Kyungguk Min

Whistler anisotropy instabilities as the source of banded chorus: Van Allen Probes observations and particle-in-cell simulations

Magnetospheric banded chorus is enhanced whistler waves with frequencies ωr<Ωe, where Ωe is the electron cyclotron frequency, and a characteristic spectral gap at ωr≃Ωe/2. This paper uses spacecraft observations and two-dimensional particle-in-cell simulations in a magnetized, homogeneous, collisionless plasma to test the hypothesis that banded chorus is due to local linear growth of two branches of the whistler anisotropy instability excited by two distinct, anisotropic electron components of significantly different temperatures. The electron densities and temperatures are derived from Helium, Oxygen, Proton, and Electron instrument measurements on the Van Allen Probes A satellite during a banded chorus event on 1 November 2012. The observations are consistent with a three-component electron model consisting of a cold (a few tens of eV) population, a warm (a few hundred eV) anisotropic population, and a hot (a few keV) anisotropic population. The simulations use plasma and field parameters as measured from the satellite during this event except for two numbers: the anisotropies of the warm and the hot electron components are enhanced over the measured values in order to obtain relatively rapid instability growth. The simulations show that the warm component drives the quasi-electrostatic upper band chorus and that the hot component drives the electromagnetic lower band chorus; the gap at ∼Ωe/2 is a natural consequence of the growth of two whistler modes with different properties.

Externally driven plasmaspheric ULF waves observed by the Van Allen Probes

We analyze data acquired by the Van Allen Probes on 8 November 2012, during a period of extended low geomagnetic activity, to gain new insight into plasmaspheric ultralow frequency (ULF) waves. The waves exhibited strong spectral power in the 5–40 mHz band and included multiharmonic toroidal waves visible up to the eleventh harmonic, unprecedented in the plasmasphere. During this wave activity, the interplanetary magnetic field cone angle was small, suggesting that the waves were driven by broadband compressional ULF waves originating in the foreshock region. This source mechanism is supported by the tailward propagation of the compressional magnetic field perturbations at a phase velocity of a few hundred kilometers per second that is determined by the cross-phase analysis of data from the two spacecraft. We also find that the coherence and phase delay of the azimuthal components of the magnetic field from the two spacecraft strongly depend on the radial separation of the spacecraft and attribute this feature to field line resonance effects. Finally, using the observed toroidal wave frequencies, we estimate the plasma mass density for L = 2.6–5.8. By comparing the mass density with the electron number density that is estimated from the spectrum of plasma waves, we infer that the plasma was dominated by H+ ions and was distributed uniformly along the magnetic field lines. The electron density is higher than the prediction of saturated plasmasphere models, and this “super saturated” plasmasphere and the uniform ion distribution are consistent with the low geomagnetic activity that prevailed.

Fast magnetosonic waves driven by shell velocity distributions

Using linear dispersion theory and particle-in-cell simulations, we explore the ion Bernstein instability driven by the shell-type ion velocity distribution which is related to the excitation of fast magnetosonic waves in the terrestrial magnetosphere. We first demonstrate a novel idea to construct the shell velocity distribution out of multiple Maxwellian ring-beam velocity distributions. Applying this technique, we find that the convergence of the linear theory instability can be achieved with only a moderate number of ring-beam components. In order to prove that such an approximation is legitimate and the linear theory instabilities evaluated are indeed valid, we use the exact shell distribution to carry out a number of one dimensional particle-in-cell simulations corresponding to multiple wave propagation angles adjacent to the direction at which the most unstable waves are expected to grow. The agreement between the linear dispersion analysis and the simulation results is generally very good: enhanced waves are organized along the linear theory dispersion curves in the frequency-wave number space, and relative wave amplitudes are ordered as the linear theory growth rates very well. However, the simulations show a few extra branches that are not expected from the linear dispersion analysis. A close examination of these extra branches suggests that they are not simulation artifacts and particularly related to the ring/shell-type distributions with large ring/shell speed (v>∼1.5 vA, where vA is the Alfven speed). In addition, our results show that substantial wave growth can occur at nonintegral harmonics of the proton cyclotron frequency at wave normal angles substantially far away from the perpendicular direction, which may provide an alternative explanation of the off-harmonic peaks of some fast magnetosonic waves observed in space.

Study of EMIC wave excitation using direct ion measurements

With data from Van Allen Probes, we investigate electromagnetic ion cyclotron (EMIC) wave excitation using simultaneously observed ion distributions. Strong He band waves occurred while the spacecraft was moving through an enhanced density region. We extract from helium, oxygen, proton, and electron mass spectrometer measurement the velocity distributions of warm heavy ions as well as anisotropic energetic protons that drive wave growth through the ion cyclotron instability. Fitting the measured ion fluxes to multiple sinm-type distribution functions, we find that the observed ions make up about 15% of the total ions, but about 85% of them are still missing. By making legitimate estimates of the unseen cold (below ∼2 eV) ion composition from cutoff frequencies suggested by the observed wave spectrum, a series of linear instability analyses and hybrid simulations are carried out. The simulated waves generally vary as predicted by linear theory. They are more sensitive to the cold O+ concentration than the cold He+ concentration. Increasing the cold O+ concentration weakens the He band waves but enhances the O band waves. Finally, the exact cold ion composition is suggested to be in a range when the simulated wave spectrum best matches the observed one.

Solar cycle variation of plasma mass density in the outer magnetosphere: Magnetoseismic analysis of toroidal standing Alfvén waves detected by Geotail

We study the variation of plasma mass density in the outer magnetosphere over a solar cycle using mass density estimated from the frequency of fundamental toroidal standing Alfven waves observed by the Geotail spacecraft. We identify wave events using ion bulk velocity data covering 1995–2006 and use events in the 0400–0800 magnetic local time sector for statistical analysis. We find that the F10.7 index is a dominant controlling factor of the mass density. For the equatorial mass density ρeq* that is normalized to the value at L = 11, we obtain an empirical formula logρeq*=−0.136+1.78×10−3F10.7, where the units of ρeq* and F10.7 are amu cm−3 and solar flux units (sfu; 1 sfu =10−22 W m−2 Hz−1), respectively. This formula indicates that ρeq* changes by a factor of 1.8, if F10.7 changes from 70 sfu (solar minimum) to 210 sfu (solar maximum). A formula derived in a similar manner using GOES magnetometer data indicates that, for the same range of F10.7, the mass density at L ∼ 7 varies by a factor of 4.1 We attribute the smaller factor at L = 11 to the lower O+/H+ number density ratio at higher L, the stronger F10.7 dependence of the O+ outflow rate than the H+ outflow rate, and entry of solar wind H+ ions to the outer magnetosphere.

Proton velocity ring-driven instabilities in the inner magnetosphere: Linear theory and particle-in-cell simulations

Linear dispersion theory and electromagnetic particle-in-cell (PIC) simulations are used to investigate linear growth and nonlinear saturation of the proton velocity ring-driven instabilities, namely, ion Bernstein instability and Alfven-cyclotron instability, which lead to fast magnetosonic waves and electromagnetic ion cyclotron waves in the inner magnetosphere, respectively. The proton velocity distribution is assumed to consist of 10% of a ring distribution and 90% of a low-temperature Maxwellian background. Here two cases with ring speeds vr/vA=1 and 2 (vA is the Alfven speed) are examined in detail. For the two cases, linear theory predicts that the maximum growth rate γm of the Bernstein instability is 0.16Ωp and 0.19Ωp, respectively, and γm of the Alfven-cyclotron instability is 0.045Ωp and 0.15Ωp, respectively, where Ωp is the proton cyclotron frequency. Two-dimensional PIC simulations are carried out for the two cases to examine the instability development and the corresponding evolution of the particle distributions. Initially, Bernstein waves develop and saturate with strong electrostatic fluctuations. Subsequently, electromagnetic Alfven-cyclotron waves grow and saturate. Despite their smaller growth rate, the saturation levels of the Alfven-cyclotron waves for both cases are larger than those of the Bernstein waves. Resonant interactions with the Bernstein waves lead to scattering of ring protons predominantly along the perpendicular velocity component (toward both decreasing and, at a lesser extent, increasing speeds) without substantial change of either the parallel temperature or the temperature anisotropy. Consequently, the Alfven-cyclotron instability can still grow. Furthermore, the free energy resulting from the pitch angle scattering by the Alfven-cyclotron waves is larger than the free energy resulting from the perpendicular energy scattering, thereby leading to the larger saturation level of the Alfven-cyclotron waves.

Regime transition of ion Bernstein instability driven by ion shell velocity distributions

Linear kinetic dispersion theory is used to investigate a regime transition of the ion Bernstein instability driven by a proton velocity distribution with positive slopes with respect to the perpendicular velocity, ∂fp(v∥∼0,v⊥)/∂v⊥>0. The unstable waves arising from this instability are ion Bernstein waves with proton cyclotron harmonic dispersion. However, in the inner magnetosphere, particularly inside of the plasmapause where plasmas are dominated by a cold background, the instability leads to ion Bernstein waves which approximately follow the cold plasma dispersion relation for fast magnetosonic waves and are, therefore, fast magnetosonic-like. Subsequently, the relevant waves have been termed fast magnetosonic waves and many studies have assumed the cold plasma dispersion relation to describe them. On the other hand, how the dispersion properties of ion Bernstein waves become fast magnetosonic-like has not yet been well understood. To examine this regime transition of the instability, we perform linear dispersion analyses using a two-component proton model of fp(v) = fM(v) + fs(v), where fM is a Maxwellian velocity distribution and fs is an isotropic shell velocity distribution. The results show that the unstable waves are essentially ion Bernstein waves; however, when the shell proton concentration becomes sufficiently small (less than 10), the unstable waves approach the cold plasma dispersion relation for fast magnetosonic waves and become fast magnetosonic-like. Although a reduced proton-to-electron mass ratio of 100 has been used for convenience, which reduces the number of unstable modes involved by lowering the lower hybrid frequency, this does not change the overall regime transition picture revealed in this study.

Van Allen Probes Observations of Second Harmonic Poloidal Standing Alfvén Waves

Long-lasting second-harmonic poloidal standing Alfvén waves (P2 waves) were observed by the twin Van Allen Probes (Radiation Belt Storm Probes, or RBSP) spacecraft in the noon sector of the plasmasphere, when the spacecraft were close to the magnetic equator and had a small azimuthal separation. Oscillations of proton fluxes at the wave frequency (∼10 mHz) were also observed in the energy (W) range 50–300 keV. Using the unique RBSP orbital configuration, we determined the phase delay of magnetic field perturbations between the spacecraft with a 2nπ ambiguity. We then used finite gyroradius effects seen in the proton flux oscillations to remove the ambiguity and found that the waves were propagating westward with an azimuthal wave number (m) of ∼−200. The phase of the proton flux oscillations relative to the radial component of the wave magnetic field progresses with W , crossing 0 (northward moving protons) or 180∘ (southward moving protons) at W ∼ 120 keV. This feature is explained by drift-bounce resonance (mωd ∼ ωb) of ∼120 keV protons with the waves, where ωd and ωb are the proton drift and bounce frequencies. At lower energies, the proton phase space density (FH+ ) exhibits a bump-on-tail structure with ∂FH+∕∂W > 0 occurring in the 1–10 keV energy range. This FH+ is unstable and can excite P2 waves through bounce resonance (ω∼ωb), where ω is the wave frequency.

Field line distribution of mass density at geostationary orbit

The distribution of mass density along the field lines affects the ratios of toroidal (azimuthally oscillating) Alfven frequencies, and given the ratios of these frequencies, we can get information about that distribution. Here we assume the commonly used power law form for the field line distribution, ρm = ρm,eq(LRE/R)α, where ρm,eq is the value of the mass density ρm at the magnetic equator, L is the L shell, RE is the Earths radius, R is the geocentric distance to a point on the field line, and α is the power law coefficient. Positive values of α indicate that ρm increases away from the magnetic equator, zero value indicates that ρm is constant along the magnetic field line, and negative α indicates that there is a local peak in ρm at the magnetic equator. Using 12 years of observations of toroidal Alfven frequencies by the Geostationary Operational Environmental Satellites, we study the typical dependence of inferred values of α on the magnetic local time (MLT), the phase of the solar cycle as specified by the F10.7 extreme ultraviolet solar flux, and geomagnetic activity as specified by the auroral electrojet (AE) index. Over the mostly dayside range of the observations, we find that α decreases with respect to increasing MLT and F10.7, but increases with respect to increasing AE. We develop a formula that depends on all three parameters, α3Dmodel=2.2+1.3·cosMLT·15∘+0.0026·AE·cos(MLT−0.8)·15∘+2.1·10−5·AE·F10.7−0.010·F10.7, that models the binned values of α within a standard deviation of 0.3. While we do not yet have a complete theoretical understanding of why α should depend on these parameters in such a way, we do make some observations and speculations about the causes. At least part of the dependence is related to that of ρm,eq; higher α, corresponding to steeper variation with respect to magnetic latitude, occurs when ρm,eq is lower.

Signatures of electron Landau resonant interactions with chorus waves from THEMIS observations

Simultaneous observations of electron phase space density (PSD) and chorus waves for more than 4 years by the Time History of Events and Macroscale Interactions during Substorms (THEMIS) are analyzed to identify signatures of the electron Landau resonant interactions with chorus waves in the radiation belts. Chorus waves play an important role in the radiation belt dynamics by effectively interacting with electrons. Landau resonant interactions arise when the waves are not exactly parallel propagating. Such interactions lead to “plateaus” along v∥ in the electron velocity distributions, where v∥is the parallel (with respect to the background magnetic field) component of the electron velocity. The analyzed electron PSDs often demonstrate local minima in the derivative of the velocity distribution along v∥ near the Landau resonant velocity calculated from the simultaneous in situ wave observations. These minima are, therefore, direct signatures and solid evidence of the electron Landau resonant interactions with chorus waves.