Nonlinear theory of mirror instability near its threshold

An asymptotic model based on a reductive perturbative expansion of the drift kinetic and Maxwell’s equations is used to demonstrate that, near the instability threshold, the nonlinear dynamics of mirror modes in a magnetized plasma with anisotropic ion temperatures involves a subcritical bifurcation, leading to the formation of small-scale structures with amplitudes comparable with the ambient magnetic field. The text was submitted by the authors in English.     

Dynamical model for nonlinear mirror modes near threshold

Using a reductive perturbative expansion of the Vlasov-Maxwell (VM) equations for magnetized plasmas, a pseudodifferential equation of gradient type is derived for the nonlinear dynamics of mirror modes near the instability threshold. This model, where kinetic effects arise at a linear level only, develops a finite-time singularity, indicating the existence of a subcritical bifurcation. A saturation mechanism based on the local variations of the ion Larmor radius, is then phenomenologically supplemented. In contrast with previous models where saturation is due to the cooling of a population of trapped particles, the resulting equation correctly reproduces results of numerical simulations of VM equations, such as the development of magnetic humps from an initial noise, and the existence of stable large-amplitude magnetic holes both below and slightly above threshold.     

Nonlinear effects in the convective instability of a binary mixture in a porous medium near threshold

An amplitude equation is derived near threshold for both the stationary and the oscillatory instabilities and an oscillatory behavior in time for the Nusselt and the Froude number is predicted for the oscillatory instability.     

Nonlinear theory of the ablative Rayleigh-Taylor instability

A fully nonlinear sharp-boundary model of the ablative Rayleigh-Taylor instability is derived and closed in a similar way to the self-consistent closure of the linear theory. It contains the stabilizing effect of ablation and accurately reproduces the results of 2D DRACO simulations. The single-mode saturation amplitude, bubble and spike evolutions in the nonlinear regimes, and the seeding of long-wavelength modes via mode coupling are determined and compared with the classical theory without ablation. Nonlinear stability above the linear cutoff is also predicted.     

Kinetic theory of fluctuations near a convective instability

The kinetic theory of density and velocity fluctuations below and above the first convective instability in a Benard cell is presented. Results are given in a form valid for all fluid densities. In particular, the singular behavior near the instability point is computed and a detailed comparison with that near a critical point is made. Mode coupling effects, involving the viscous and the heat mode, that determine the singular behavior of the thermal conductivity near the critical point, are also responsible for the singular behavior of the pair correlation function and in particular the density-density correlation function near the instability point. The anomalous density fluctuations could be measured directly by microwave scattering experiments, while the velocity fluctuation could be measured by laser Doppler velocimetry.     

Scaling theory of transient phenomena near the instability point

A general scaling theory of transient phenomena is formulated near the instability point for the moments of the relevant intensive macrovariable, for the generating function, and for the probability distribution function. This scaling theory is based on a generalized scale transformation of time. The whole range of time is divided into three regions, namely the initial, scaling, and final regions. The connection procedure between the initial region and the scaling region is studied in detail. This scaling treatment has overcome the difficulty of divergence of the variance for a large time which was encountered in the -expansion, and this scaling theory yields correct values of moments to order unity for an infinite time. Some instructive examples are discussed for the purpose of clarifying the concepts of the scaling theory.     

Scaling theory of relaxation and fluctuation near the instability point

The idea of generalized scale transformation of time is introduced to evaluate asymptotically the relaxation and fluctuation in non-equilibrium systems. This scaling theory is demonstrated to be very powerful in discussing the relaxation just from the instability point.     

pp → ppπnear threshold in pionless effective theory

The total cross-section of the pp → ppπ⁰ reaction near threshold is calculated in pionless effective field theory with a di-baryon and external pions. The amplitudes for a leading one-body and subleading contact neutral pion production vertex are obtained including the initial- and final-state interactions. After estimating a low-energy constant in the contact vertex, we compare our results for the total cross-section with the experimental data.     

Nonlinear theory of surface helical instability of a semiconducting plasma

Nonlinear equations characterizing the surface helical instability (SHI) of a semiconducting plasma in semispace are examined. Solutions for the first, zeroth, and second harmonics of the unstable wave are found. Dispersion relations and equations giving the amplitude and nonlinear frequency shift of the fundamental (first) harmonic are obtained.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 59–64, December, 1979.     

超薄镜破坏阈值的研究

新一代空间相机的非球面主镜由一些超轻超薄的分块镜组成，由于目前通用的空间光学反射镜材料非常有限且大部分均为脆性材料，在力的作用下产生强制性的变形将引起镜体大的应力甚至破碎，所以必须研究超薄镜的破坏阈值。首先将弹性力学中应力强度因子的概念引入主动光学中，证明了应力强度因子即传统意义的材料破坏阈值。提出材料表面的微裂纹是材料脆性断裂的根本原因。介绍了一种计算材料应力强度因子的方法。最后针对超薄平面镜模型进行了实例计算，得到了超薄镜的破坏阈值与其尺寸、厚度、支承条件、表面粗糙度之间的关系。     

On the theory of a detuned single mode laser near threshold

A theory of a detuned single mode laser near threshold is given using the Fokker-Planck equation technique. The Fokker-Planck equation is solved by an eigenfunction expansion. The eigenfunctions and the corresponding eigenvalues are determined by a nonhermitian operator and are calculated numerically in the threshold region. The dependence of the linewidth from the detuning is shown. In the intensity distribution the detuning enters only via a change of the scaling parameter. For the linewidth, however, an additional broadening is found. Finally it is shown that in certain cases the correlation function must not be approximated by a single exponential term.     

Hydrodynamic modes,soft modes and fluctuation spectra near the threshold of a current instability

We give a full threedimensional treatment of the stability and the fluctuations of the uniform stationary current state in a voltage-controlled current instability. We consider a model which exhibits bulk negative differential conductivity due to Bragg scattering of hot electrons. The model consists of Langevin equations for the mean momentum and the mean energy of the charged carriers, coupled to Maxwell's equations. We investigate the normal modes and the fluctuation spectra of this system, in particular the occurrence of soft modes and of critical fluctuations at the stability limit of the uniform current state. It is shown that the nature of the normal modes is strongly determined by the electromagnetic interactions between the carriers, giving rise to hydrodynamic flux modes and to dielectric relaxation modes. As the threshold field is approached, the dielectric relaxation modes soften and couple strongly to the flux modes. It is shown that as a consequence of this coupling the exponential decay of the correlation functions due to ordinary dielectric relaxation is followed at very long times by a power law decay due to the hydrodynamic modes.Work supported by the Swiss National Science Foundation     

Laser instability below threshold

The zero solution of a semiclassical set of equations describing a perfectly tuned laser-saturable absorber system may not be stable below the previously found threshold. A new type of steady-state solution which oscillates with intensity-dependent frequency has been found.