Magnetic fields from phase transitions

In this paper two examples of the generation cosmological magnetic fields (CMF) are given. The first is the string dynamo seed cosmological magnetic field estimated as Bseed∼10-24 Gauss from a static spin polarised cylinder in Einstein-Cartan-Maxwell spacetime. The string dynamo seeds from a static spin polarised cylinder is given by B∼σ2R2 where σ is the spin-torsion density while R is the string radius. The B-field value above is able to seed galactic dynamo. In the BBN the magnetic fields around 1012 Gauss give rise to a string radius as small as 1017lP where lP is the Planck length. The second is the CMF from axionic torsion field which is given by Bseed∼10-27 Gauss which is stronger than the primordial magnetic field BBICEP2∼10-30 Gauss from the BICEP2 recent experiment on primordial gravitational waves and cosmological inflation to axionic torsion. The interaction Lagrangean between axionic torsion scalar ϕ and magnetic fields used in this last example is given by f2(ϕ)FμνFμν. A similar lagrangean has been used by K. Bamba et al. [JCAP 10 (2012) 058] so generate magnetic fields without dynamo action. Since axionic torsion can be associated with axionic domain walls both examples discussed here could be consider as topological defects examples of the generation of primordial magnetic fields in universes endowed with spacetime torsion.

We study the generation of magnetic fields during the stage of particle\nproduction resulting from spinodal instabilities during phase transitions out\nof equilibrium. The main premise is that long-wavelength instabilities that\ndrive the phase transition lead to strong non-equilibrium charge and current\nfluctuations which generate electromagnetic fields. We present a formulation\nbased on the non-equilibrium Schwinger-Dyson equations that leads to an exact\nexpression for the spectrum of electromagnetic fields valid for general\ntheories and cosmological backgrounds and whose main ingredient is the\ntransverse photon polarization out of equilibrium. This formulation includes\nthe dissipative effects of the conductivity in the medium. As a prelude to\ncosmology we study magnetogenesis in Minkowski space-time in a theory of N\ncharged scalar fields to lowest order in the gauge coupling and to leading\norder in the large N within two scenarios of cosmological relevance. The\nlong-wavelength power spectrum for electric and magnetic fields at the end of\nthe phase transition is obtained explicitly.\n It follows that equipartition between electric and magnetic fields does not\nhold out of equilibrium. In the case of a transition from a high temperature\nphase, the conductivity of the medium severely hinders the generation of\nmagnetic fields, however the magnetic fields generated are correlated on scales\nof the order of the domain size, which is much larger than the magnetic\ndiffusion length. Implications of the results to cosmological phase transitions\ndriven by spinodal unstabilities are discussed.\n

It is generally accepted that the magnetic fields of planets and stars are produced by the self-exciting dynamo process (first proposed by Larmor) and that observed near-alignments of magnetic dipole axes with rotation axes are due to the influence of Coriolis forces on underlying fluid motions. The detailed role of rotation in the generation of cosmical magnetic fields has yet to be elucidated but useful insight can be obtained from general considerations of the governing magnetohydrodynamic equations. A magnetic field B cannot be maintained or amplified by fluid motion u against the effects of ohmic decay unless (a) the magnetic Reynolds number R = ULno is sufficiently large, and (b) the patterns of B and u are sufficiently complicated (where U is a characteristic flow speed, a characteristic length and J and o are typical values of the magnetic permeability and electrical conductivity respectively). Axisymmetric magnetic fields will always decay (a result that suggests that palaeomagnetic and archaeomagnetic data might show evidence that departures from axial symmetry in the geomagnetic field are systematically less during the decay phase of a polarity ‘ reversal ’ or * excursion ’ than during the recovery phase). Dynamo action is stimulated by Coriolis forces, which promote departures from axial symmetry in the pattern of uwhen B is weak, and is opposed by Lorentz forces, which increase in influence as B grows in strength. If equilibrium is attained when Coriolis and Lorentz forces are roughly equal in magnitude then the system becomes ‘ magnetostrophic' and the strengths of the internal and external parts of the field, and respectively, satisfy B i < B 8 R 1/2 and B e < B 8 R -1/2 if B 8 = UL~1 *X)/c f)i » (p being the mean density of the fluid and Q the angular speed of rotation). The slow and dispersive ‘magnetohydrodynamic inertial wave’ with a frequency that depends on the square of the Alfven speed [B]/(up) 1/2 and inversely on Q exemplifies magnetostrophic flow. Such waves probably occur in the electrically conducting fluid interiors of planets and stars, where they play an important role in the generation of magnetic fields as well as in other processes, such as the topographic coupling between the Earth’s liquid core and solid mantle.

Primordial magnetic fields (PMFs) can seed additional small-scale matter fluctuations, leading to the formation of dense, early-collapsing dark matter structures known as minihalos. These minihalos may dramatically amplify the dark matter annihilation signal if dark matter is composed of self-annihilating thermal relic particles such as WIMPs. In this work, we analyse the annihilation signal from minihalos with prompt central cusps, \rho \propto r^{-3/2} ρ ∝ r − 3 / 2 , formed due to the enhanced power spectrum induced by PMFs, using gamma-ray observations of the Virgo cluster. We consider benchmarks motivated by cosmological phase transitions, focusing in particular on the electroweak and QCD transitions, where we assume maximal magnetic energy density and horizon-sized coherence length at generation (upper-limit scenarios). In addition, we include a data-driven case corresponding to the best-fit present-day PMF amplitude inferred from DESI BAO and Planck CMB measurements. Under these assumptions, we find that PMFs can place stringent bounds on WIMP annihilation. Magnetic fields with amplitudes matching the DESI–Planck best-fit values are in strong tension with self-annihilating WIMPs across a wide mass range extending beyond the () scale, while the electroweak- and QCD-phase-transition toy-model benchmarks would exclude thermal relics with masses below 300\,\mathrm{GeV} 300 G e V and 3\,\mathrm{TeV} 3 T e V , respectively. Although weaker PMFs would yield weaker annihilation signals, our results demonstrate that whenever PMFs enhance small-scale structure, indirect-detection limits on dark matter must be revisited.

We investigate primordial magnetogenesis within a quantum bouncing model driven by a scalar field, focusing on various non-minimal couplings between the electromagnetic field and the scalar field. We test three cases: no coupling, a Cauchy coupling with gradual decay, and a Gaussian coupling with rapid fall-off. By exploring these scenarios, we assess a wide range of coupling strengths across different scales. The scalar field, with an exponential potential, behaves as pressureless matter in the asymptotic past of the contracting phase, as stiff matter around the bounce, and as dark energy during the expanding phase. Our findings reveal that, among the tested cases, only the Gaussian coupling can explain the generation of primordial magnetic fields on cosmological scales.

We consider dynamo action under the combined influence of turbulence and large-scale shear in sheared jets. Shear can stretch turbulent magnetic field lines in such a way that even turbulent motions showing mirror symmetry become suitable for generation of a large-scale magnetic field. We derive the integral induction equation governing the behaviour of the mean field in jets. The main result is that sheared jets may generate a large-scale magnetic field if shear is sufficiently strong. The generated mean field is mainly concentrated in a magnetic sheath surrounding the central region of a jet, and it exhibits sign reversals in the direction of the jet axis. Typically, the magnetic field in a sheath is dominated by the component along the jet that can reach equipartition with the kinetic energy of particles. The field in the central region of jets has a more disordered structure.

We present results of analytical studies and 2D3V PIC simulations of electron-positron plasma cloud collisions. We concentrate on the problem of quasi-static magnetic field generation. It is shown from linear theory, using relativistic two-fluid equations for electron-positron plasmas, that the generation of a quasi-static magnetic field can be associated with the counter-streaming instability. A two-dimensional relativistic particle simulation provides good agreement with the above linear theory and that, in the nonlinear stage of the instability, about 5.3 % of the initial plasma flow energy can be converted to magnetic field energy. It is also shown from the simulation that the quasi-static magnetic field undergoes a collision-less change of structure, leading to large scale, long living structures and the production of high-energy particles. These processes may be important for understanding of production of high-energy particles in the region where two pulsar winds collide.

The generation of a quasistationary magnetic field in a plasma interacting with a weakly focused low-intensity short laser pulse has been studied. It has been shown that the magnetic field changes direction at times comparable with the free path time of effective electrons. Generation also occurs after the switching off of the short pulse and the maximum field is proportional to the duration of the pulse and is reached at times larger than the free path time of the suprathermal electrons.

By using a two-dimensional (2D) relativistic fully electromagnetic particle-in-cell code, the interaction process of counterstreaming pair (electron–positron) plasmas is investigated. The counterstreaming plasmas become unstable against the collisionless electromagnetic counterstreaming instability, similar to the Weibel instability. In the linear phase, magnetic and electric fields with the scale of skin depth size are generated through the electromagnetic counterstreaming instability. The behavior of plasma in the nonlinear phase is also made clear. The small-scale magnetic fields coalesce with each other, merging through the inverse cascade process which occurs characteristically in 2D dynamics, and change into larger unit. The large-scale magnetic fields propagate more slowly than the initial plasma flow as a low-frequency wave. Behind the magnetic fields, plasmas are isotropically heated by the mixing of counterstreaming plasmas. On the other hand, the electric fields propagate the same as the initial plasma flow. Ahead of the generated magnetic fields, the electric field component along the stream is amplified through the electrostatic counterstreaming instability and the electrostatic shock waves are formed. High-energy particles are also produced from the electrostatic shocks. These simulation results may be applied to the synchrotron gamma-ray burst model.

Using the boundary-layer equations as a basis, the author considers the propagation of plane jets of conducting fluid in a transverse magnetic field (noninductive approximation). The propagation of plane jets of conducting fluid is considered in several studies [1–12]. In the first few studies jet flow in a nonuniform magnetic field is considered; here the field strength distribution along the jet axis was chosen in order to obtain self-similar solutions. The solution to such a problem given a constant conductivity of the medium is given in [1–3] for a free jet and in [4] for a semibounded jet; reference [5] contains a solution to the problem of a free jet allowing for the dependence of conductivity on temperature. References [6–8] attempt an exact solution to the problem of jet propagation in any magnetic field. An approximate solution to problems of this type can be obtained by using the integral method. References [9–10] contain the solution obtained by this method for a free jet propagating in a uniform magnetic field. The last study [10] also gives a comparison of the exact solution obtained in [3] with the solution obtained by the integral method using as an example the propagation of a jet in a nonuniform magnetic field. It is shown that for scale values of the jet velocity and thickness the integral method yields almost-exact values. In this study [10], the propagation of a free jet is considered allowing for conduction anisotropy. The solution to the problem of a free jet within the asymptotic boundary layer is obtained in [1] by applying the expansion method to the small magnetic-interaction parameter. With this method, the problem of a turbulent jet is considered in terms of the Prandtl scheme. The Boussinesq formula for the turbulent-viscosity coefficient is used in [12]. This study considers the dynamic and thermal problems involved with a laminar free and semibounded jet within the asymptotic boundary layer, propagating in a magnetic field with any distribution. A system of ordinary differential equations and the integral condition are obtained from the initial partial differential equations. The solution of the derived equations is illustrated by the example of jet propagation in a uniform magnetic field. A similar solution is obtained for a turbulent free jet with the turbulent-exchange coefficient defined by the Prandtl scheme.

Generation of extremely-low frequency magnetic fields with standard available commercial equipment: Implications for experimental bioelectromagnetics work

We calculate the gravitational wave spectrum generated by sound waves during a cosmological phase transition, incorporating several advancements beyond the current state-of-the-art. Rather than relying on the bag model or similar approximations, we derive the equation of state directly from the effective potential. This approach enables us to accurately determine the hydrodynamic quantities, which serve as initial conditions in a generalised hybrid simulation. This simulation tracks the fluid evolution after bubble collisions, leading to the generation of gravitational waves. Our work thus provides a self-consistent numerical calculation of gravitational waves for the real singlet extension of the standard model. Our computational method is adaptable to any particle physics model, offering a fast and reliable way to calculate gravitational waves generated by sound waves. With fewer approximations, our approach provides a robust foundation for precise gravitational wave calculations and allows for the exploration of model-independent features of gravitational waves from phase transitions.

Transition from research to application requires understanding of the basic behavior of transducers, field generators, and in particular, the magnetization process, domain dynamics, and polarization switching of ME effects to applied electric or magnetic fields. The CME (converse magnetoelectric) effect is investigated for the first time here in the context of three different multiferroic heterostructures with the goal of promoting their application in devices, such as transducers, sensors, and field generators. This investigation demonstrates experimentally and theoretically that tuning of magnetic properties of the heterostructures can be controlled through applied electric field. Significant CME effect is found in all three heterostructures: FeCoV/PZN-PT (31 Oe cm kV-1), Metglas/PMN-PT (23 Oe cm kV-1), and FeGa/PMN-PT (12.5 Oe cm kV-1). The tunabilities of remanence (Mr), coercivity (Hc), and squareness (SQ = Mr / Ms) are demonstrated. A sensitive dependence of CME effect on the magnitude of the applied electric field is discovered in the time and frequency domains, especially near the electric coercive field, and an alternative path to magnetization reversal is identified. The change in sign of magnetization is shown in the vicinity of magnetic coercivity. Tuning of induced magnetic fringe field (4.5 Oe cm kV-1) is shown for the FeGa/PMN-PT heterostructure, which could be used as a magnetic field generator. Results of low temperature characteristics of magnetization and magnetostriction of a novel terbium-doped FeGa alloy show this material can be applied to actuators and sensors requiring operability in wide temperature ranges. Indirect electric-field tuning can also be applied to patch antennas with a dielectric substrate. A novel low-profile (λ0/17) rectangular patch antenna with a corrugated metallization layer is designed here using a genetic algorithm optimization. The reflection coefficient of the simulated antenna is replicated using an antenna fabricated based on the optimized model. The morphology of the corrugated layer is shown to induce coupling modes in the antenna, which can in turn result in the enhancement and tuning of transverse magnetic mode resonances. This antenna prototype provides a cheaper and lighter alternative to existing planar patch antennas with magnetic substrates.

The dynamics of five dimensional Wilson line phases at finite temperature is studied in the one-loop approximation. We show that at temperatures of order T \sim 1/L, where L is the length of the compact space, the gauge symmetry is always restored and the electroweak phase transition appears to be of first order. Particular attention is devoted to the study of a recently proposed five dimensional orbifold model (on S1/Z2) where the Wilson line phase is identified with the Higgs field (gauge-Higgs unification). Interestingly enough, an estimate of the leading higher-loop ``daisy'' (or ``ring'') diagram contributions to the effective potential in a simple five dimensional model, seems to suggest that the electroweak phase transition can be studied in perturbation theory even for Higgs masses above the current experimental limit of 114 GeV. The transition is still of first order for such values of the Higgs mass. If large localized gauge kinetic terms are present, the transition might be strong enough to give baryogenesis at the electroweak transition.

Multi-field synergistic regulation enhanced multicaloric effect in all-d-metal Ni37Co13Mn35Ti15 alloy