Large-scale magnetic structures of coronal mass ejections

Based on the studies on the source regions of a group of coronal mass ejections, we have identified two types of large-scale magnetic structures, and suggested that they are intrinsic components of solar magnetism, their destabilization, expansion, and eruption into the interplanetary space are the basic physical processes which lead to the coronal mass ejections. These two types of large-scale structures are giant magnetic loops connecting the two active belts on the opposite hemispheres of the Sun, and the giant filaments (filament channels) and their related magnetic structures. The latter often appear as two parallel rows of sunspots and plage fields, which align side by side in the full disk daily and synoptic magnetograms. The magnetic neutral lines of these large-scale structures are usually longer than 50 heliographic degrees. We name this type of structure “super A configuration”. Sometimes, they are shown as very long filaments and related large-scale magnetic fields. As these magnetic structures are of very large scale, they extend to a great altitude into the corona, they are not easily recognized in magnetic field observations which are usually aimed at solar flare studies. To identify these large-scale structures becomes a key to understanding and predicting coronal mass ejections.     

Diagnosis of solar chromospheric magnetic field

This paper discusses the measurements of the chromospheric magnetic field and the spatial configuration of the field at the lower solar atmosphere inferred by the distribution of the solar photospheric and chromospheric magnetic fields. Some questions in the study of the chromospheric magnetic field are also presented.     

Catastrophe of coronal magnetic flux ropes in fully open magnetic field

The catastrophe of coronal magnetic flux ropes is closely related to solar explosive phenomena, such as prominence eruptions, coronal mass ejections, and two-ribbon solar flares. Using a 2-dimensional, 3-component ideal MHD model in Cartesian coordinates, numerical simulations are carried out to investigate the equilibrium property of a coronal magnetic flux rope which is embedded in a fully open background magnetic field. The flux rope emerges from the photosphere and enters the corona with its axial and annular magnetic fluxes controlled by a single "emergence parameter". For a flux rope that has entered the corona, we may change its axial and annular fluxes artificially and let the whole system reach a new equilibrium through numerical simulations. The results obtained show that when the emergence parameter, the axial flux, or the annular flux is smaller than a certain critical value, the flux rope is in equilibrium and adheres to the photosphere. On the other hand, if the critical value is exceeded, the flux rope loses equilibrium and erupts freely upward, namely, a catastrophe takes place. In contrast with the partly-opened background field, the catastrophic amplitude is infinite for the case of fully-opened background field.     

Vector magnetic field in solar polar region

By means of ‘deep integration’ observations of a videomagnetograph the vector magnetic field was first systematically measured near the solar south polar region on April 12, 1997 when the Sun was in the minimal phase between the 22nd and 23rd solar cycle. It was found that the polar magnetic field deviated from the normal of solar surface by about 42.2° ± 3.2°, a stronger magnetic element may have smaller inclination, and that within the polar cap above heliolatitude of 50°, the unsigned and net flux densities were 7.8 × 10⁻⁴) T and −3.4×10⁻⁴T, respectively, and consequently, the unsigned and net fluxes were about 5.5 × 10²² and − 2.5 × 10²² Mx. The net magnetic flux, which belongs to the large-scale global magnetic field of the Sun, roughly appmaches the order of the interplanetary magnetic field (IMF) measured at distance of 1 AU. Project supported by the National Natural Science Foundation of China (Grant No. 19791090).     

铁磁性设备补偿磁场的数学模型及其应用

研究用永磁体对铁磁性设备进行磁场补偿的问题,建立了补偿磁场的数学模型.将设备划分成若干个小长方体后,基于磁矩量法建立了数学模型,并对补偿磁场进行拟合.在计算模型中的耦合系数矩阵时,用多个点的平均值作为耦合系数的有效值,提高了计算结果的可靠性和稳定性.并且,针对永磁体距离设备很近时,设备呈现出的非线性磁化特性,通过优化方法求解各个单元的等效磁化率,这种方法不需要知道铁磁材料的磁化曲线和设备结构,便于计算和实际应用.最后,通过实验设计与数值计算,得到了永磁体对设备进行补偿的磁场分布,模型计算结果与实际测量数据误差11%以内,这说明该模型能够满足工业要求,具有实际应用价值.     

Calculation of the magnetic field due to a bioelectric current dipole in an ellipsoid

The bioelectric current dipole model is important both theoretically and computationally in the study of electrical activity in the brain and stomach due to the resemblance of the shape of these two organs to an ellipsoid. To calculate the magnetic field B due to a dipole in an ellipsoid, one must evaluate truncated series expansions involving ellipsoidal harmonics , which are products of Lamé functions. In this article, we extend a strictly analytic model (G. Dassios and F. Kariotou, J. Math. Phys. 44 (2003), 220–241), where B was computed from an ellipsoidal harmonic expansion of order 2. The present derivations show how the field can be evaluated to arbitrary order using numerical procedures for evaluating the roots of Lamé polynomials of degree 5 or higher. This can be accomplished using an optimization technique for solving nonlinear systems of equations, which allows one to acquire an understanding of the truncation error associated with the harmonic series expansion used for the calculation. Funding was provided by the National Institute of Health, Grant No. 1RO1 DK 58697 and by the Veterans’ Affairs Research Service.     

Instability of a planar liquid layer in an alternating longitudinal magnetic field with non-zero mean

The conducting liquid interface is found to undulate in an alternating magnetic field. It was shown earlier that ifM =B ₀ ²/μηω, B₀, ω, μ andη being the amplitude (complex) of the alternating longitudinal magnetic field imposed at the interface, the angular frequency of the field, the magnetic permeability and the viscosity respectively, and ifM _c was the critical value ofM then the planar layer was stable or unstable according asM < M _c orM > M _c. In this paper we have determined the stability criterion when in addition to the alternating longitudinal field there acts a uniform field in the same direction. After comparing our results with those obtained earlier, in the absence of the uniform field, we find that the additional uniform field has a significant destabilizing effect.     

Catastrophe of coronal magnetic flux ropes in fully open magnetic field

The catastrophe of coronal magnetic flux ropes is closely related to solar explosive phenomena, such as prominence eruptions, coronal mass ejections, and two-ribbon solar flares. Using a 2-dimensional, 3-component ideal MHD model in Cartesian coordinates, numerical simulations are carried out to investigate the equilibrium property of a coronal magnetic flux rope which is embedded in a fully open background magnetic field. The flux rope emerges from the photosphere and enters the corona with its axial and annular magnetic fluxes controlled by a single “emergence parameter”. For a flux rope that has entered the corona, we may change its axial and annular fluxes artificially and let the whole system reach a new equilibrium through numerical simulations. The results obtained show that when the emergence parameter, the axial flux, or the annular flux is smaller than a certain critical value, the flux rope is in equilibrium and adheres to the photosphere. On the other hand, if the critical value is exceeded, the flux rope loses equilibrium and erupts freely upward, namely, a catastrophe takes place. In contrast with the partly-opened background field, the catastrophic amplitude is infinite for the case of fully-opened background field     

Inhibition or enhancement of chaotic convection via inclined magnetic field

In this paper, we investigate the onset of convection in a horizontal layer of fluid which is heated from the underside. An inclined magnetic field is applied to the layer. The Galerkin truncated approximations were used to obtain a Lorenz-like model. The nonlinear system was solved by the fourth-order Runge–Kutta method. The results show that the Hartmann number and the angle of inclination of the magnetic field could inhibit or enhance the onset of chaotic convection.     

Integrable model of a two-dimensional singular spherical oscillator in a constant magnetic field

We propose an analogue of a two-dimensional singular oscillator (Smorodinsky-Winternitz oscillator) on a sphere, which is exactly solvable in the classical sense both without and with a constant magnetic field. We find the explicit classical solutions. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 156, No. 1, pp. 131–137, July, 2008.     

Derivation of lower critical magnetic field for anisotropic Ginzburg-Landau model in superconductivity

In this paper, the authors discuss the vortex structure of an anisotropic Ginzburg-Landau model for superconducting thin film proposed by Du. We obtain the estimate for the lower critical magnetic field $ H_{C_1 } $ H_{C_1 } which is the first critical value of h _ex corresponding to the first phase transition in which vortices appear in the superconductor. We also find local minimizers of the anisotropic superconducting thin film with a large parameter κ, and for the applied magnetic field near the critical field we discuss the asymptotic behavior of the local minimizers.     

The dressed nonrelativistic electron in a magnetic field

We consider a nonrelativistic electron interacting with a classical magnetic field pointing along the x₃‐axis and with a quantized electromagnetic field. When the interaction between the electron and photons is turned off, the electronic system is assumed to have a ground state of finite multiplicity. Because of the translation invariance along the x₃‐axis, we consider the reduced Hamiltonian associated with the total momentum along the x₃‐axis and, after introducing an ultraviolet cutoff and an infrared regularization, we prove that the reduced Hamiltonian has a ground state if the coupling constant and the total momentum along the x₃‐axis are sufficiently small. We determine the absolutely continuous spectrum of the reduced Hamiltonian and, when the ground state is simple, we prove that the renormalized mass of the dressed electron is greater than or equal to its bare one. We then deduce that the anomalous magnetic moment of the dressed electron is nonnegative. Copyright © 2006 John Wiley & Sons, Ltd.     

Influence of moving magnetic field on three dimensional Couette flow

A three dimensional steady fully developed MHD Couette flow of a viscous incompressible electrically conducting fluid is analysed. The lower stationary porous plate is subjected to a periodic injection velocity and the upper porous plate in uniform motion to a constant suction velocity. A magnetic field of uniform strength applied normal to the planes of the plates is fixed with the moving plate. Neglecting the induced magnetic field, an approximate solution for the flow field is obtained and discussed with the help of graphs.     

Experimental studies of axial magnetic fields generated in ultrashort-pulse laser-plasma interaction

The quasistatic axial magnetic fields in plasmas produced by ultrashort laser pulses were measured by measuring the Faraday rotation angle of the backscattered emission. The spatial distribution of the axial magnetic field was obtained with a peak value as high as 170 Tesla. Theory suggests that the axial magnetic field is generated by dynamo effect in laser-plasma interaction.     

Effects of an induced magnetic field on the peristaltic flow of a third‐order fluid

In this article, we carry out the effect of an induced magnetic field on the peristaltic transport of an incompressible conducting third order fluid in a symmetric channel. The flow analysis has been developed for low Reynolds number and long wave length approximation. Analytical solutions have been established for the axial velocity, stream function, magnetic force function, and axial‐induced magnetic field. The effects of pertinent parameters on the pressure rise per wavelength are investigated by using numerical integration. Besides this, we study the effect of these parameters on the pressure gradient and axial induced magnetic field. The phenomena of trapping and pumping are also discussed. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010     

Asymptotics of a solution of a nonlinear system of diffusion of a magnetic field into a substance

We study the asymptotic behavior at large time of a solution to a system of nonlinear integro-differential equations which arises in mathematical modeling of diffusion of a magnetic field into a substance. We establish the corresponding stabilization rate.     

The 2D magnetohydrodynamic system with Euler-like velocity equation and partial magnetic diffusion

When the velocity equation of the incompressible 2D magnetohydrodynamic (MHD) system is inviscid, the global well-posedness and stability problem in the whole space ${\mathbb{R}}^2$ case remains an extremely challenging open problem. Broadman, Lin, and Wu (SIAM J. Math. Anal. 52(5) (2020): 5001-5035) were able to establish the global well-posedness and stability near a background magnetic field when there is damping in one velocity component. Their work exploited the stabilizing effect of the background magnetic field. This paper presents new progress. We are able to prove the global well-posedness and stability even when the magnetic diffusion is degenerate and only in the vertical direction. The velocity equation is still inviscid and has damping only in the vertical component. The proof of this new result overcomes two main difficulties, the potential rapid growth of the velocity due to the lack of dissipation or horizontal damping and the control of nonlinearity associated with the magnetic field. By discovering the key hidden smoothing effects and incorporating them in the construction of a two-layered energy function, we are able to obtain uniform bounds on the solution in the H³-norm when the initial perturbation is near the background magnetic field. In addition, we prove that certain Lebesgue and Sobolev norms of the solution approach zero as time approaches infinity.     

Stability estimate for an inverse problem for the wave equation in a magnetic field

In this article, we prove stability estimate of the inverse problem of determining the magnetic field entering the magnetic wave equation in a bounded smooth domain in ? ^d from boundary observations. This information is enclosed in the hyperbolic (dynamic) Dirichlet-to-Neumann map associated to the solutions to the magnetic wave equation. We prove in dimension d ≥ 2 that the knowledge of the Dirichlet-to-Neumann map for the magnetic wave equation measured on the boundary determines uniquely the magnetic field and we prove a Hölder-type stability in determining the magnetic field induced by the magnetic potential.     

Spectral confinement and current for atoms in strong magnetic fields

We study confinement of the ground state of atoms in strong magnetic fields to different subspaces related to the lowest Landau band. Using the results on confinement we can calculate the quantum current in the entire semiclassical region B?Z³.