Characteristics of Langmuir electric field waveforms and power spectra exhibiting nonlinear behavior in Earth's foreshock

Abstract

[1] Langmuir wave characteristics in the Earth's foreshock were examined to identify possible nonlinear wave behavior for two case studies with data from the Cluster Wideband Data Plasma Wave Receiver. The occurrence rates of four types of power spectra near the foreshock edge were determined: (1) spectra with power at the local plasma frequency f pe only, (2) spectra with power at f pe and 2f pe , (3) spectra with double peaks near f pe , and (4) spectra with double peaks near f pe and peaks at low frequencies indicative of ion acoustic waves. For electric field waveform amplitudes between 0.1 and 22.0 mV/m, most power spectra fell into the f pe only and double-peaked categories. The maximum Langmuir wave amplitudes and bump-on-tail reduced electron distribution functions from Cluster PEACE data were more consistent with saturation of wave growth by electrostatic decay than modulational instabilities. However, few spectra had the double peaks near f pe and ion acoustic waves indicative of electrostatic decay, suggesting other processes may also be at work. For amplitudes greater than 22.0 mV/m, most power spectra fell into the f pe and 2f pe category, but many of the harmonics were too weak to be clearly distinguished from harmonics caused by instrumental effects.

A linear model for amplitude modulation of Langmuir waves in weak electron-beam plasma interaction

“…Characteristic features are the significant amplitude modulation and the formation of Langmuir wave packets with a scale of 5-10 wavelengths of the mode with the largest temporal growth rate, and zero points of the envelope. The field amplitude reaches values in the mV/m range, which is consistent with the order of magnitude seen in observations (Hospodarsky et al, 1994;Kellog et al, 1996;Kojima et al, 1997;Pottelette et al, 1999;Sigsbee et al, 2010). We emphasize that the strong modulation seen here comes about only by the beating of Langmuir waves with different wavenumbers and different amplitudes.…”

“…Figure 5 displays such a power spectrum, but the double peak is not well enough developed compared with that, e.g., seen in Fig. 3d of Sigsbee et al (2010).…”

“…Among them are Voyager (Gurnett et al, 1981); Galileo (Gurnett et al, 1993;Hospodarsky et al, 1994); Wind (Kellog et al, 1996); Geotail (Kojima et al, 1997); Fast (Pottelette et al, 1999); and Cluster (Sigsbee et al, 2010). The observed Langmuir envelopes are highly structured and have occasionally the form of a chain of wave packets with nearly the same temporal scale.…”

Ion dynamics in electron beam–plasma interaction: particle-in-cell simulations

“…Electron beam-generated Langmuir wave forms, observed for more than 30 years under various space plasma conditions, often exhibit a spectral double peak near to the ambient plasma frequency ω pe (Gurnett et al, 1993;Hospodarsky et al, 1994;Hospodarsky and Gurnett, 1995;Kellog et al 1996;Bale et al, 1996;Kojima et al, 1997;Pottelette et al, 1999;Sigsbee et al, 2010;Graham and Cairns, 2013a). It is commonly assumed to be produced by the interference of the dominant Langmuir wave of the instability and a second Langmuir wave of comparable amplitude but slightly different frequency.…”

“…Among them are spectra with power at ω pe only (e.g., Sigsbee et al, 2010), a double peak in absence of ion acoustic activity (e.g., Sigsbee et al, 2010), multiple spectral peaks (e.g., Graham and Cairns, 2013a), a single peak with side-band structure (e.g., Gurnett at al., 1981;Thejappa et al, 2013), Langmuir eigenmodes localized in density wells (Ergun et al, 2008;Graham and Cairns, 2013b) and waveforms resulting from the interaction of Langmuir waves with electrostatic whistler/lower hybrid waves instead of ion sound (Stasiewicz et al, 1996).…”