E. V. Yushkov's research while affiliated with Moscow Center For Continuous Mathematical Education and other places

The small-scale magnetic energy generation in a turbulent velocity field is studied by two different approaches. One of them is based on the Kazantsev-Kraichnan model developed for turbulence with short-time velocity correlations, and the other uses the shell model of magnetohydrodynamic turbulence, describing the turbulent energy cascade on a finite number of spectral shells. We have found that the injection of weak magnetic field at the initial moment in both models leads to an exponential growth of magnetic energy and tried to determine whether these effects are of the same or different nature. The investigations have shown that the rates of growths and magnetic energy spectra in two approaches can be very much different, which can be attributed to the contradictions of the model assumptions and unknown correlation time. The discussion of these contradictions allows us to formulate a possible explanation, which is likely related to the fact that the small-scale magnetic field generation is under the influence of some spectral subrange, rather than the entire kinetic spectrum. Varying the correlation time of the velocity field and considering the spectral regions, we have determined the range of kinetic energy spectrum responsible for the small-scale dynamo generation.

The properties of nonlinear parametric resonance are investigated using the example of the low-mode Parker dynamo model. This model is a system of four ordinary differential equations and in the simplest approximation describes the processes of generation and oscillation of large-scale magnetic fields in stellar systems. In the absence of nonlinear effects, the problem under consideration, by analogy with a system of harmonic oscillations, admits an asymptotic division of multiple resonant frequencies. However, despite the fact that at first glance at these frequencies it is reasonable to expect an amplification of the amplitude in the nonlinear case, it is demonstrated that in the presence of nonlinear terms, the behavior of the system is significantly more complex. In particular, generation suppression can be observed at resonant or low frequencies, while amplification occurs in the immediate vicinity of the resonance or at sufficiently high frequencies. The reasons are discussed for this behavior, as well as the possibility of the influence of parametric resonance on the establishment of planetary dynamo cycles.

The effect of periodic pumping on dynamo generation in the simplest Parker model is studied in this work. Pumping is understood in the sense that the periodic parameters oscillations in the dynamo system leads to a change in the rate of the exponential growth of the mean magnetic field. And since the Parker model simultaneously describes its time oscillations as the field grows, this phenomenon is very similar to parametric resonance in the classical model of a harmonic oscillator. With the help of asymptotic analysis and numerical simulation, we demonstrate both pump regions similar to parametric resonance, as well as different amplification regions at high driving force frequencies, and suppression regions at low frequencies, find the gain maximum and investigate the behavior of the critical pump frequency separating the regions of generation and suppression.

We study the relation between stellar dynamo-wave propagation and the structure of the stellar magnetic field. Modeling dynamo waves by the well-known Parker migratory dynamo, we vary the intensity of dynamo drivers in order to obtain activity-wave propagation toward the Equator (as in the solar-activity cycle) or towards the Poles. We match the magnetic field in the dynamo-active shell with that in the surrounding stellar material, using a simple dissipative magneto-hydrodynamic system for the transition region. Introducing a weak asymmetry between the stellar hemispheres, we study phase shifts of the dipole, quadrupole, and octupole magnetic components at various distances from the star to demonstrate that a several-percent asymmetry in dynamo drivers is sufficient to obtain a realistic relation between solar dipole and quadrupole moments. We study the behavior of the stellar current sheets and show that for the poleward-propagating activity it is substantially different from solar ones. In particular, we demonstrate conditions in which the conical current sheets propagate opposite to the solar directions.

We study the relation between stellar dynamo-wave propagation and the structure of the stellar magnetic field. Modeling dynamo waves by the well-known Parker migratory dynamo, we vary the intensity of dynamo drivers in order to obtain activity-wave propagation toward the Equator (as in the solar-activity cycle) or towards the Poles. We match the magnetic field in the dynamo active shell with that in the surrounding stellar material, using a simple dissipativ magnetohydrodynamic system for the transition region. Introducing a weak asymmetry between the stellar hemispheres, we study phase shifts of the dipole, quadrupole, and octupole magnetic components at various distances from the star to demonstrate that several-percent asymmetry in dynamo drivers are sufficient to obtain a realistic relation between solar dipole and quadrupole moments. We study the behavior of the stellar current sheets and show that for the poleward propagating activity it is substantially different from solar ones. In particular, we demonstrate conditions in which the conical current sheets propagate opposite to the solar directions.

We present analysis of about one hundred bipolar structures of positive polarity identified in ten quasi-perpendicular crossings of the Earth’s bow shock by the Magnetospheric Multiscale spacecraft. The bipolar structures have amplitudes up to a few tenths of local electron temperature, spatial scales of a few local Debye lengths, and plasma frame speeds of the order of local ion-acoustic speed. We argue that the bipolar structures of positive polarity are slow electron holes, rather than ion-acoustic solitons. The electron holes are typically above the transverse instability threshold, which we argue is due to high values of the ratio w_pe/w_ce between electron plasma and cyclotron frequencies. We speculate that the transverse instability can strongly limit the lifetime of the electron holes, whose amplitude is above a certain threshold, which is only a few mV/m in the Earth’s bow shock. We suggest that electron surfing acceleration by large-amplitude electron holes reported in numerical simulations of high-Mach number shocks might not be as efficient in realistic shocks, because the transverse instability strongly limits the lifetime of large-amplitude electron holes at w_pe/w_ce values typical of collisionless shocks in nature.

Substorm growth phase in the magnetotail is characterized by formation of a thin current sheet (CS) becomes unstable due to external or internal drivers. Such instability results in magnetic field line reconnection, the substorm onset. The CS thinning, as a key process of substorm dynamics, has been included into many global and local simulations of the magnetotail magnetic reconnection. However, recent observations indicate that the evolution of plasma characteristics and magnetic field configuration during the CS thinning can differ from predictions of the classical adiabatic scenario. In this study, we combine two most extensive datasets of the CS evolution, as observed by Cluster and THEMIS missions for 2001–2009 and 2015, respectively. We show that for a wide range of downtail distances and dawn‐dusk direction there are quite similar quantitative characteristics of the thinning: the magnetic field line stretching (north‐south magnetic field decrease), the intensification of the current density, and the evolution of plasma temperatures and densities. We confirm that the process cannot be directly associated with increase of the lobe magnetic pressure. Using advantages of multispacecraft measurements and CS flapping motion, we demonstrate that the thinning is usually result in the equatorial density increase and plasma temperature decrease. We discuss the revealed evolution features in the context of the thermodynamical CS characteristics for contemporary thinning models.