
interval from ∼ 19:00 to 23:02 UT late in the recovery phase
and late in the day on 1 January 2016 when the Van Allen Probes and GOES
spacecraft observed the strong compressional Pc5 pulsations of interest to
this study.
The latter interval (bottom panels) was marked by strong variations in the
solar wind dynamic pressure. Shading marks an interval of depressed magnetic
field strengths and generally anticorrelated enhanced densities, velocities,
and solar wind dynamic pressures. The cone angle, θ, defined as the
angle between the IMF and the Sun–Earth line was less than 45∘ during
this interval. The magnetic field was briefly aligned with the Sun–Earth
line (Bx) at the center of the interval from 20:00–21:00 UT. For most of the
∼ 4 h long shaded interval, IMF Bx (By) was predominantly
positive (negative) and the Bz component remained almost constant near 0 nT,
indicating a spiral and equatorial IMF configuration. The total magnetic
field strength decreased from 7.9 nT at 18:00 UT to 2.2 nT at 19:48 UT, and
the solar wind velocity and dynamic pressure increased from 426 km/s and
0.62 nPa at 18:00 UT to 457 km/s and to 3.37 nPa at 20:47 UT, respectively.
At ∼ 22:20 UT almost all parameters returned to their initial
undisturbed values.
Trajectories of RBSP-A (red), RBSP-B (blue), G-13 (black), and
G-15 (purple) from 15:00 to 24:00 UT on 1 January 2016 in the X–Y and X–Z
GSM planes. Open circles mark the beginning of the spacecraft trajectories
which are duskward for the GOES spacecraft and duskward at apogee for the
Van Allen Probes. The thick line segments indicate the locations of the
spacecraft at the times when compressional Pc5 magnetic field pulsations
occurred. Dots mark their locations where weak pulsations (A < 5 nT)
occurred.
Figure 2 presents RBSP-A, RBSP-B, G-13 (MLT is ∼ UT -5, where MLT represents magnetic local time), and G-15
(MLT is ∼ UT-9) trajectories from 15:00 to 24:00 UT on 1 January 2016 in the X–Y and X–Z GSM planes. Open circles mark the beginning of
the spacecraft trajectories which are duskward for the GOES spacecraft and
duskward at apogee for the Van Allen Probes. All of the spacecraft were
north of the equator when in the dayside magnetosphere. The thick line
segments (dots) indicate the locations of the spacecraft at the times when
(weak) Pc5 magnetic field pulsations occurred.
Observations of the solar wind dynamic pressure at Wind (time
shifted) and the total magnetic field strength at G-13 and G-15 from 18:00 to 24:00 UT. The arrows connect enhancements of the solar wind dynamic
pressure to corresponding compressions of the magnetosphere.
Figure 3 compares lagged Wind solar wind dynamic pressure variations with
G-13 and G-15 observations of the dayside magnetospheric magnetic field. The
arrows connect enhancements of the solar wind dynamic pressure to
corresponding compressions of the magnetosphere. To determine the lag time
between the Wind and GOES-15 observations, we related individual
magnetosphere compressions to corresponding dynamic pressure variations.
Additionally, we confirmed these empirically derived lag times with simple
ballistic estimates based on the solar wind velocity and the distance of
Wind from Earth. It is relatively easy to associate the GOES magnetic field
enhancements with corresponding features in the solar wind dynamic pressure
at the beginning and the end of the interval but less easy from 19:50 to
21:20 UT corresponding to ∼ 20:45 and 22:15 UT at the GOES
spacecraft. The lag time from Wind to the Earth is not uniform and depends
on IMF orientation. At the beginning and end of the interval, when the IMF
was spiral (Bx > 0, By < 0), the lag was in the range of
∼ 46 to 58 min. Consistent with expectations, the lag became
greater for the interval from ∼ 19:50 to 21:20 UT when the IMF
was nearly radial (By and Bz ∼ 0 nT). The reasonable
correspondence of the magnetosphere compressions to solar wind dynamic
pressure variations demonstrates that Wind was a good monitor for solar wind
conditions and that a series of pressure enhancements were applied to the
magnetosphere during the interval of interest. Pc5 pulsation amplitudes at
G-13 and G-15 were greater during the interval of enhanced solar wind dynamic
pressure and magnetospheric magnetic field strengths than they were at
earlier and later times.
(a, b) G-15 and G-13 (a) total magnetic field strength from 18:00 to 24:00 UT on 1 January 2016. RBSP-A and RBSP-B (b) total magnetic field
strength from 18:40 to 21:10 UT and from 20:40 to 23:10 UT on 1 January 2016, respectively, Beneath the panels are listed the universal time (UT)
and magnetic local time (MLT).
Pulsation observationsSpatial characteristics of Pc5 pulsations
Consider the spatial, temporal, and spectral characteristics of the
compressional Pc5 pulsations. Figure 4a shows G-13 and G-15 observations of
the total magnetic field strength from 18:00 to 24:00 UT. The spacecraft
observed long-duration Pc5 pulsations over a wide longitudinal region in the
pre- and postnoon magnetosphere from 10:00 to 15:20 MLT (Fig. 2). G-15
observed weak, less than ∼ 5 nT amplitude, Pc5 waves from
18:28 to 19:04 UT prior to the main event. During the main event from
19:04 to 23:00 UT, the magnetosphere was compressed (Fig. 3), magnetic
field strengths increased, and the amplitude of these waves increased to
values ranging from 10 to 16 nT with peak amplitudes prior to local noon.
G-13 observed weak Pc5 pulsations with amplitudes of 2–4 nT throughout most
of the time interval from 16:40 UT (not shown) to 21:00 UT. During the
interval from 19:34 UT (∼ 14:45 MLT) to 20:10 UT (∼ 15:20 MLT), the pulsations reached slightly stronger
amplitudes of 5–8 nT. At 23:02 UT all Pc5 wave activity at both GOES
stopped.
Figure 4b shows the RBSP-A and RBSP-B total magnetic field strength from 18:40 to 21:10 UT and from 20:40 to 23:10 UT, respectively, on 1 January 2016. Taken together, RBSP-A and RBSP-B observed Pc5 pulsations that occupied
the inner dayside magnetosphere from 5.26 to 5.75 Re and from 09:56 to
12:44 MLT (Fig. 2). Prior to the arrival of the strong solar wind dynamic
pressure variations from 18:15 to 18:55 UT, RBSP-A observed very weak
pulsations with Pc5 periods and amplitudes of 1–3 nT (not visible at this
scale). After the compression of the magnetosphere just after 19:00 UT, the
pulsation amplitude at RBSP-A increased to values ranging from 10 to 15 nT
with the peak amplitude occurring prior to local noon (Fig. 4b). RBSP-B
observed similar compressional Pc5 pulsations from 20:46 UT that ceased
simultaneously with the end of the magnetospheric compression at about 23:02 UT.
RBSP-A and RBSP-B magnetic field observations in field-aligned
coordinates from 18:40 to 21:10 UT and from 20:40 to 23:10 UT on
1 January 2016, respectively.
To determine the type of the Pc5 waves, we converted the magnetic field
observations from GSE into the field-aligned coordinate system (FAC). Here the Z axis
lies parallel to the locally averaged magnetic field. The Y axis points
approximately azimuthally eastward and is transverse to B and to the outward
radius vector. The X axis completes the right-handed system and is directed
approximately radially outward from Earth. Figure 5 presents RBSP-A and RBSP-B
magnetic field observations in FAC. The Bz component is the value of the
total magnetic field after subtraction of a 16 min sliding average. The
Pc5 pulsations are observed in all three components, but the amplitudes of
the azimuthal By and radial Bx components are rather small and do not exceed
7 nT. The compressional Bz component is much more pronounced for both
spacecraft, reaching amplitudes of 14–15 nT before local noon. Consequently,
the pulsations are primarily compressional. The Bz component oscillated out
of phase with the Bx component at RBSP-A and in phase at RBSP-B and in
quadrature with the By component. Simultaneous RBSP-A and RBSP-B electric and
magnetic field measurements provide an opportunity to study the mode of the
Pc5 waves. Determining the harmonic mode of the Pc5 waves requires us to
consider the phase of the azimuthal component of the electric field, Ey, with
respect to the radial component of the magnetic field Bx as a function of
latitude (Takahashi et al., 2011). Figure 6 shows that the phase of the Ey
component leads that of the Bx component by 90∘ at RBSP-A from
19:10 to 20:00 UT; therefore, the Pc5 waves are second harmonic in
nature.
Spectral characteristics
We calculated dynamic spectra for the magnetic field pulsations. Figure 7
presents the radial, azimuthal, and compressional components of the dynamic
spectra of the magnetic field at RBSP-A and RBSP-B from 18:00 to 21:10 UT and
from 20:00 to 23:10 UT on 1 January 2016, respectively. The color bar on
the right shows the scale for power for frequencies ranging from 0 to 41 mHz in each component. The magnetic field exhibited several wideband
enhancements at frequencies ranging from 4 to 29 mHz. As expected for
compressional Pc5 pulsations, both GOES spacecraft observed the strongest
power densities in the Bz component at dominant frequencies of
∼ 4.5–6 mHz. Red arrows in the Bz panels of Fig. 7 for
RBSP-A and RBSP-B indicate the double-frequency pulsations at ∼ 5.5 and ∼ 11 mHz. We calculated Fourier spectra for the
three components of the RBSP-A and RBSP-B magnetic field in 600 s
sliding-average mean FAC for each 30 min interval during the event.
Figure 8 presents examples of Fourier spectra calculated for the RBSP-A and
RBSP-B magnetic field from 19:30 to 20:00 UT and from 22:30 to 23:00 UT,
respectively, on 1 January 2016. The red arrows show the dominant
frequencies at 5.5 and 5 mHz observed at the two spacecraft, corresponding
to periods of 170–200 s. RBSP-A and RBSP-B were situated 3 h in local
time apart; the similar frequencies indicate that conditions in the dayside
magnetosphere remained steady for a long time and over a broad region.
The phase difference between the RBSP-A azimuthal component of the
electric field (red curve is boxcar smoothed) and the radial component of
the magnetic field Bx in field-aligned coordinates (dashed curve) from 19:10 to 20:00 UT on 1 January 2016. The amplitude of Ey was multiplied by a
factor of 3 to better display the visual effects.
In passing, we note the presence of Pc4 pulsations. Returning to Fig. 7,
we see enhanced power densities at frequencies of ∼ 22–29 mHz with dominant frequencies from 23 to 27 mHz primarily in the radial Bx
component. These can be ascribed to poloidal Pc4 produced simultaneously
with the Pc5 but likely with another energy source. The frequencies of the
Pc4 pulsations decrease with increasing radial distance, as expected for
resonant standing Alfvén waves (Sugiura and Wilson, 1964). Pulsation
periods depend upon the magnetic field line length, the magnetic field
magnitude, and the ion density. Shorter field line lengths and enhanced
magnetic field strengths closer to Earth decrease pulsation periods. Blue
arrows in Fig. 8 indicate Pc4 pulsations at ∼ 25–27 mHz.
Three-component dynamic spectra of magnetic field data at RBSP-A
and RBSP-B from 18:00 to 21:10 UT and from 20:00 to 23:10 UT on 1 January 2016, respectively. Beneath the panels are listed the universal time (UT),
magnetic local time (MLT), radius (Re), and Z (SM) in Earth radii.
Figure 9 presents dynamic spectra for the G-13 and G-15 magnetic field in FAC
from 18:00 to 24:00 UT on 1 January 2016. Spectral power was calculated
for frequencies from 0 to 48 mHz. Like the RBSP-A and RBSP-B magnetic field
spectra, there are two broad frequency band enhancements corresponding to
Pc4 and Pc5 frequencies. The dominant frequencies for the compressional Pc5
pulsations occur from 4.5 to 6.5 mHz. These frequencies are similar to those
observed by Van Allen Probes, and we suppose that they were generated by the
same sources. The Pc4 pulsations are most pronounced in the radial Bx
component and display strongest spectral power densities in the frequency
range from 13 to 21 mHz. These frequencies are lower than those observed by
Van Allen Probes, since the GOES spacecraft were located further radially
outward from Earth (Sugiura and Wilson, 1964). The frequencies of the
long-lasting Pc4 pulsations observed by G-15 depended on local time. They
decreased from 20–22 mHz in the prenoon magnetosphere to 14–17 mHz near
local noon, perhaps in response to differing conditions (e.g., densities).
Takahashi at el. (1984) noted that an increase in plasma mass density from
morning to afternoon is typical at geosynchronous orbit. Since the
frequencies of the Pc4 pulsations depended on local time and radial distance
from Earth, their sources must be more localized than those for the Pc5
pulsations.
Fourier spectra calculated for the radial, azimuthal, and
compressional components of the RBSP-A and RBSP-B magnetic field in 5 min
sliding-average mean field-aligned coordinates from 19:30 to 20:00 UT and from 22:30 to 23:00 UT on 1 January 2016, respectively.
Particle signatures
Energetic particle observations provide further information concerning this
event. We inspected RBSP-A and RBSP-B MagEIS observations of energetic particles
from 18:30 to 21:00 UT and from 20:40 to 23:10 UT on 1 January 2016,
respectively, and found that the intensities of electrons with energies from
tens of kiloelectron volts to 2 MeV oscillated with Pc5 periods corresponding to those of
the magnetic field. Figure 10a and b show an example of RBSP-A observations
of electron fluxes (a) in the energy range of from 31.5 to 1704 keV from
18:30 to 21:00 UT and (b) their expanded view for selected energies from
19:20 to 20:00 UT. The energetic electron fluxes oscillated out of phase
with the compressional Bz component of Pc5 magnetic field pulsations and did
not display any phase differences across all energies. The depth of
modulation (the peak to valley ratio) is greater for higher-energy electrons,
consistent with the results by Liu et al. (2016), who interpreted similar
observations in terms of mirror-mode waves. The lower-energy electron fluxes
displayed more noticeable enhancements as a response to the compressions of
the magnetosphere. Kivelson and Southwood (1985) noted that the maintenance
of pressure balance in low-frequency compressional waves usually requires
the presence of some pitch angle anisotropy, and the antiphase relation
between the plasma and magnetic field pressures suggests that particle pitch
angle distributions peak near 90∘. Figure 11 presents RBSP-A and
RBSP-B observations of pitch angle distributions for electrons with energies
from 54 to 1060 keV from 18:30 to 21:00 UT and from 20:40 to 23:10 UT
on 1 January 2016, respectively. The figure confirms that pitch angle
distributions peak near 90∘. Furthermore, it shows that the
electron intensities display quasi-periodic enhancements at all energies
with the strongest at pitch angles near 90∘.
Three components of dynamic spectra of the magnetic field data at
G-15 and G-13 from 18:00 to 24:00 UT on 1 January 2016. Beneath the
panels are listed the universal time (UT), magnetic local time (MLT in SM),
L, and Z (SM) in Earth radii.
Double-frequency pulsations
When RBSP-A and RBSP-B were in the vicinity of the geomagnetic equator, the
compressional Pc5 pulsations displayed peculiar features indicating
frequency doubling. The compressional components oscillated with a frequency
twice that of the transverse component. Coleman (1970) was the first to
report observations of such events in the geosynchronous magnetic field.
Higuchi et al. (1986) called them harmonic structures when the first and
second harmonics exhibited similar amplitudes and transitional structures
when the amplitudes of the alternating peak were different. Takahashi
(1987b) interpreted double-frequency oscillations in terms of a model
invoking the second-harmonic structure of an antisymmetric standing wave in
which the location of the equatorial node of field-aligned displacement
oscillates in phase with the wave. Cheng and Qian (1994) presented a model
for the magnetic field perturbations during the pulsations reported by
Takahashi et al. (1987a, 1990). Figure 6 in the paper of Korotova et al. (2013) illustrates how low-latitude spacecraft can observe two magnetic
field strength enhancements per wave cycle when the equatorial node
oscillates latitudinally up and down in phase with an antisymmetric
compressional wave. Right at the equator the spacecraft observes identical
amplitudes for the two compressions. At any other latitude the two
compressions at the spacecraft will have different magnitudes and the
imbalance between them increases when the spacecraft moves farther from the
equator. Takahashi et al. (1987b) showed that a latitudinal shift of a
fraction of a degree can turn a harmonic Bz structure into a nonharmonic
structure. Spacecraft located far from the magnetic equator do not observe
frequency doubling but just a single enhancement. Korotova et al. (2013)
derived the latitudinal structure of the waves by invoking north–south
sloshing of the low-latitude node.
(a, b) RBSP-A observations of electron fluxes (a) in the energy
range from 31.5 to 1704 keV from 18:30 to 21:00 UT and (b) their
expanded view for selected energies from 19:20 to 20:00 UT.
Figure 12a and b present (a) RBSP-A and RBSP-B observations of double-frequency
magnetic pulsations and (b) their locations in the X–Y GSM and X–Z SM
planes. Dashed lines in Fig. 12a indicate intervals when the double-frequency pulsations in Bz are most prominent: 20:45 to 20:54 UT at RBSP-A and
21:03 to 21:31 UT at RBSP-B in these line plots. However, the amplitudes
of the second harmonic are generally much lower than those of the first
harmonic. At these times, e.g., from 20:05 to 20:45 UT at RBSP-A and
from 21:35 to 21:55 UT at RBSP-B, the second-harmonic compressions in Bz are barely
perceptible in these line plots. Model predictions for the magnetic field
perturbations associated with an equatorial node whose latitude oscillates
in phase with an antisymmetric poloidal wave indicate that the ratio of the
amplitudes of the first-to-second harmonic compressions should change with
latitude, being ∼1 at the average position of the
low-latitude node and ∼0 at and beyond the maximum latitude
to which the oscillating node can reach (Takahashi et al., 1987b). To
determine the meridional motion of the magnetic field node, we measured
amplitudes of the first and second harmonics of the compressional
pulsations. We found that RBSP-A observed ratios near 1 at ZSM=∼0.08 Re, while RBSP-B observed ratios near 1 at ZSM=∼0.10 Re. These are the locations where the southward-moving
spacecraft pass through the mean positions of the equatorial node. Figure 12a shows that RBSP-A observed second harmonics from ZSM=0.25 to
0.04 Re, while RBSP-B observed them from ZSM=0.19 to -0.08 Re.
Consequently, we believe that the equatorial node oscillated with an
amplitude of at least 0.15 to 0.18 Re. Note, however, that the ratio of the
first-to-second harmonics does not show a smooth transition as the
spacecraft move equatorward. Either the amplitude of the compressional
pulsation or the meridional oscillation in the equatorial node varied in
time, probably abruptly.
RBSP-A and RBSP-B observations of pitch angle distributions for
electrons in the energy range from 54 to 1060 keV, from 18:30 to 21:00 UT and from 20:40 to 23:10 UT on 1 January 2016, respectively.
Figure 10a and b show that the compressional pulsations modulated energetic
electrons observed by RBSP-A, and we should therefore expect to find the
signatures of the double-frequency pulsations not only in the magnetic field
but also in the fluxes of particles. Takahashi et al. (1990) reported
AMPTE/CCE (Charge Composition Explorer) observations of compressional Pc5 pulsations that exhibited
harmonically related transverse and compressional magnetic oscillations that
modulated the flux of medium-energy protons (E>10 keV) with
double frequency but did not discuss the event in detail. We report the
first evidence for meridional sloshing of the equatorial node in the
simultaneous compressional Pc5 pulsations and variations of electron fluxes
and electron densities observed by MagEIS and Hope, respectively. Figure 13
presents RBSP-A (left panel) and RBSP-B (right panel) electron fluxes for
energies at 31.9 and 54.8 keV, electron densities, and the Bz component
of the magnetic field in FAC from 19:00 to 21:00 UT and at RBSP-B from
20:46 to 22:10 UT. The panels in the bottom of Fig. 13 present expanded
views of 20 min intervals with the double-frequency pulsations. The Bz
component of the magnetic field varies with double frequencies out of phase
with the fluxes of electrons and densities. This study gives better
insight into the nodal structure of the waves and helps to clarify their
source.
(a, b) RBSP-A and RBSP-B observations of double-frequency pulsations
(a) from 20:00 to 20:56 UT and from 20:48 to 21:55 UT, respectively,
and (b) their locations in the X–Y GSM and X–Z SM planes. Red and blue
dashed lines mark the intervals with harmonic structure of double-frequency
pulsations.
Testing Pc4-5 pulsation generation mechanisms
We tested several causes for the Pc4-5 pulsations, including solar wind
pressure pulses, the KH instability on the magnetopause, drift-bounce
resonant particle interactions, and the mirror-mode instability. First, with
the exception of the interval from 19:35 to 19:55 UT, the Wind
observations shown in Fig. 1 provide no evidence for periodic solar wind
drivers in the Pc5 range, be they density variations or IMF
fluctuations, thus ruling out solar wind pressure pulses as the
direct cause of the Pc4-5 pulsations. We then considered the possibility of
KH waves. These waves are expected when the solar wind velocity is high and
both the magnetosheath and magnetospheric magnetic fields lie transverse to
the magnetosheath flow, i.e., on the flanks of the magnetosphere when the IMF
points southward or in particular northward (e.g., Guo et al., 2010). As
shown in Fig. 1, the solar wind velocity during the interval when the Pc5
events occurred was only moderate, 400–460 km/s. Furthermore, the IMF did
not point either strongly northward or southward. Therefore, we conclude
that the compressional Pc5 pulsations were excited by processes internal to
the magnetosphere.
Panels for RBSP-A (a, b) and RBSP-B (c, d) present electron fluxes
for energies at 31.9 and 54.8 keV from EMFISIS, electron densities from
HOPE and the Bz component of the magnetic field in field-aligned coordinates
from MagEIS from 19:00 to 21:00 UT and from 20:46 to 22:10 UT,
respectively. Dotted lines mark the intervals of observations of
double-frequency pulsations. Panels (b, d) present
expanded views of 20 min intervals with the double-frequency pulsations to
better visualize their features.
Southwood (1981) and Kivelson and Southwood (1985) described how the
resonant drift-bounce interaction of particles with an
azimuthally propagating wave generates large-amplitude ULF waves in an
inhomogeneous background field. For this to happen, the wave frequency
ω must satisfy the resonance condition:
ω-mωd-Nωb=0,
where ωd and ωb are the angular drift and bounce
frequencies, respectively; N is an integer; and m is the azimuthal wave number. Southwood
(1973) predicted that particle flux oscillations just above and below the resonant energy should be 180∘ out of phase. As Fig. 10a and b demonstrate, RBSP-A did not observe any such phase
reversal in the electrons as a function of energy. We exclude the
drift-bounce resonance as the cause of these compressional Pc5 pulsations.
Finally, we examined the mirror instability criterion. The mirror
instability is a kinetic phenomenon that occurs spontaneously in anisotropic
high-β plasmas when the ratio of perpendicular to parallel pressures
is large (Southwood and Kivelson, 1993). The test for the mirror instability
is approximately given as follows:
Γ=1+β⊥(1-T⊥/T//)<0,
where T// and T⊥ are the plasma temperatures parallel and
perpendicular, respectively, to the ambient magnetic field, and β⊥ is the
ratio of the perpendicular component of the thermal plasma pressure to the
magnetic pressure. For our calculations, we obtained the magnetic field data
from EMFISIS and thermal plasma pressures perpendicular and parallel to the
magnetic field from RBSPICE. We used the density and temperature from HOPE
to calculate the parallel and perpendicular thermal pressures within the
energy range covered by this instrument, but we found these pressures to be
small compared to those from RBSPICE. Consequently, our calculations neglect
the contributions from HOPE to the thermal pressures.
(a, b) RBSP-A and RBSP-B plasma and magnetic field parameters
characterizing the pulsations. Subpanels in each panel show the
magnetic pressure, perpendicular plasma pressure, the ratio of the plasma
temperatures perpendicular and parallel to the magnetic field, beta, and the
results for the mirror instability criterion on 1 January 2016. Shaded grey
areas indicate the times when the drift-mirror instability is satisfied
(<1).
Figure 14a and b show RBSP-A and RBSP-B plasma and magnetic field parameters
characterizing the pulsations. The upper panels indicate that magnetic field
and plasma pressures vary in antiphase during the Pc5 pulsations. However,
the total pressure is not balanced as might be expected for mirror-mode
waves. We suppose that this is because the RBSPICE (or even the RBSPICE + HOPE) plasma instruments do not observe the entire plasma distribution.
Assuming that the total plasma pressure is proportional to the fraction that
RBSPICE does observe, we scaled the thermal plasma pressures observed by
RBSPICE upward to values that cause the sum of the magnetic and
perpendicular thermal plasma pressure variations associated with the waves
to be approximately constant during the intervals from 19:03 to 19:14 UT for RBSP-A and from 22:32 to 22:56 UT for RBSP-B. The upward scaling
factors were 1.97 and 1.69, respectively. We then applied these factors to
both the perpendicular and parallel pressures. The third subpanels of Fig. 14a and b show the values of β⊥ calculated from these scaled
pressures. Shaded grey areas in the fourth subpanels show when the drift-mirror instability is satisfied (<0). As the test for the mirror
instability is satisfied throughout most of the intervals of enhanced
temperature (pressure) anisotropy and β>1 at RBSP-A and
RBSP-B, we attribute the compressional Pc5 pulsations observed on 1 January 2016 to the mirror instability.
Conclusions
We used Van Allen Probes and GOES multipoint magnetic field, electric field,
plasma, and energetic particle observations to study the nature of
compressional Pc5 pulsations at the end of a strong magnetic storm on
1 January 2016. From ∼ 19:00 to 23:02 UT the magnetosphere
was compressed and transient increases of the total magnetic field strength
occurred every 20–40 min. During this interval the spacecraft observed
compressional Pc5 pulsations over a large longitudinal extent. The solar
wind pressure enhancements initiated and/or amplified compressional wave
activity in the dayside magnetosphere. The pulsations occupied the dayside
magnetosphere from 5.26 to 6.6 Re and from 09:56 to 15:20 MLT. Successive
solar wind pressure increases and magnetospheric compressions enhanced the
amplitude of Pc5 wave activity to values from 10 to 16 nT. The strongest
amplitudes occurred prior to local noon. They were observed when the IMF
cone angle was less than 45∘. We studied the wave mode of the Pc5
pulsations and found that they had an antisymmetric structure.
The greatest spectral power densities observed at RBSP-A and RBSP-B occurred in
the north or south (Bz) component of the magnetic field at frequencies of
∼ 4.5–6.0 mHz. The two spacecraft observed similar
frequencies, indicating that conditions within the dayside magnetosphere
remained steady for a long time and over a broad region. Enhanced spectral
power densities at frequencies of ∼ 22–29 mHz in the radial Bx
component can be attributed to the simultaneous generation of poloidal Pc4
pulsations by a different mechanism. The frequencies of the Pc4 pulsations
diminished with increasing radial distance. The dominant frequencies for the
compressional Pc5 pulsations observed by GOES resembled those observed by
RBSP-A and RBSP-B, and we suppose that they were generated by the same sources.
Pc4 pulsations observed by the GOES spacecraft displayed frequencies that
were lower than those observed by RBSP-A and RBSP-B, since the GOES spacecraft
were located further radially outward from Earth. Since the frequencies of
the Pc4 pulsations depended on local time and radial distance from Earth,
their sources must be more localized than those for the Pc5 pulsations.
When the spacecraft were in the vicinity of the geomagnetic equator, RBSP-A
observed meridional sloshing of the equatorial wave node from ZSM=0.25 to 0.04 Re, while RBSP-B observed them from ZSM=0.19 to -0.08 Re. Consequently, we believe that the motion of the meridional oscillation
of the position of the equatorial node was at least 0.15 to 0.18 Re. We
found that RBSP-A observed ratios near 1 at ZSM=∼0.08 Re, while RBSP-B observed ratios near 1 at ZSM=∼0.10 Re. These were the locations where the southward-moving spacecraft
RBSP-A and RBSP-B passed through the mean positions of the equatorial node at
ZSM=∼0.08 Re and at ZSM=∼0.10 Re, respectively. We report the first evidence for meridional
sloshing of the equatorial node in the double-frequency variations of
electron fluxes and electron density observed by MagEIS and HOPE,
respectively.
The energetic particles observed by RBSP-A and RBSP-B showed a regular
periodicity over a broad range of energies from tens of electron volts to 2 MeV with
periods corresponding to those of the compressional component of the ULF
magnetic field. The electron intensities exhibited quasi-periodic
enhancements at all energies with the most intense at pitch angles near
90∘. The energetic electron fluxes oscillated out of phase with
the magnetic field and did not display any phase shift across all energies.
The depth of modulation was larger for higher-energy electrons. We searched
for possible solar wind triggers and discussed generation mechanisms for the
compressional Pc5 pulsations in terms of drift-mirror instability and drift-bounce resonance. We interpret the compressional Pc5 waves in terms of
drift-mirror instability.
Data availability
Data used in the paper are available publicly at https://cdaweb.gsfc.nasa.gov/istp_public/, last access: 1 March 2020. GOES data were obtained from http://satdat.ngdc.noaa.gov/sem/goes/data/new_full/, last access: 2 January 2019. The electric field data were obtained from http://www.space.umn.edu/rbspefw-data/ (Wygant and Breneman, 2017), last access: 30 January, 2020.
Author contributions
GK drafted and wrote the paper with participation of
all coauthors. DS conceived the ideas. ME, ST, HS, and CK were consulted regarding the
data analysis. RR contributed to software development. MB was consulted regarding the drift-mirror instability test.
Competing interests
The authors declare that they have no conflict of interest.
Acknowledgements
We thank the Van Allen Probes project and experiment teams for their efforts to provide high-quality observations. We acknowledge NASA GSFC's CDAWeb site for providing access to the observations.
Financial support
Galina Korotova was supported by NASA contract no. 80NSSC19K0440. Michael Balikhin is grateful to the UK Science and Technology Facilities Council (STFC) (grant ST/R000697/1). David Sibeck was supported by GSFC WBS 605745.04.01, corresponding to the Van Allen Probes project. The work by the EFW team at the University of Minnesota was supported by APL contract to UMN 922613 under a NASA contract to APL NAS5-01072.
Review statement
This paper was edited by Georgios Balasis and reviewed by two anonymous referees.
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