Danny Summers

Ion cyclotron waves at Io are important for understanding the complex interactions between Io and Jupiter's magnetosphere. In this study, we analyze the spatial distributions of ion cyclotron waves at Io using data from seven close flybys of Io—five by Galileo and two by Juno. We find that the amplitudes of ion cyclotron waves vary from several nT to ∼100 nT. The averaged wave amplitude reaches its peak at ∼2 R_I downstream of Io and diminishes significantly with increasing distance from Io. While ion cyclotron waves are primarily observed downstream of Io, they also occur upstream but with much weaker amplitudes. Notably, these waves are absent within Io's Alfvén wings and plasma wake, likely due to the unique plasma environment in these regions. Our findings shed new light on the distribution properties of ion cyclotron waves at Io, which provide key inputs for exploring the interactions between Io and Jupiter.

We introduce a new particle distribution function in plasma physics called the subtracted-kappa (S-K) distribution. This new distribution incorporates a loss-cone feature and an enhanced high-energy tail characterized by the spectral index κ. The S-K distribution is a generalization of the well-known subtracted-Maxwellian and approaches the latter distribution in the limit as κ→∞. Further, the S-K distribution usefully includes the bi-kappa and kappa-loss-cone distributions as special cases. Two sources of free plasma energy are provided by the S-K distribution, namely, the loss cone property and the thermal anisotropy. Both free energy sources can excite wave growth. In this paper, we briefly consider the influence of the S-K distribution on three wave phenomena: (a) linear growth of whistler-mode waves generated by an injection of hot electrons into a cold plasma, (b) dispersion of R-mode and L-mode electromagnetic waves in a hot plasma, and (c) transition from linear to nonlinear growth of electromagnetic waves as determined by a critical boundary in the input-parameter space. There are many possibilities for future projects involving the S-K distribution. Charged particle distributions in space typically possess a pronounced high-energy tail that can be modeled approximately by a kappa distribution, and so the S-K distribution is an ideal tool for analyzing kinetic waves and microinstabilities in space plasmas.

We present a physical mechanism for generating ∼GeV ions in the Jovian radiation belts. The mechanism is called relativistic turning acceleration (RTA) and involves a special form of nonlinear wave trapping by electromagnetic ion cyclotron (EMIC) waves. Necessary conditions for RTA include a near‐equatorial source of EMIC waves, strong wave amplitudes (of the order of a few percent of the background magnetic field strength), and a source of ions of sufficiently high energy. RTA occurs when a fraction of equator‐ward moving ions encounters pole‐ward moving waves, and, in so doing, becomes entrapped and undergoes a turning motion. The trapped ions then move poleward in the same direction as the waves and eventually become detrapped, but during the turning motion the ions undergo significant acceleration. We rigorously verify this process by providing the theory of nonlinear interactions between relativistic protons and coherent EMIC waves. The RTA process has been previously established for the analogous whistler mode wave‐electron interaction. We carry out particle simulations for protons at R = 2R_J (where R_J = Jovian radius) interacting with EMIC waves of amplitude B_w = 0.02B_0eq (where B_0eq = background magnetic field strength at the equator). We confirm that a large portion of test protons experience RTA and that some protons of critical energy 240 MeV can be accelerated to 10 GeV in a period of 5 s. The nonlinear acceleration process is crucially controlled by the trapping condition 0 < S < 1 where S is the inhomogeneity factor.

Highly energetic (>1 MeV) electrons are typically generated in the Earth's outer radiation belt during geomagnetically disturbed times. Such “killer” electrons can be produced by electron cyclotron resonance with whistler‐mode waves. We model this process by a relativistic Fokker‐Planck diffusion equation for the electron distribution function f(E), where E is the normalized electron kinetic energy. The equation involves an energy diffusion coefficient D(E) and an advection coefficient A(E), which depend on the wave spectral energy density. For two types of wave energy spectrum, a Gaussian and a power law with spectral index q, we seek large‐E steady‐state solutions for f(E). For lower‐band chorus, for both Gaussian and power law spectra, we find that with k = D₀T₀, where D₀ is a diffusion parameter and T₀ is the e‐folding timescale for electron loss. For a full‐band whistler spectrum, we find that if 2 < q < 4 then ; in the special case q = 4, we obtain the power law solution f ∼ E^−δ, where . We compare the analytical electron spectra obtained with the phase‐space density profiles observed by the Van Allen Probes.

The variations in radiation belt boundaries reflect competition between acceleration and loss physical processes of energetic electrons, which is an important issue for radiation belts of planets with an internal magnetic field (e.g., Earth, Jupiter, and Saturn). Based on high-quality measurements from Van Allen Probes spanning the years 2014–2018, we develop an empirical model of the energy-dependent boundaries of Earth's electron radiation belt slot region, showing that the lower boundary follows a logarithmic function of the electron energy while the upper boundary is controlled by two competing energy-dependent processes, namely compression and recovery. The compression process relates linearly to a 15 hr averaged Kp index, while the recovery process is found to be approximately proportional to time. Detailed data-model comparisons demonstrate that our model, using only the Kp index and time epoch as inputs, reconstructs the slot region boundaries in real time for 200 keV to 2 MeV electrons under varying geomagnetic conditions. Such a data-driven empirical model is prerequisite to understanding the dynamic changes of the slot region in response to both solar and geomagnetic activities. The model can be readily incorporated into future global simulations of radiation belt electron dynamics in Earth's inner magnetosphere and provide new insights into the study of Saturn's and Jupiter's radiation belt variability.

Based on Van Allen Probes observations, in this study we perform a statistical analysis of the spectral intensities of plasmaspheric hiss at L‐shells of 1.8–3.0 in the slot region. Our results show that slot region hiss power intensifies with a strong day‐night asymmetry as the level of substorm activity or L‐shell increases. Using the statistical spectral profiles of plasmaspheric hiss, we calculate the drift‐ and bounce‐averaged electron pitch angle diffusion coefficients and subsequently obtain the resultant electron loss timescales through 1‐D Fokker‐Planck simulations. We find that slot region electron loss timescales vary significantly from <1 day to several years, showing a strong dependence on electron energy, L‐shell and substorm activity. We also construct an empirical model of slot region electron loss timescales due to scattering by plasmaspheric hiss, which agrees well with the 1‐D simulation results and can be readily used in modeling the dynamics of slot region electrons.

Kappa distributions possess an enhanced high‐energy tail characterized by a spectral index κ. Here we consider how kappa distributions influence the whistler mode instability. In a relativistic regime, we analyze the effects of the bi‐kappa and kappa loss‐cone distributions on the linear and nonlinear growth of whistler mode waves. We find that for κ = 2, the linear growth rate corresponding to the bi‐kappa distribution exceeds that for a bi‐Maxwellian distribution (κ = ∞) for electron anisotropies less than a critical value. The threshold wave amplitude for nonlinear growth corresponding to a hot injected bi‐kappa distribution can be sensitively dependent on the value of κ, but also depends crucially on the electron anisotropy, parallel hot electron temperature, and wave frequency. We plot time profiles of the wave magnetic field, frequency, total nonlinear growth rate and local nonlinear growth rate, and examine how these depend on κ. The sweep (chirp) rates of the whistler mode chorus waves are found to be in the range of observed values, for the adopted plasma parameters. For a given value of the loss‐cone parameter σ, realistic whistler mode wave profiles may only exist for a restricted range of κ. For example, for σ ≥ 4, realistic wave profiles require κ ≥ 4 as well as a sufficiently large anisotropy. In summary, this new study finds that the influence of kappa distributions on the whistler mode instability is complex, not least because the instability depends on several system parameters as well as κ.

In this study, we investigate the effects of polarization reversal of electromagnetic ion cyclotron (EMIC) waves at the crossover frequencies on computations of bounce‐averaged pitch angle diffusion coefficients of radiation belt electrons and ring current protons. We find that inclusion of polarization reversal can cause significant changes of H⁺ band‐induced particle diffusion coefficients, while scattering by the He⁺ band is almost unaffected. Our results show that the pure L‐mode approach, which has been widely implemented in previous studies, tends to underestimate the diffusion coefficients of ultrarelativistic (>4 MeV) electrons and overestimate those of 10–50 and >100 keV protons caused by H⁺ band EMIC waves. Especially for >100 keV protons, the differences in diffusion coefficients can be larger by an order of magnitude. We confirm that the polarization reversal can contribute importantly to the scattering loss of radiation belt electrons and ring current protons by H⁺ band EMIC waves.

Observations show that particle velocity distributions in space plasmas generally exhibit a non-Maxwellian high-energy tail that can be well fitted with kappa distributions. To better understand the correlation between realistic particle velocity distributions and plasma wave excitation, we investigate the linear cyclotron instability of multiband electromagnetic ion cyclotron (EMIC) waves in a kappa plasma containing hot anisotropic protons, which provides the free energy for the wave growth. We find that the effects of superthermal plasmas on EMIC wave instability have a strong dependence on the emission band, temperature anisotropy A _hp, and parallel beta β _hp of hot protons. For H⁺ and He⁺ band EMIC waves, the maximum growth rates exhibit distinct behaviors with the variation of the spectral index κ of kappa distributions for different A _hp values. The maximum growth rates decrease with increasing κ-value for low A _hp and increase with increasing κ-value for high A _hp. For O⁺ band waves, the effects of superthermal plasmas on the maximum growth rate are strongly controlled by β _hp. For low β _hp, the growth rate decreases monotonically with increasing κ-value for all A _hp. For high β _hp, increase of κ-value tends to enhance the wave growth for intermediate A _hp and to suppress the wave growth otherwise. Our results also indicate that the presence of a high-energy tail tends to decrease the real frequency corresponding to the maximum growth rate for all three bands. While the minimum electron resonant energy for O⁺ band EMIC waves decreases as the κ-value increases, the minimum electron resonant energies for H⁺ and He⁺ band waves remain unaffected.

We have conducted a one‐dimensional electromagnetic particle simulation with a parabolic magnetic field to reproduce whistler‐mode hiss emissions in the plasmasphere. We assume a bi‐Maxwellian distribution with temperature anisotropy for energetic electrons injected into the plasmasphere and find that hiss emissions are generated with spectrum characteristics typical of those observed by spacecraft near the magnetic equator. The hiss emissions contain fine structures involving rising tone and falling tone elements with variation in frequencies. The amplitude profile of the spectra agrees with the optimum wave amplitude derived from the nonlinear wave growth theory. The simulation demonstrates that hiss emissions are generated locally near the magnetic equator through linear and nonlinear interactions with energetic electrons with temperature anisotropy. The coherent hiss emissions efficiently scatter resonant electrons of 2.5–80 keV into the loss cone.