Plasmas support a wide variety of plasma waves that carry information to remote observers (Lee et al. 2014; Hwang 2015). Ultra-Low Frequency (ULF) waves in the ion cyclotron range of frequency, which can interact with electrons and ions (Rauch & Roux 1982;Horne & Thorne 1997; Song et al. 1999), are often observed in planetary magnetospheres (Russell et al. 2008; Boardsen et al. 2012) as well as in Earth’s magnetosphere and ionosphere (Kim et al. 2010, 2011b).
In the ion cyclotron frequency range, the wave dispersion relations can be simplified to
For perpendicular propagation (
which is Buchsbaum frequency (bi-ion frequency (bi-ion frequency) (Buchsbaum 1960). For oblique propagation (
Between each pair of gyrofrequencies, there is a mode conversion location that is referred to as the Ion-Ion Hybrid (IIH) resonance, with a corresponding frequency (
The IIH resonance can exhibit significant differences because of the different conditions in planetary magnetospheres. For Mercury, where the magnetic field is relatively weak, the wavelength of field-aligned modes can be comparable to the size of the magnetosphere. Therefore, IIH waves oscillate globally along the magnetic field lines for Mercury, similar to the field line resonance on Earth (Othmer et al. 1999; Glassmeier et al. 2003, 2004; Klimushkin et al. 2006; Kim et al. 2008, 2011a, 2013, 2015a, b). On the other hand, on Earth, the magnetic field strength is larger and the wavelength is shorter, which typically localizes mode converted waves between the Buchsbaum cutoff locations, which occur at around 10 degrees latitude. The modes that result from mode conversion are typically linearly polarized ElectroMagnetic Ion Cyclotron (EMIC) waves, which can be generated via mode conversion near the IIH resonance location (Lee et al. 2008). These waves have a significantly different polarization from EMIC waves, which are excited by proton temperature anisotropy (Cornwall 1965; Kennel & Petschek 1966; Williams & Lyons 1974a, b; Taylor & Lyons 1976). Because the incoming FW absorption at the IIH resonance (the generation of linearly polarized EMIC waves) occurs at a limited wave frequency and heavy ion density ratio, linearly polarized waves can be used as a diagnostic tool to estimate the heavy ion density ratio (Kim et al. 2015c).
In planetary magnetospheres, as the mode-converted IIH waves near the magnetic equator propagate to higher magnetic latitudes, the waves reach cutoff (
Recent 2D full wave simulations of Mercury’s dipolar magnetosphere (Kim et al. 2015a), which assumed constant particle densities, clearly showed the reflection of the IIH resonant waves at the Buchsbaum resonance location and wave tunneling through the wave stopgap between cutoff and resonance. However, as shown in Eq. (4), the Buchsbaum frequency is a function of the heavy ion density concentration ratio as well as the ambient magnetic field strength. Therefore, it is useful to examine the solutions of IIH resonant waves in more detail to determine how the wave structure and absorption of energy depend on variations in the magnetic field strength and density.
In this paper, we use a multi-ion fluid wave code to demonstrate mode conversion that occurs at the IIH resonance when impulsive FWs enter the plasma with a 2D inhomogeneous density structure, which is assumed to result from the sputtering of material from the surface of Mercury. We find that mode converted IIH waves can be localized in the density well along the magnetic field line, and also exhibit harmonic frequency structure.
We employ the fluid wave simulation model developed by Kim & Lee (2003). Similar to previous wave simulations (Kim et al. 2008, 2013), we adopt the plasma conditio ns present on Mercury, and thus the background magnetic field (B0 = 86 nT) and the electron density (
Because sodium is one of the major heavy ions on Mercury (Zurbuchen et al. 2011; Raines et al. 2014), we adopt an electron-proton-sodium plasma, similar to previous numerical studies (Kim et al. 2008, 2011a). We assume the sodium density (
[Fig. 1.] Ratio of Na+ density to the electron density in the X-Z plane. The sodium concentration has a minimum at the center of the simulation domain. The dashed lines show selected locations of X and Z; X0 (Z0) = 0.5 and 0.7 for Figs. 3 and 4.
The simulation is driven by imposing an impulse in
We stored the time history of the electromagnetic fields at each grid point (
Figs. 3(a) and 3(b) show the time history of the transverse component of
The wave time history along the
Fig. 4 shows the wave spectra of
[Fig. 4.] Wave spectra of the Ex and Ey components along X for (a) Z = 0.55 and (b) Z = 0.7 and along Z for (c) X = 0.55 and (d) X = 0.7, respectively. Dashed lines represent the calculated Buchsbaum frequencies along Z.
The FWs in the
In this paper, we show how mode-converted IIH waves can be localized in a heavy ion density well in slab coordinates. Because the Buchsbaum frequency increases as the heavy ion density concentration ratio increases, an irregular ion density structure along the field line can lead to an asymmetric structure of the Buchsbaum frequency. Our results, therefore, emphasize the importance of field-aligned heavy ion density structures for ULF wave propagation. It should be noted that equilibria in magnetospheres with rotational disks generally have density structures along the magnetic field lines due to centrifugal acceleration, which concentrates the heavy ions into the magnetodisk.
In Fig. 5, we demonstrate how asymmetry in the ion density ratio affects the field-aligned wave propagation. We assumed the field-aligned density structure of
[Fig. 5.] (a) Arbitrary H+ and Na+ density ratios along the magnetic field line at LM = 2; (b) the solid line is the calculated Buchsbaum frequency along the magnetic field line by adopting the heavy ion density ratio from (a), the dashed line is the Buchsbaum frequency forηNa = 20%, and the dashed-dotted line is the sodium gyrofrequency. Here, the gray-filled area is where an IIH wave with 1 Hz can propagate; thus, IIH waves generated near the magnetic equator can be localized between -21.7 < Λ < 15 and 20.5 < Λ < 27.9.
Interestingly, the Buchsbaum resonance is also a cutoff condition of the Left-Hand Polarization (LHP) EMIC waves (Johnson et al. 1995). In Earth’s magnetosphere, as these waves propagate along
In summary, we investigate how mode-conversion at the IIH resonance occurs when heavy ion density has transverse and longitudinal inhomogeneity in slab coordinates. The multi-ion simulation results show that the IIH waves have a continuous band across the field line, which is consistent with previous numerical studies. These waves also have harmonic structures in frequency domain and are also localized in the field-aligned heavy ion density well.