Effect of pressure anisotropy on magnetorotational instability

It is shown that two new instabilities of hybrid type can occur in a rotating magnetized plasma with anisotropic pressure, i.e., the rotational firehose instability and the rotational mirror instability. In the case of β_∥ > β_⊥, where β_∥ and β_⊥ are the ratios of the parallel and perpendicular plasma pressure to the magnetic field pressure, the pressure anisotropy tends to suppress both new instabilities; in the case β_⊥ > β_∥, it leads to their strengthening. In the latter case, the perturbations considered can be unstable even if the Velikhov instability criterion is not satisfied. The text was submitted by the authors in English.     

The Velikhov and anti-Velikhov effects in the theory of magnetorotational instability

A theory of magnetorotational instability (MRI) allowing an equilibrium plasma pressure gradient and nonaxisymmetry of perturbations is developed. This approach reveals that in addition to the Velikhov effect driving the MRI due to negative rotation frequency profile, dΘ²/dr < 0, there is an opposite effect (the anti-Velikhov effect) weakening this driving (here, Θ is the rotation frequency and r is the radial coordinate). It is shown that in addition to the Velikhov mechanism, two new mechanisms of MRI driving are possible, one of which is due to the pressure gradient squared and the other is due to the product of the pressure and density gradients. The analysis includes both the one-fluid magnetohydrodynamic plasma model and the kinetics allowing collisionless effects. In addition to the pure plasma containing ions and electrons, the dusty plasma is considered. The charged dust effect on stability is analyzed using the approximation of immobile dust. In the presence of dust, a term with the electric field appears in the one-fluid equation of plasma motion. This electric field affects the equilibrium plasma rotation and also gives rise to a family of instabilities of the rotating plasma, called the dust-induced rotational instabilities. The article is published in the original.     

Experimental observation of discrete modulational instability

We report the first experimental observation of modulation instability in a discrete optical nonlinear array.     

Experimental evidence for magnetorotational instability in a Taylor-Couette flow under the influence of a helical magnetic field

A recent Letter [R. Hollerbach and G. Rüdiger, Phys. Rev. Lett. 95, 124501 (2005)] has shown that the threshold for the onset of the magnetorotational instability in a Taylor-Couette flow is dramatically reduced if both axial and azimuthal magnetic fields are imposed. In agreement with this prediction, we present results of a Taylor-Couette experiment with the liquid metal alloy GaInSn, showing evidence for the existence of the magnetorotational instability at Reynolds numbers of order 1000 and Hartmann numbers of order 10.     

New type of magnetorotational instability in cylindrical taylor-couette flow

We study the stability of cylindrical Taylor-Couette flow in the presence of combined axial and azimuthal magnetic fields, and show that adding an azimuthal field profoundly alters the previous results for purely axial fields. For small magnetic Prandtl numbers Pm, the critical Reynolds number Re(c) for the onset of the magnetorotational instability becomes independent of Pm, whereas for purely axial fields it scales as Pm-1. For typical liquid metals, Re(c) is then reduced by several orders of magnitude, enough that this new design should succeed in realizing this instability in the laboratory.     

Weakly nonlinear analysis of the magnetorotational instability in a model channel flow

We show by means of a perturbative weakly nonlinear analysis that the axisymmetric magnetorotational instability (MRI) of a viscous, resistive, incompressible rotating shear flow subject to a background vertical magnetic field in a thin channel gives rise to a Ginzburg-Landau equation for the disturbance amplitude. For small magnetic Prandtl number (P(m)), the saturation amplitude is proportional square root P(m) and the resulting momentum transport scales as R(-1), where R is the hydrodynamic Reynolds number. Simplifying assumptions, such as linear shear base flow, mathematically expedient boundary conditions, and continuous spectrum of the vertical linear modes, are used to facilitate this analysis. The asymptotic results are shown to comply with numerical calculations using a spectral code. They suggest that the transport due to the nonlinearly developed MRI may be very small in experimental setups with P(m)<1.     

Experimental observation of speckle instability in Kerr random media

In a disordered nonlinear medium the transmitted speckle pattern was predicted to become unstable as a result of the positive feedback between intensity fluctuations and local variations of the refractive index. We show experimental evidence of speckle instability for light transversally scattered in a liquid crystal cell, where a two-dimensional controlled disorder is imprinted by suitable illumination of a photoconductive wall and nonlinearity is obtained through optical reorientation of the liquid crystal molecules. The speckle pattern spontaneously oscillates at discrete frequencies above a critical threshold, whose dependence on the scattering mean free path confirms the crucial role of disorder in the feedback process.     

Experimental observation of modulation instability and optical spatial soliton arrays in soft condensed matter

In this Letter we report observations of optically induced self-organization of colloidal arrays in the presence of unpatterned counterpropagating evanescent waves. The colloidal arrays formed along the laser propagation axis are shown to be linked to the breakup of the incident field into optical spatial solitons, the lateral spacing of the arrays being related to modulation instability of the soft condensed matter system.     

Experimental characterization of onset of acoustic instability in a nonpremixed half-dump combustor

This paper reports work on a nonpremixed half-dump combustor, in which methane is injected at the backward-facing step, and mixes and burns with the air flowing past the step in the unsteady recirculation zone. The flow and geometric parameters are widely varied, to gradually change from conditions of low-amplitude noise to excitation of high-amplitude discrete tones. The purpose of the work is to focus on the transition from the former condition to the latter, and to mark the onset of instability. Dimensionless groups such as the Helmholtz and Strouhal numbers are formed based on the observed dominant frequencies, whose variation with the air flow Reynolds number is used to identify the oscillations as those due to the natural acoustic modes or the vortex shedding process. High-speed chemiluminescence imaging reveals shedding of vortical structures in the flame zone. With variation in the conditions, flow-acoustic lock-on and transition from one vortex shedding mode to another is marked by nonlinearity in the corresponding amplitude variations. Such conditions are identified as the onset of instability in terms of the ratio of the flow time scale to the acoustic time scale and mapped against the operating fuel-air equivalence ratio of the combustor.     

Experimental verification of the shear-modified ion-acoustic instability

The predicted shear-induced shift of the wave phase velocity, the essence of the shear-modified ion-acoustic (SMIA) instability mechanism that reduces ion Landau damping for otherwise damped ion-acoustic waves [V. Gavrishchaka et al., 80, 728 (1998)], is verified with direct measurements in a strongly magnetized laboratory plasma. The SMIA growth rate is shown to increase with increasing shear, as predicted. SMIA wave propagation is shown to be possible at both small and large angles to the magnetic field, consistent with space observations of ion-acoustic-like waves.     

Experimental study of the multipolar vortex instability

The instability of a vortex subjected to a stationary dipolar or tripolar constraint is studied experimentally by using a rotating deformable cylinder on which two or three rollers are applied. As the Reynolds number and the aspect ratio of the cylinder are varied, different modes of instability are observed and their wavelength and frequency are compared to theoretical predictions. Secondary instability and cyclic breakup are also evidenced in the elliptic geometry.     

Experimental study of the parallel velocity shear instability

The parallel velocity shear instability (PVSI) is experimentally investigated in a double-ended Q machine in which the shear in the ion flow is produced by suitable shaping of the axial magnetic field. Instability fluctuation levels approaching nearly 100% are often observed.     

Neutrino trigger of the magnetorotational mechanism of a natal-pulsar kick

A mechanism generating a natal-neutron-star kick and involving only standard neutrinos is discussed. In this mechanism, the neutrino effect on the plasma of the supernova-core envelope in a magnetorotational explosion accompanied by the generation of a strong toroidal magnetic field leads to a redistribution of the magnetic field B in the “upper” and “lower” hemispheres of the supernova-core envelope. The emerging asymmetry of the magnetic-field pressure may generate a natal-pulsar kick.