Current‐driven Langmuir oscillations and formation of wave packets via modulational instability: Relevance to STEREO observations

Abstract

Recently, it has been shown that Langmuir oscillations (LOs) at the plasma frequency can be driven by an electron current without any electrostatic instability. This current may appear due to a (small) drift of the whole electron population against the ions or by beam electrons after their relaxation to a plateau‐like distribution. The consequences of LOs for nonlinear wave phenomena in this scenario are studied by means of kinetic plasma simulations. It is shown that the electric field of LOs can act as a pump wave and generate Langmuir envelope solitons via the modulational instability. In this way, both counterstreaming Langmuir and ion‐acoustic waves arise with the same wave number. For solar wind conditions the Doppler shift leads to the generation of satellite peaks with frequencies symmetric around the plasma frequency. Simultaneously, a peak appears in the ion‐acoustic branch. These results agree well with recent STEREO observations in the solar wind.

Parametric Decay of Beam‐Generated Langmuir Waves and Three‐Wave Interaction in Plateau Plasmas: Implications for Type III Radiation

“…For selected times we display (a) the electron velocity distribution function, (b) the dispersion of Langmuir/electron-acoustic waves, (c) the power spectrum of the electric field, and (d) the ion density power spectrum. The four panels corresponding to increasing time should reflect the following processes: (1) ω e t 1 = 90: beam instability shortly after ignition, (2) ω e t 2 = 450: plateau formation close to saturation and onset of induced ion density fluctuations, (3) ω e t 3 = 1,050: plateau formation completed, parametric decay of beam-driven Langmuir wave (k = k L ) into Langmuir oscillations (k = 0) and an ion acoustic wave (k~k L ), (4) ω e t 4 > 3,000, beyond the present simulation, modulational instability, and tail heating induced by Langmuir oscillations (Sauer & Sydora, 2016).…”

“…Whereas one of the peaks was interpreted by beam excitation, for the other one different mechanisms have been considered, such as modulational instability, classical parametric decay, and particle trapping. In own studies (Baumgärtel, ; Sauer & Sydora, , ; Sauer et al, ), Langmuir oscillations driven by the beam/plateau current have been introduced as a new concept. In particular, the interpretation of Langmuir amplitude modulations in the recent paper by Sauer et al () by parametric decay of current‐driven Langmuir oscillations is very similar to the present approach.…”

“…The development of the power spectrum of both the electric field and the ion‐density disturbance is presented in the color plots of Figure . Possible stages of beam relaxation have been considered before in two recent papers (Sauer et al, ; Sauer & Sydora, ). In a similar way, the evolution of beam with plasma interaction can roughly be divided into the following stages: (i) Beam instability and plateau formation associated with the growth of density fluctuations within ω e t ≤ 450, (ii) transition region in the range 450 ≤ ω e t ≤ 750 with first signatures of wave number shift toward smaller values and further growth of density fluctuations, and finally (iii) a region of a well‐developed quasi‐stationary state of parametric interaction of electrostatic waves in a broad wave number spectrum, reaching from k ~ 0 up to the value k L ~ ω e / V b of maximum instability, with induced density fluctuations in the range around k L .…”

Parametric decay of current‐driven Langmuir waves in plateau plasmas: Relevance to solar wind and foreshock events

“…This paper is closely related to recent work [ Sauer and Sydora , , , hereafter referred to as SS15 and SS16, respectively] which was devoted to current‐driven Langmuir oscillations at the electron plasma frequency ( ω e ) and their consequences for the interpretation of beam‐plasma interaction in the solar wind and planetary foreshock regions. Whereas in SS15 the simultaneous existence of both Langmuir oscillations and beam‐excited Langmuir waves with wave number k ∼ ω e / V b ( V b : beam velocity) as a cause for amplitude modulation has been considered, the paper SS16 is devoted to the evidence that the Langmuir oscillations which remain after beam relaxation may act as a pump wave of modulational instability by which wave packets are formed.…”

“…The transition from an unstable beam to a saturated state has been described in several kinetic studies using particle‐in‐cell (PIC) and Vlasov models [e.g., Kasaba et al , ; Matsukiyo et al , ; Silin et al , ; Baumgärtel , ; Briand et al , ; Sauer and Sydora , ]. The dispersion of high‐frequency electrostatic waves which belong to such plateau plasmas represents a superposition of the Langmuir mode with an electron‐acoustic mode owing to the second plasma population and has been described in former papers by us [ Sauer and Sydora , , , ]. The distribution function of a plateau plasma can be represented as a superposition of shifted Maxwellians, as done by Silin et al [].…”