Identifying Ultra Low Frequency Waves in the Lunar Plasma Environment Using Trajectory Analysisand Resonance Conditions

Abstract

Recent studies show that localized crustal magnetic fields on the lunar surface can reflect a significant portion of the incoming solar wind protons. These reflected ions can drive a wide range of plasma waves. It is difficult to determine the intrinsic properties of low-frequency waves with single-spacecraft observations, which can be heavily Doppler shifted. We describe a technique to combine trajectory analysis of reflected protons with the Doppler shift and resonance conditions to identify ultralow-frequency waves at the Moon. On 31 January 2014 plasma waves were detected by one of the Acceleration, Reconnection, Turbulence and Electrodynamics of the Moon's Interaction with the Sun (ARTEMIS) probes as it approached the lunar wake; these waves were not detected by the second ARTEMIS probe located upstream in the undisturbed solar wind. The observed waves had a frequency below the local ion cyclotron frequency and had right-hand circular polarization in the reference frame of the Moon. By solving the Doppler shift and the cyclotron resonance equations, we determined the conditions for reflected ions to excite the observed waves. Simulated trajectories of reflected ions correspond to ARTEMIS ion observations and support the hypothesis that reflected ions are the primary driver of the waves. By combining trajectory analysis with the resonance conditions, we identify scenarios where ions that satisfy the resonance conditions are present in the right location to generate the observed waves. Using this method, we can uniquely identify the observed waves as upstream propagating right-hand polarized waves, subject to the assumption that they are generated by cyclotron resonance with ions.

Figure 1.

ARTEMIS observations taken on 31 January 2014 from 17:45 to 19:00: (a) magnetic field magnitude and components in Selenocentric Solar Ecliptic (SSE) coordinates near the Moon (B1) and in the undisturbed upstream solar wind (B2), (b) polarization in the spacecraft frame (positive indicates right handed) as a function of frequency from wavelet calculations with the local proton cyclotron frequency overlaid (black), (c) ion differential energy flux (eV/(eV cm⁻² s sr)) as a function of phi, (d) ion differential energy flux as a function of energy over the entire phi range and (e) over a phi range that excludes the solar wind, (f) ion density of the entire distribution (black) and the nonsolar wind component (red), and (g) simulated flux of reflected ions in arbitrary units. The dashed line indicates when the probe crossed into the lunar wake.

Figure 2.

Solution sets for (a) angular frequency in solar wind frame, (b) wave number, (c) phase velocity in solar wind frame, and (d) wavelength. All are plotted versus the reflected ion velocity in the wave propagation direction. Red (blue) solutions satisfy equations for right (left)-handed waves. Black dash-dotted line in Figure 2a marks ion cyclotron frequency cutoff. Purple dashed lines indicate magnitude of solar wind velocity in the wave propagation direction. Black dashed lines indicate cutoffs at twice the solar wind velocity. Green color bars at the bottom of the plots show valid solution ranges.

Figure 3.

(a) Velocity field plot of simulated data in the solar wind frame of ions that satisfy the right (left)-handed conditions are in red (blue) scale. Probe orbit is in green. Magnetic field direction is indicated by the purple line, and upstream k direction is indicated by the gray line. (b) Velocity field plot of the same ions in the Moon frame. Average phase velocity of right (left)-handed solutions is depicted by red (blue) line. Probe orbit is in green on both plots.

Figure 4.

Upstream region where wave-particle interactions can be detected by ARTEMIS probe for intrinsically right (left)-handed waves is depicted as red (blue) plane. Reflected ions that have the necessary velocity in the propagation direction and are in the correct geometric plane to interact with intrinsically right (left)-hand wave are in red (blue). Probe orbit is in green. Magnetic field direction is indicated by dashed black line.

Figure 5.

Wave and ion event on 1 September 2011. (left) ARTEMIS observations of (from top to bottom) ion differential energy flux as a function of energy over the entire phi range and over a phi range that excludes the solar wind, magnetic field magnitude and components in SSE coordinates, and polarization in the spacecraft frame (positive indicates right handed) as a function of frequency from wavelet calculations with the local proton cyclotron frequency overlaid (black). The dashed line indicates when the probe crossed into the lunar wake. (right) Upstream region where wave-particle interactions can be detected by the ARTEMIS probe and reflected ions that meet the velocity and spatial requirements are portrayed using the same convention as in Figure 4. Additional gray dashed line indicates upstream k direction.

Figure 6.

Wave and ion event on 29 October 2011 presented in same format as Figure 5.

Figure 7.

Wave and ion event on 6 November 2016 presented in same format as Figure 5. Light blue plane/ions in Figure 7 (right) are solutions for intrinsically left-handed downstream propagating waves.