Langmuir Turbulence and Solar Radio Bursts

Langmuir waves and turbulence resulting from an electron beam-plasma instability play a fundamental role in the generation of solar radio bursts. We report recent theoretical advances in nonlinear dynamics of Langmuir waves. First, starting from the generalized Zakharov equations, we study the parametric excitation of solar radio bursts at the fundamental plasma frequency driven by a pair of oppositely propagating Langmuir waves with different wave amplitudes. Next, we briefly discuss the emergence of chaos in the Zakharov equations. We point out that chaos can lead to turbulence in the source regions of solar radio emissions. This revised version was published online in August 2006 with corrections to the Cover Date.     

Universal scaling laws for fully-developed magnetic field turbulence near and far upstream of the Earth’s bow shock

We analyze the multifractal scaling of the modulus of the interplanetary magnetic field near and far upstream of the Earth’s bow shock, measured by Cluster and ACE, respectively, from 1 to 3 February 2002. The maximum order of the structure function is carefully estimated for each time series using two different techniques, to ensure the validity of our high-order statistics. The first technique consists of plotting the integrand of the pth order structure function, and the second technique is a quantitative method which relies on the power-law scaling of the extreme events. We compare the scaling exponents computed from the structure functions of magnetic field differences with the predictions obtained by the She–Lévêque model of intermittency in anisotropic magnetohydrodynamic turbulence. Our results show a good agreement between the model and the observations near and far upstream of the Earth’s bow shock, rendering support for the modelling of universal scaling laws based on the Kolmogorov phenomenology in the presence of sheet-like dissipative structures.     

The evolution of globular clusters

Taking a wide range of the initial conditions, including spatial density distribution and mass function etc, the dynamical evolution of globular clusters in the Milky Way is investigated in detail by means of Monte Carlo simulations. Four dynamic mechanisms are considered: stellar evaporation, stellar evolution, tidal shocks due to both the disk and bulge, and dynamical friction. It is found that stellar evaporation dominates the evolution of low-mass clusters and all four are important for massive ones. For both the power-law and lognormal initial clusters mass functions, we can find the best-fit models which can match the present-day observations with their main features of the mass function almost unchanged after evolution of several Gyr. This implies that it is not possible to determine the initial mass function only based on the observed ones today. Moreover, the dispersion of the modelled mass functions mainly depends on the potential wells of host galaxies with the almost constant peaks, which is consistent with current observations.     

The planetary–exoplanetary environment: A nonlinear perspective

A review of the fundamental physical processes in the planetary–exoplanetary environment is presented, with emphasis on nonlinear phenomena. First, we discuss briefly the detection of exoplanets and search for radio emissions from exoplanets. Next, we give an overview of the concepts of waves, instabilities, chaos and turbulence in the planetary–exoplanetary environment based on our present knowledge of the solar-terrestrial environment. We conclude by discussing cyclotron masers and chaos in nonthermal radio emissions in the planetary–exoplanetary environment.     

Chaotic Temporal Variability of Magnetospheric Radio Emissions

Nonthermal magnetospheric radio emissions provide the radio signatures of solar-terrestrial connection and may be used for space weather forecasting. A three-wave model of auroral radio emissions at the fundamental plasma frequency was proposed by Chian et al. (1994) involving resonant interactions of Langmuir, whistler and Alfvén waves. Chaos can appear in the nonlinear evolution of this three-wave process in the magnetosphere. We discuss two types of intermittency in radio signals driven by temporal chaos: the type-I Pomeau-Manneville intermittency and the interior crisis-induced intermittency. Examples of time series for both types of intermittency are presented. This revised version was published online in August 2006 with corrections to the Cover Date.     

Foreword: Advances in space environment research

Space Science Reviews -     

Dynamical Systems Approach to Space Environment Turbulence

Space plasmas are dominated by waves, instabilities and turbulence. Dynamical systems approach offers powerful mathematical and computational techniques to probe the origin and nature of space environment turbulence. Using the nonlinear dynamics tools such as the bifurcation diagram and Poincaré maps, we study the transition from order to chaos, from weak to strong chaos, and the destruction of a chaotic attractor. The characterization of the complex system dynamics of the space environment, such as the Alfvén turbulence, can improve the capability of monitoring Sun-Earth connections and prediction of space weather. This revised version was published online in August 2006 with corrections to the Cover Date.     

Polynomial Hamiltonian systems with a nilpotent critical point

The study of Hamiltonian systems is important for space physics and astrophysics. In this paper, we study local behavior of an isolated nilpotent critical point for polynomial Hamiltonian systems. We prove that there are exact three cases: a center, a cusp or a saddle. Then for quadratic and cubic Hamiltonian systems we obtain necessary and sufficient conditions for a nilpotent critical point to be a center, a cusp or a saddle. We also give phase portraits for these systems under some conditions of symmetry.