Due to differences in solar illumination, a geomagnetic field line may have one footpoint in a dark ionosphere while the other ionosphere is in daylight. This may happen near the terminator under solstice conditions. In this situation, a resonant wave mode may appear which has a node in the electric field in the sunlit (high conductance) ionosphere and an antinode in the dark (low conductance) ionosphere. Thus, the length of the field line is one quarter of the wavelength of the wave, in contrast with half-wave field line resonances in which both ionospheres are nodes in the electric field. These quarter waves have resonant frequencies that are roughly a factor of 2 lower than the half-wave frequency on the field line. We have simulated these resonances using a fully three-dimensional model of ULF waves in a dipolar magnetosphere. The ionospheric conductance is modeled as a function of the solar zenith angle, and so this model can describe the change in the wave resonance frequency as the ground magnetometer station varies in local time. The results show that the quarter-wave resonances can be excited by a shock-like impulse at the dayside magnetosphere and exhibit many of the properties of the observed waves. In particular, the simulations support the notion that a conductance ratio between day and night footpoints of the field line must be greater than about 5 for the quarter waves to exist.

The arrival of the Juno satellite at Jupiter has led to an increased interest in the dynamics of the Jovian magnetosphere. Jupiter’s auroral emissions often exhibit quasi-periodic oscillations with periods of tens of minutes. Magnetic observations indicate that ultra-low-frequency (ULF) waves with similar periods are often seen in data from Galileo and other satellites traversing the Jovian magnetosphere. Such waves can be associated with field line resonances, which are standing shear Alfvén waves on the field lines. Using model magnetic fields and plasma distributions, the frequencies of field line resonances and their harmonics on field lines connecting to the main auroral oval have been determined. Time domain simulations of Alfvén wave propagation have illustrated the evolution of such resonances. These studies indicate that harmonics of the field line resonances are common in the 10-40 minute band.

The ionospheric Alfvén resonator (IAR) is a structure formed by the rapid decrease in the plasma density above a planetary ionosphere. This results in a corresponding increase in the Alfvén speed that can provide partial reflection of Alfvén waves. At Earth, the IAR on auroral field lines is associated with the broadband acceleration of auroral particles, sometimes termed the Alfvenic aurora. This arises since phase mixing in the IAR reduces the perpendicular wavelength of the Alfvén waves, which enhances the parallel electric field due to electron inertia. This parallel electric field fluctuates at frequencies of 0.1-20.0 Hz, comparable to the electron transit time through the region, leading to the broadband acceleration. The prevalence of such broadband acceleration at Jupiter suggests that a similar process can occur in the Jovian IAR. A numerical model of Alfvén wave propagation in the Jovian IAR has been developed to investigate these interactions. This model describes the evolution of the electric and magnetic fields in the low-altitude region close to Jupiter that is sampled during Juno’s perijove passes. In particular, the model relates measurement of magnetic fields below the ion cyclotron frequency from the MAG and Waves instruments on Juno and electric fields from Waves to the associated parallel electric fields that can accelerate auroral particles.