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.     

Large Scale Flows in the Solar Convection Zone

We discuss the current theoretical understanding of the large scale flows observed in the solar convection zone, namely the differential rotation and meridional circulation. Based on multi-D numerical simulations we describe which physical processes are at the origin of these large scale flows, how they are maintained and what sets their unique profiles. We also discuss how dynamo generated magnetic field may influence such a delicate dynamical balance and lead to a temporal modulation of the amplitude and profiles of the solar large scale flows.     

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.     

Planetary Dynamos from a Solar Perspective

Direct numerical simulations of the geodynamo and other planetary dynamos have been successful in reproducing the observed magnetic fields. We first give an overview on the fundamental properties of planetary magnetism. We review the concepts and main results of planetary dynamo modeling, contrasting them with the solar dynamo. In planetary dynamos the density stratification plays no major role and the magnetic Reynolds number is low enough to allow a direct simulation of the magnetic induction process using microscopic values of the magnetic diffusivity. The small-scale turbulence of the flow cannot be resolved and is suppressed by assuming a viscosity far in excess of the microscopic value. Systematic parameter studies lead to scaling laws for the magnetic field strength or the flow velocity that are independent of viscosity, indicating that the models are in the same dynamical regime as the flow in planetary cores. Helical flow in convection columns that are aligned with the rotation axis play an important role for magnetic field generation and forms the basis for a macroscopic α-effect. Depending on the importance of inertial forces relative to rotational forces, either dynamos with a dominant axial dipole or with a small-scale multipolar magnetic field are found. Earth is predicted to lie close to the transition point between both classes, which may explain why the dipole undergoes reversals. Some models fit the properties of the geomagnetic field in terms of spatial power spectra, magnetic field morphology and details of the reversal behavior remarkably well. Magnetic field strength in the dipolar dynamo regime is controlled by the available power and found to be independent of rotation rate. Predictions for the dipole moment agree well with the observed field strength of Earth and Jupiter and moderately well for other planets. Dedicated dynamo models for Mercury, Saturn, Uranus and Neptune, which assume stably stratified layers above or below the dynamo region, can explain some of the unusual field properties of these planets.     

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.