Global exact controllability of ideal incompressible magnetohydrodynamic flows through a planar duct

This article is concerned with the global exact controllability for ideal incompressible magnetohydrodynamics in a rectangular domain where the controls are situated in both vertical walls. First, global exact controllability via boundary controls is established for a related Elsässer type system by applying the return method, introduced in [Coron J.M., Math. Control Signals Systems, 5(3) (1992) 295--312]. Similar results are then inferred for the original magnetohydrodynamics system with the help of a special pressure-like corrector in the induction equation. Overall, the main difficulties stem from the nonlinear coupling between the fluid velocity and the magnetic field in combination with the aim of exactly controlling the system. In order to overcome some of the obstacles, we introduce ad-hoc constructions, such as suitable initial data extensions outside of the physical part of the domain and a certain weighted space.

Influence of the hypermagnetic field noise on the baryon asymmetry generation in the symmetric phase of the early universe

We study a matter turbulence caused by strong random hypermagnetic fields (HMFs) that influence the baryon asymmetry evolution due to the Abelian anomalies in the symmetric phase in the early Universe. Such a matter turbulence is stipulated by the presence of the advection term in the induction equation for which a fluid velocity is dominated by the Lorentz force in the Navier–Stokes equation. For random HMFs, having nonzero mean squared strengths, we calculate the spectra for the HMF energy and the HMF helicity densities. The latter function governs the evolution of the fermion asymmetries in the symmetric phase before the electroweak phase transition (EWPT). In the simplest model based on the first SM generation for the lepton asymmetries of $$e_\mathrm {R,L}$$ e R , L and $$\nu _{e_\mathrm {L}}$$ ν e L , we calculate a decline of all fermion asymmetries including the baryon asymmetry, given by the ‘t Hooft conservation law, when one accounts for a turbulence of HMFs during the universe cooling down to EWPT. We obtain that the stronger the mean squared strength of random initial HMFs is, the deeper the fermion asymmetries decrease, compared to the case in the absence of any turbulence.

Kinematic dynamos in triaxial ellipsoids

Planetary magnetic fields are generated by motions of electrically conducting fluids in their interiors. The dynamo problem has thus received much attention in spherical geometries, even though planetary bodies are non-spherical. To go beyond the spherical assumption, we develop an algorithm that exploits a fully spectral description of the magnetic field in triaxial ellipsoids to solve the induction equation with local boundary conditions (i.e. pseudo-vacuum or perfectly conducting boundaries). We use the method to compute the free-decay magnetic modes and to solve the kinematic dynamo problem for prescribed flows. The new method is thoroughly compared with analytical solutions and standard finite-element computations, which are also used to model an insulating exterior. We obtain dynamo magnetic fields at low magnetic Reynolds numbers in ellipsoids, which could be used as simple benchmarks for future dynamo studies in such geometries. We finally discuss how the magnetic boundary conditions can modify the dynamo onset, showing that a perfectly conducting boundary can strongly weaken dynamo action, whereas pseudo-vacuum and insulating boundaries often give similar results.

Testing the Magnetohydrodynamic Analysis Software with Natural Convection and Geodynamo Problems

В рамках метода контрольного объема разработан программный код для численного решения задач неидеальной магнитной гидродинамики вязкой несжимаемой жидкости на структурированных разнесенных сетках в сферических координатах. При дискретизации уравнения индукции магнитного поля использован алгоритм ограниченного переноса (Сonstrained Transport Algorithm) и схема QUICK с методом отложенной коррекции для аппроксимации конвективных членов. Для решения уравнений гидродинамики использован алгоритм SIMPLER. Программный код разработан для моделирования естественной конвекции и гидромагнитного динамо во вращающемся шаре или сферическом слое. Представлены результаты решения тестовых задач естественной конвекции и геодинамо с вакуумными граничными условиями, демонстрирующие достаточно точное соответствие результатам эталонных расчетов. Программное обеспечение разработано для ускорителей вычислений, поддерживающих технологию CUDA, с использованием набора расширений к языку программирования Фортран.   Using the control volume method we developed the software for the numerical solution of viscous incompressible fluid resistive magnetohydrodynamics problems on structured staggered meshes in spherical coordinates. The constrained transport algorithm and the QUICK method with delayed correction for the approximation of the convective terms were used for the discretization of the magnetic field induction equation. The SIMPLER algorithm was applied to solving the hydrodynamic equations. We developed software for modeling natural convection and the hydromagnetic dynamo in a rotating sphere or spherical shell. We proposed an algorithm for the numerical solution of the geodynamo problem with vacuum boundary conditions. The results of solving natural convection and geodynamo benchmark problems with vacuum boundary conditions are presented; they demonstrate a fairly accurate agreement with the reference calculations. The software supports CUDA-enabled accelerators and uses a set of extensions to the Fortran programming language.

Developing a Hybrid Three-Dimensional Model of a Plasma Cloud Undergoing Collisionless Expansion into a Rarefied Ionised Magnetized Medium

The paper presents the results of developing a hybrid three-dimensional model of collisionless interaction in plasma flows. This model considers ions in kinetical terms (simulated as a set of individual particles) and describes electrons in terms of continuum mechanics (simulated as a fluid). We present the system of equations behind the mathematical model and the physical conditions limiting its applicability. The system includes equations describing ion motion in electromagnetic fields, the quasineutrality equation, equations for calculating the total current density, non-radiative Maxwell's equations, and the generalised Ohm's law. We outline a numerical method for solving our hybrid model equations and describe an algorithm for solving the system of equations over time. We focus on the numerical method for solving the induction equation, which takes possible discontinuous solutions into account and preserves the divergence-free condition for the magnetic field. The paper discusses the issues of increasing the spatial approximation accuracy for the numerical scheme used to solve the induction equation. We present numerical simulation results for collisionless expansion of a plasma cloud into a rarefied ionised gas in the presence of an external magnetic field. These results were obtained using our computer code that implements the hybrid model described. The paper demonstrates some numerical properties of the digital simulation developed, specifically, how the order of accuracy for the numerical scheme approximation designed to solve the induction equation affects numerical simulation results

Unified theories metrics and primordial magnetic fields in Riemann–Cartan spacetime

Several spacetime metrics in teleparallel geometry of Einstein like unified field theory (UFT) are presented. Cosmic magnetic fields are obtained in terms of the early universe torsion and other stages of the universe. For example, in one of the metrics, integration of the 2-form torsion 0-component is written in terms of magnetic flux, from Faraday’s induced equation. These ideas were obtained from a recent paper we published [Class. Quantum Grav. (2015)] on non-stationary teleparallel metrics, where at coherent length of 10 kpc a magnetic field of [Formula: see text] Gauss is obtained. At early universe, a torsion of 1 MeV leads us to a magnetic field of the order of [Formula: see text] Gauss which is weaker than the Bierman battery effect magnetic field of the order of [Formula: see text] Gauss. Hence this new metric indicates that unifield theory metrics a la Schrödinger may be used to obtain primordial magnetic fields. Other tests of this metric led to the nowadays magnetic field of [Formula: see text] Gauss from the torsion at present universe (at the laboratory using dual maser obtained by Kostelecky et al. [Phys. Rev. Lett.]) of [Formula: see text] GeV. Cartan torsion has been frequently associated to topological defects in crystals or in pseudo-magnetic torsional fields. In this paper, we discuss how from teleparallel gravity one may obtain a theory of electromagnetism from metrics in spacetime. Topological defects given by Letelier [Class. Quantum Grav. 12 (1995) 1133] and Tod [Class. Quantum Grav. 11(5) (1994)] metrics can also be associated with pseudo-magnetic fields. Electromagnetism is geometrized via a bimetric theory of gravity where one metric is responsible for Ampere’s law and the other by the Faraday induction equation which gives rise to dynamo equation.

Universal dynamo paradigm for solar activity, Higgs fields and disasters

There is still a problem of a correct and accurate description of the dynamo and its uses in various fields of physics. To solve this problem, a special and universal representation of dynamo is proposed. The magnetic induction equation of dynamo is presented in the form of a Lienard relaxation oscillator with cubic nonlinear restoring force corresponding to the Mexican hat or champagne bottle potential which is used to determine the Higgs fields which are considered here in its general sense. Universal dynamo paradigm in field theory which can be used to describe disasters is proposed. Using solar activity as an example, it is shown how a dynamo induces a magnetic analogue of the Higgs fields with a broken symmetry of the magnetic field. Various dynamo modes are considered and different dynamo numbers are estimated. The dynamo effect can be used in field theory as an alternative to spontaneous symmetry breaking. Opportunities for the promotion of the new dynamo paradigm are discussed.

Estimation of Electrical Conductivity and Magnetization Parameter of Neutron Star Crusts and Applied to the High-Braking-Index Pulsar PSR J1640-4631

Young pulsars are thought to be highly magnetized neutron stars (NSs). The crustal magnetic field of a NS usually decays at different timescales in the forms of Hall drift and Ohmic dissipation. The magnetization parameter ω B τ is defined as the ratio of the Ohmic timescale τ O h m to the Hall drift timescale τ H a l l . During the first several million years, the inner temperature of the newly born neutron star cools from T = 10 9 K to T = 1.0 × 10 8 K, and the crustal conductivity increases by three orders of magnitude. In this work, we adopt a unified equations of state for cold non-accreting neutron stars with the Hartree–Fock–Bogoliubov method, developed by Pearson et al. (2018), and choose two fiducial dipole magnetic fields of B = 1.0 × 10 13 G and B = 1.0 × 10 14 G, four different temperatures, T, and two different impurity concentration parameters, Q, and then calculate the conductivity of the inner crust of NSs and give a general expression of magnetization parameter for young pulsars: ω B τ ≃ ( 1 − 50 ) B 0 / ( 10 13 G) by using numerical simulations. It was found when B ≤ 10 15 G, due to the quantum effects, the conductivity increases slightly with the increase in the magnetic field, the enhanced magnetic field has a small effect on the matter in the low-density regions of the crust, and almost has no influence the matter in the high-density regions. Then, we apply the general expression of the magnetization parameter to the high braking-index pulsar PSR J1640-4631. By combining the observed arrival time parameters of PSR J1640-4631 with the magnetic induction equation, we estimated the initial rotation period P 0 , the initial dipole magnetic field B 0 , the Ohm dissipation timescale τ O h m and Hall drift timescale τ H a l l . We model the magnetic field evolution and the braking-index evolution of the pulsar and compare the results with its observations. It is expected that the results of this paper can be applied to more young pulsars.

On the origin of magnetic driven winds and the structure of the galactic dynamo in isolated galaxies

ABSTRACT We investigate the build-up of the galactic dynamo and subsequently the origin of a magnetic driven outflow. We use a set-up of an isolated disc galaxy with a realistic circum-galactic medium (CGM). We find good agreement of the galactic dynamo with theoretical and observational predictions from the radial and toroidal components of the magnetic field as function of radius and disc scale height. We find several field reversals indicating dipole structure at early times and quadrupole structure at late times. Together with the magnetic pitch angle and the dynamo control parameters Rα, Rω, and D, we present strong evidence for an α2–Ω dynamo. The formation of a bar in the centre leads to further amplification of the magnetic field via adiabatic compression which subsequently drives an outflow. Due to the Parker instability the magnetic field lines rise to the edge of the disc, break out, and expand freely in the CGM driven by the magnetic pressure. Finally, we investigate the correlation between magnetic field and star formation rate. Globally, we find that the magnetic field is increasing as function of the star formation rate surface density with a slope between 0.3 and 0.45 in good agreement with predictions from theory and observations. Locally, we find that the magnetic field can decrease while star formation increases. We find that this effect is correlated with the diffusion of magnetic field from the spiral arms to the interarm regions which we explicitly include by solving the induction equation and accounting for non-linear terms.