Predictions Of Quasilinear Theory Research Articles

Long-term dynamics driven by resonant wave–particle interactions: from Hamiltonian resonance theory to phase space mapping

In this study we consider the Hamiltonian approach for the construction of a map for a system with nonlinear resonant interaction, including phase trapping and phase bunching effects. We derive basic equations for a single resonant trajectory analysis and then generalize them into a map in the energy/pitch-angle space. The main advances of this approach are the possibility of considering effects of many resonances and to simulate the evolution of the resonant particle ensemble on long time ranges. For illustrative purposes we consider the system with resonant relativistic electrons and field-aligned whistler-mode waves. The simulation results show that the electron phase space density within the resonant region is flattened with reduction of gradients. This evolution is much faster than the predictions of quasi-linear theory. We discuss further applications of the proposed approach and possible ways for its generalization.

A galaxy dynamo by Supernova-driven interstellar turbulence

AbstractSupernovae are the dominant energy source for driving turbulence within the interstellar plasma. Until recently, their effects on magnetic field amplification in disk galaxies remained a matter of speculation. By means of self-consistent simulations of supernova-driven turbulence, we find an exponential amplification of the mean magnetic field on timescales of a few hundred million years. The robustness of the observed fast dynamo is checked at different magnetic Reynolds numbers, and we find sustained dynamo action at moderate Rm. This indicates that the mechanism might indeed be of relevance for the real ISM.Sensing the flow via passive tracer fields, we infer that SNe produce a turbulent α effect which is consistent with the predictions of quasilinear theory. To lay a foundation for global mean-field models, we aim to explore the scaling of the dynamo tensors with respect to the key parameters of our simulations. Here we give a first account on the variation with the supernova rate.

Transport of perpendicular edge momentum by drift-interchange turbulence and blobs

Turbulence in the vicinity of the last closed surface transports plasma momentum away from the core region toward the wall, and hence provides a momentum “source” that can induce net core plasma rotation as well as sheared flows in the edge. Here, numerical simulations of this process for the binormal (approximately poloidal) component of momentum are described that use a minimal two-dimensional model, in the plane perpendicular to the magnetic field, incorporating directionality (drift-waves), radial transport (Reynolds stress and blobs), and dissipation (sheath loss terms). A zonally averaged momentum conservation law is used to advance the zonal flows. The net momentum transferred to the core is shown to be influenced by a number of physical effects: dissipation, the competition between momentum transport by Reynolds stress and passive convection by particles, intermittency (the role of blobs carrying momentum), and velocity shear regulation of turbulence. It is shown that the edge momentum source adjusts to match the rate of momentum transfer into the core, keeping the edge velocity shear nearly constant. The simulation results are also compared with the predictions of quasilinear theory.

Electron acceleration by magnetosonic waves in solar flares

Results of a simulation of electron acceleration by magnetosonic waves in a solar coronal loop are presented. The dependence of the energization rate on the strength and shape of the wave spectrum is discussed. Comparisons are made with the predictions of quasilinear theory and of a model describing stochastic acceleration by waves as isotropic diffusion in momentum space.

Study of parallel diffusion of energetic particles in the interplanetary medium using spacecraft data at 1 and 5 AU

Energetic particle (1–100 MeV) pitch angle scattering in the Interplanetary Magnetic Field (IMF) is studied using spacecraft magnetometer data at 1 AU (IMP 7 and HEOS 2) and at 5 AU (Pioneer 10). Particle trajectories are followed by a computer simulation of their movement in a realistic model of the IMF. Determination of the pitch angle diffusion coefficient at 1 AU (Dμμ) leads to a parallel mean free path which is roughly independent of particle energy, λ∥≃0.03 AU. At the lowest energy our result is at least a factor of 3 larger than the predictions of quasi linear theory. Results at 5 AU lead to a radial mean free path which is between 2 to 6 times smaller than at 1 AU, probably indicating a greater importance for perpendicular diffusion at large heliodistances. In fact a roughly constant radial mean free path (λ r ≃0.01 AU) is obtained when the contribution of perpendicular diffusion at 5 AU is taken into account (Moussaset al., 1981).

Nonlinear Development of Electromagnetic Instabilities in Anisotropic Plasmas

Theory and simulation experiment are presented for a wide variety of transverse electromagnetic instabilities in plasmas with different sources and degrees of anisotropy. In each of the electron bi-Maxwellian, electron-pinch, and ion-pinch experiments, the bulk response of the system during the initial stages of instability is in good agreement with the predictions of quasilinear theory. Furthermore, the two independent energy constants which derive from the fully nonlinear Vlasov-Maxwell equations are found to remain constant to very good accuracy, even when the magnetic field energy reaches a substantial fraction of the total system energy. In each simulation experiment it is found that the magnetic energy saturates once the magnetic bounce frequency has increased to a value comparable to the linear growth rate prior to saturation, i.e., when ω¯B∼γ¯k. It is concluded that amplitude limitation for Weibel instabilities is a result of magnetic trapping for a broad range of system parameters. In many experiments a large remnant anisotropy in kinetic energy persists long after saturation.

Experimental Test of the Quasilinear Theory of the Gentle Bump Instability

The nonlinear evolution of the instability resulting from a gentle bump on the tail of the electron velocity distribution of a plasma was investigated experimentally. An electron beam with a large velocity spread was injected along the axis of a collisionless plasma column immersed in a strong magnetic field. The equilibrium wave amplitude, spectral shape, and electron velocity distribution were measured and found to be in good agreement with the predictions of quasilinear theory, providing the beam met the requirements of the theory. When the beam was too strong to be a gentle bump, deviations from quasilinear theory appeared.

Electron Heating by Electron-Ion Beam Instabilities

Rapid electron heating by two counterstreaming ion beams has been observed in computer experiments. The results are compared with the predictions of quasilinear theory and found to be in substantial agreement.