E. V. Yushkov

Kinetic models of magnetic flux ropes observed in the Earth magnetosphere

Magnetic flux ropes (MFR) are universal magnetoplasma structures (similar to cylindrical screw pinches) formed in reconnecting current sheets. In particular, MFR with scales from about the ion inertial length to MHD range are widely observed in the Earth magnetosphere. Typical MFR have force-free configuration with the axial magnetic field peaking on the MFR axis, whereas bifurcated MFR with an off-axis peak of the axial magnetic field are observed as well. In the present paper, we develop kinetic models of force-free and bifurcated MFR and determine consistent ion and electron distribution functions. The magnetic field configuration of the force-free MFR represents well-known Gold-Hoyle MFR (uniformly twisted MFR). We show that bifurcated MFR are characterized by the presence of cold and hot current-carrying electrons. The developed models are capable to describe MFR observed in the Earth magnetotail as well as MFR recently observed by Magnetospheric Multiscale Mission at the Earth magnetopause.

Formation of a quasi-one-dimensional current sheet in the laboratory experiment and in the Earth’s magnetotail

Two-dimensional current sheets (CSs) generated in the CS-3D laboratory device are considered. Results obtained in the laboratory experiment are compared with spacecraft observations of CSs in the Earth’s magnetotail. The longitudinal and transverse CS structures, as well as CS evolution during the thinning process are studied. It is demonstrated that the CSs obtained in the laboratory experiments and those observed by spacecraft possess common properties: they have the same dimensionless spatial scales, similar distributions of the normal component of the magnetic field along the sheet, and similar ratios between the current density and the normal component of the magnetic field. The results of comparison allow one to guess some details of the structure and dynamics of the Earth’s magnetotail CS. In particular, on the basis of the laboratory experiment, it is concluded that the formation of a quasi-one-dimensional CS in the magnetotail at distances of x ∼ −15RE from the Earth (where RE is the Earth’ radius) is accompanied by the growth of the amplitude B0 of the tangential component of the magnetic field and that the field B0 in the quasi-stationary state increases tailward. The critical value of the current density is likely equal to

Traveling-wave solution to a nonlinear equation in semiconductors with strong spatial dispersion

j_0 = eN_e \sqrt {2T_i m_i }

Global unsolvability of one-dimensional problems for Burgers-type equations

, where Ne is the electron density and

Existence and blow-up of solutions of a pseudoparabolic equation

\sqrt {2T_i m_i }

An asymptotic analysis of a small-scale dynamo in a mirror-asymmetric random velocity field

is the ion thermal velocity. The current density cannot substantially exceed this value. Moreover, the CS thickness cannot be substantially smaller then the ion Larmor radius or the ion inertial length.

Kinetic models of sub-ion cylindrical magnetic hole

The third-order nonlinear differential equation (uxx − u)t + uxxx + uux = 0 is analyzed and compared with the Korteweg-de Vries equation ut + uxxx − 6uux = 0. Some integrals of motion for this equation are presented. The conditions are established under which a traveling wave is a solution to this equation.

Asymptotic analysis of a kinematic dynamo in a mirror-symmetric magnetic field

In this paper, we study the global solvability of well-known equations used to describe nonlinear processes with dissipation, namely, the Burgers equation, the Korteweg–de Vries–Burgers equation, and the modified Korteweg–de Vries–Burgers equation. Using a method due to Pokhozhaev, we obtain necessary conditions for the blow-up of global solutions and estimates of the blow-up time and blow-up rate in bounded and unbounded domains. We also study the effect of linear and nonlinear viscosity on the occurrence of a gradient catastrophe in finite time.

Two-dimensional self-similar plasma equilibria

We obtain sufficient blow-up conditions for the solution of a nonlinear differential problem with given initial and boundary conditions. We prove the solvability of this problem in any finite cylinder under some restrictions on the nonlinear operators.

Magnetic helicity generation in the frame of Kazantsev model

Abstract We analyse the asymptotic and numerical solution of the Kazantsev equations for large magnetic Reynolds numbers . For instantaneously correlated random velocity field we obtain the necessary conditions of mirror-asymmetric dynamo processes. We show that simultaneously with longitudinal correlation function, the correlation function for magnetic helicity is also enhanced. We estimate the Rm-threshold for magnetic field generation, the generation rate and their dependencies on helicity parameter. By iterative methods (realised on quasi-uniform grids) we carry out numerical experiments, which confirm the correctness of obtained theoretical asymptotics and estimates.