Two-component model of strong Langmuir turbulence: Scalings, spectra, and statistics of Langmuir waves

Abstract

A two-component model of strong Langmuir turbulence is developed, in which intense coherent Langmuir wave packets nucleate from and collapse amid a sea of low-level background waves. Power balance between these two components determines the overall scalings of energy density and power dissipation in the turbulence, and of the rate of formation, number density, volume fraction, and characteristic nucleation time of collapsing wave packets. Recent insights into the structure and evolution of collapsing wave packets are employed to estimate the spectra and field statistics of the turbulence. Extensive calculations using the Zakharov equations in two and three dimensions demonstrate that the predictions of the model are in excellent agreement with numerical results for scalings, spectra, and the distribution of fields in the turbulence in isotropic systems; strong support is thus found for the nucleation model. The scaling behavior proves to be insensitive to the form of the damping of the waves at large wave numbers. Wave collapse is approximately inertial between the nucleation and dissipation scales, yielding power-law energy spectra and field distributions in this range. The existence of a fixed arrest scale manifests itself in exponentially decreasing energy and dissipation spectra at high wave numbers and exponentially decreasing field distributions at high field strengths. It is suggested that such an exponential decrease may explain the field distributions seen in recent beam–plasma experiments. Generalizations to turbulence driven anisotropically by beams or governed by equations other than the Zakharov equations are outlined. It is shown that a previously unrecognized scaling observed in beam-driven systems is correctly predicted by the generalized model.

Stochastic growth of localized plasma waves

“…27 On large scales, multiple collapses can occur concurrently, with new wave packets forming elsewhere, mostly at the sites of previous collapses, each surrounded by lower level incoherent waves. 27,39 This is termed strong turbulence, and leads to nonuniform waves, qualitatively similar to those in space plasmas. An example of 2D strong turbulence is seen in Fig.…”

“…4. 27,39 Power-law distributions of field strength are expected in strong turbulence, with P(E)ϰE Ϫ5 at E rms ӶEՇE t and P(E)ϰexp(ϪE 2 /E t 2 ) at E t ՇE, 27,39,40 where E t is a characteristic field at the end of collapse. Power-law field statistics are also found when averaged over a single collapse.…”

Langmuir Turbulence and Suprathermal Electrons

“…The strong turbulence theory ignores the wave-particle effect, and is a macroscopic theory. Even though Zakharov's strong turbulence theory continues to be investigated by many researchers (see the reviews by Goldman 1984 andRobinson 1997), the theory remains controversial to this date, and various numerical simulations and experiments to confirm the theory are inconclusive (Robinson and Newman 1990;Vyacheslavov et al 2002;Erofeev 2002). …”

Progress on Coronal, Interplanetary, Foreshock, and Outer Heliospheric Radio Emissions

“…Figure 5 is also inconsistent with the strong Langmuir turbulence process of wave collapse saturating the wave growth, since this process should produce a power-law tail at high E in the P (log E) distribution (Robinson & Newman 1990). Despite early enthusiasm (Papadopoulos, Goldstein & Smith 1974;Smith, Goldstein & Papadopoulos 1979;Thejappa et al 1993), detailed tests of collapse theory against the observed Langmuir waves provide multiple strong arguments against collapse occurring frequently or playing a significant role in type III bursts (Robinson, Cairns & Gurnett 1993;Cairns & Robinson 1995b, 1998Robinson 1997).…”