Dwight R. Nicholson

Nonlinear Langmuir waves during type III solar radio bursts

Type III solar radio bursts are thought to be associated with intense levels of electron beam excited Langmuir waves. We numerically study the nonlinear evolution of these waves, in time and in two spatial dimensions, due to their coupling to other waves. For parameters appropriate to one-half the Earth-Sun distance, we find nonlinear effects to be important, as in previous one-dimensional work. However, a new and important phenomenon, two-dimensional soliton collapse, is found to occur. This collapse, induced directly by the wave packet nature of the beam excited waves, produces two-dimensional wave spectra extending over a much broader range of wavenumbers than has been predicted by inhomogeneous quasi-linear theory. Our results compare favorably with certain aspects of recent observations. We neglect the background magnetic field; while substantially justified for the present parameters, this neglect may require reexamination at locations closer to the Sun.

Damped nonlinear Schrödinger equation

High frequency electrostatic plasma oscillations described by the nonlinear Schrodinger equation in the presence of damping, collisional or Landau, are considered. At early times, Landau damping of an initial soliton profile results in a broader, but smaller amplitude soliton, while collisional damping reduces the soliton size everywhere; soliton speeds at early times are unchanged by either kind of damping. For collisional damping, soliton speeds are unchanged for all time.

Cascade and collapse of Langmuir waves in two dimensions

The temporal evolution of intense Langmuir waves in an unmagnetized plasma of two spatial dimensions is studied numerically. When the inequality W≳ (kλe)2 is satisfied, the evolution quickly leads to a state of collapsing solitons. Here, W is the ratio of electric field energy density to the particle kinetic energy density, k is a typical Langmuir wavenumber, and λe is the electron Debye length.

Radiation from a strongly turbulent plasma: Application to electron beam‐excited solar emissions

The emission of radiation at the plasma frequency and at twice the plasma frequency from beam‐excited strong Langmuir turbulence, for the case of low‐density high‐velocity warm beams, is considered. Under these conditions, Langmuir wave packets undergo (direct) collapse in a time short compared with one e folding of a beam mode. The wave packet energy density threshold for collapse depends only on the beam temperature and velocity, not on the beam density. Upper and lower limits on the volume emissivity for harmonic emission from these collapsing wave packets are found. Within most of this range, the emissivity is large enough to account for observations of second harmonic radiation during type III solar radio wave bursts. The radiation at the fundamental is many orders of magnitude larger than predicted by weak turbulence theory.

Numerical comparison of strong Langmuir turbulence models

Two models of Langmuir turbulence, the nonlinear Schrodinger equation and the Zakharov equations, are solved numerically for an initial value problem in which the electric field evolves from an almost flat initial condition via the modulational instability and finally saturates into a set of solitons. The two models agree well with each other only when the initial dimensionless electric field has an amplitude less than unity. An analytic soliton gas model consisting of equal‐amplitude, randomly spaced, zero‐speed solitons is remarkably good at reproducing the time‐averaged Fourier spectra in both cases.

Solitons and ionospheric modification

The possibility of Langmuir soliton formation and collapse during ionospheric modification is investigated. Parameters characterizing former facilities, existing facilities, and planned facilities are considered, using a combination of analytical and numerical techniques. At a spatial location corresponding to the exact classical reflection point of the modifier wave, the Langmuir wave evolution is found to be dominated by modulational instability followed by soliton formation and three-dimensional collapse. The earths magnetic field is found to affect the shape of the collapsing soliton. These results provide an alternative explanation for some recent observations.

Scattering and collpase of Langmuir waves driven by a weak electron beam

The evolution of Langmuir waves predicted by the beam‐driven Zakharov equations is studied numerically with high resolution in one and two dimensions, for parameters appropriate to type III solar radio bursts at 0.5 a.u. It is found that collapse is preceded by momentum transfer to ion‐acoustic quasimodes even in the absence of a weak solar magnetic field. The early evolution is similar in one and two dimensions. A zero momentum condensate forms in both cases, but its subsequent behavior differs in one dimension and two dimensions. The corresponding real‐space wave packets collapse rapidly in two dimensions, but evolve as slowly growing solitons in one dimension. Detailed comparisons are made with other (one‐dimensional) models of ’’strong’’ Langmuir turbulence associated with type III bursts.

Steady‐state turbulence with a narrow inertial range

Coupled two‐dimensional wave equations are solved on a computer to model Langmuir wave turbulence excited by a weak electron beam. The model includes wave growth due to beam–plasma interaction, and dissipation by Landau damping. The inertial range is limited to a relatively small number of modes such as could occur when the ratio of masses between the negative and positive ions is larger than in a hydrogen plasma, or when there is damping in long wavelength Langmuir waves. A steady state is found consisting of quasistable, collapsed wave packets. The effects of different beam parameters and the assumed narrow inertial range are considered. The results may be relevant to plasma turbulence observed in connection with type III solar bursts.

Parametric instabilities in weakly magnetized plasma

Parametric instabilities in a weakly magnetized plasma are discussed. The results are applied to waves excited by electron streams which travel outward from the Sun along solar-wind magnetic field lines, as in a type III solar radio burst.

Oscillating two‐stream instability with pump of finite extent

In one spatial dimension, the effects of finite pump length L on the oscillating two‐stream instability are considered. In the absence of damping, a purely growing instability for very small pump extent is found. Under certain conditions, the finite system exhibits faster growth rates than the corresponding infinite system.