Electrodynamics with magnetic monopoles: Photon wave mechanical theory

The quest for magnetic monopoles has captivated theoretical physicists due to their potential to reshape our understanding of electromagnetism. Despite extensive research, definitive mathematical proof of their existence remains elusive. This paper presents a rigorous mathematical framework supporting the existence of magnetic monopoles within the covariant formulation of classical electromagnetism and special relativity. Utilizing tensor calculus and the covariance form of Maxwell's equations, we derive expressions for magnetic charge density and magnetic current density through Lorentz transformations. Our approach emphasizes the expansion of tensorial equations, particularly focusing on the covariant derivatives of the electromagnetic field tensor and its dual. The results demonstrate the recovery of magnetic charge and current densities in Maxwell's equations, providing a theoretical foundation for the existence of magnetic monopoles. A magnetic monopole model is introduced, establishing the relationship between the electric field, the monopole’s magnetic charge, and their dependence on the observer's relative velocity as a direct consequence of the modified Gauss's law for magnetism. This model suggests the existence of dipole bosons—electric or magnetic—which function analogously to the Higgs boson. These dipole bosons are proposed to confer mass, charge, and spin to charged particles, whether they are electric or magnetic in nature.

Spatial distribution of magnetic field and persistent currents in Condon domain phase

Experimental and theoretical researches performed by the author (period: 1969-present) showed that magnetic spinor particles (magnetic charges) are real structural components of atoms and substance and immediate sources of all magnetic fields and magnetic manifestations in Nature. Magnetic charges, that constitute together with electrical charges atomic shells got of title: magnetons and antimagnetons (respectively with charges g− and g+ under fundamental condition: g = e). Furthermore, in addition to participating in structures of atomic shells, the magnetic charges exist in potential and even in real zones conduction of solids. The magnetic and electric spinor particles in atoms and substance exist in form such of the spinor associations as the magnetic and electric bispinors. Under influence of external magnetic field in conductor being implemented polarization of magnetic bispinors with formation of magnetic dipoles. Internal fields magnetic dipoles is directed against an external magnetic field and is a simple explanation of such a physical manifestation as diamagnetism. During the rotation of these dipoles in the conductor are formed of the vortex magnetic dipole fields, which and create an electromotive force, i.e. are responsible for the electromagnetic induction. Author proposed new magneto-electric technology called the magnetoelectric induction, as the result of which the permanent current of magnetic charges is created. However, such currents may be implemented solely in the superconductors. In the article presented the main reasons which more hundred year old hinder recognition and technical use of the real magnetic charges and their currents what considerably slow down the global scientific and technological progress.

A nonlinear force-free field is solely determined by the normal components of magnetic field and current density on the entire boundary of the domain. Methods using three components of magnetic field suffer from either overspecification of boundary conditions and/or a nonzero divergence B problem. A vector potential formulation eliminates the latter issue, yet poses difficulties in imposing normal components of both magnetic field and current density on the boundary. This challenge arises due to the inability to fix all three components of the vector potential at the boundary while the vector potential within the interior domain undergoes iterative changes. This paper explores four distinct boundary treatment approaches within the vector potential formulation. In two methods, the normal component of the vector potential is adjusted to satisfy the prescribed boundary-normal component of current density at each iteration, while the tangential components remain fixed throughout. In the other two methods, the tangential components of the vector potential are modified at each iteration, while the normal component remains fixed. Each group comprises both first-order and second-order boundary treatments. We conduct a comparative analysis of these methods against our established poloidal-toroidal formulation code and the optimization code in Solar Software. While none of the four methods outperform our poloidal-toroidal formulation code, they demonstrate comparable or superior performance compared to the latter. This research is regarded to provide insights into optimizing boundary conditions for data-driven simulations using vector potentials. 

We treat the problem of determining the magnetic sources that have been shown to come into existence when an electric charge density abruptly starts an arbitrary motion and hence an infinite speed of light becomes necessary for the satisfaction of the Lorenz condition for the scalar and vector potentials. The change that the Poynting theorem equation undergoes when an infinite speed of light constraint is enforced is the basis for the development and also use is made of the fact that the required magnetic and electric charge density functions share the same support and the same velocity in their motion. Reference to Green's functions in the source region is made to obtain the solution for the magnetic sources. The magnetic sources are computed to be in the form <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$m=Z\rho$</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\vec{M}=Z\vec{J}$</tex> where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$Z$</tex> is the wave impedance of the lossless, simple medium which can be vacuum. Also, the solution of Maxwell's equations incorporating the magnetic charge and current densities is given in terms of potentials with an infinite speed of propagation for the waves emitted by the charge functions. The magnetic scalar potential is a summation in the form of an integral of monopole moments. For <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$t &gt; 0$</tex> even though the resulting differential equations involve biharmonic operators, particular solutions of these equations are essentially solutions of Poisson's equations. When <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$t &gt; 0$</tex> the same Lorenz condition for the case with no magnetic sources appears also in this case with magnetic sources. The solutions for the potentials at <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$t=0$</tex> where the Lorenz condition fails are obtained using the Helmholtz theorem.

The explicit expression for the magnetic field, electric field, current density and charge density are presented in the transient superconducting system which has layered singularities. Time- and space-dependence of the magnetic field and the electric field in the superconductors with layered singularities to which external magnetic field is applied at t =0 is estimated by means of the computer calculation and the computer graphics.

Overview Having shown in Chapter 5 that the magnetic force must exist, we will now study the various properties of the magnetic field and show how it can be calculated for an arbitrary (steady) current distribution. The Lorentz force gives the total force on a charged particle as F = q E + q v × B . The results from the previous chapter give us the form of the magnetic field due to a long straight wire. This form leads to Ampere’s law , which relates the line integral of the magnetic field to the current enclosed by the integration loop. It turns out that Ampere’s law holds for a wire of any shape. When supplemented with a term involving changing electric fields, this law becomes one of Maxwell’s equations (as we will see in Chapter 9). The sources of magnetic fields are currents, in contrast with the sources of electric fields, which are charges; there are no isolated magnetic charges, or monopoles . This statement is another of Maxwell’s equations. As in the electric case, the magnetic field can be obtained from a potential, but it is now a vector potential ; its curl gives the magnetic field. The Biot–Savart law allows us to calculate (in principle) the magnetic field due to any steady current distribution. One distribution that comes up often is that of a solenoid (a coil of wire), whose field is (essentially) constant inside and zero outside. This field is consistent with an Ampere’s-law calculation of the discontinuity of B across a sheet of current. By considering various special cases, we derive the Lorentz transformations of the electric and magnetic fields. The electric (or magnetic) field in one frame depends on both the electric and magnetic fields in another frame. The Hall effect arises from the q v × B part of the Lorentz force. This effect allows us, for the first time, to determine the sign of the charge carriers in a current.

Stability of catheter-tissue contact in the robotic magnetic navigation (RMN) system is one of the key features that distinguishes this system from manually guided catheters. Numerous studies have shown that contact force (CF) in manually controlled catheters is as crucial for forming an optimal lesion as the duration of application or power. Catheters used in the RMN system lack a quantitative method for intraoperative monitoring of this parameter. Our study aims to partially address this gap in scientific knowledge. We conducted a total of 1200 CF measurements using the RMN system (Stereotaxis, St. Louis, MO, USA), a magnetic-guided 8 Fr RF ablation catheter (THERMOCOOL RMT Catheter, Biosense Webster, Irvine, CA, USA) inserted through a long sheath (SR0, Abbott Cardiovascular, Nathan Lane North, Plymouth, MN, USA), and a precision jewelry scale (IKEME, Guangdong, CN). We analyzed the impact on the obtained CF values of four different magnetic field vectors (transverse, sagittal, caudal, and cranial), two field strengths (0.1T and 0.08T), and three catheter extension configurations from the long sheath (with Position 1 being the least extended and Position 3 the most extended). The contact force values varied significantly across the different magnetic field vectors, field strengths, and catheter extensions from the vascular sheath. The greatest differences in achieved values were observed across the different magnetic field vectors in the Position 1, ranging from 3.52 ± 0.1 g (caudal plane) to 15.15 ± 0.05 g (cranial plane) at 0.08 Tesla (T) field strength (p < 0.001), and from 4.10 ± 0.06 g (caudal) to 15.01 ± 0.07 g (cranial) at 0.1 T, p < 0.001. Differences in other vectors reached approximately 20%. The highest CF values were obtained in Position 1, intermediate values in Position 2, and the lowest in Position 3. An exception was the transverse vector, where, particularly with a magnetic field of 0.1 T, more similar values were observed across Positions 1-3, with respective values of 8.61 ± 0.14 g, 9.36 ± 0.06 g, and 8.31 ± 0.05 g. A stronger magnetic field (0.1 T compared to 0.08 T) resulted in higher CF values, especially during measurements in the transverse vector. This effect was most pronounced in the most extended catheter from the sheath - Position 3 (with respective values of 4.54 ± 0.09 g vs. 8.31 ± 0.05 g, p < 0.001). In the sagittal, cranial, and caudal vectors, the differences were less noticeable. Different magnetic field vectors, catheter extensions from the sheath, and magnetic field strengths result in varying contact force values. For effective radiofrequency ablation lesions, these factors should be considered alongside power, duration, and other established parameters.

This paper presents a systematic review of modeling approaches for magnetic materials using the Partial Element Equivalent Circuit (PEEC) formulation, with particular emphasis on comparing equivalent physical models, system equations, and numerical characteristics. Based on the Coulombian-PEEC (C-PEEC) formulation, we conduct a comprehensive comparative analysis of the system matrix's convergence behavior across three discretized magnetic source representations: magnetization current density, magnetic flux density, and magnetic field. The comparison of numerical results shows that among these three discrete strategies, using magnetization current density as the equivalent source can significantly improve the condition number of the system matrix and enhance the numerical stability of the solution.

view Abstract Citations References Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS The magnetic versus the gravitational field in a homogeneous, incompressible, pulsating sphere of infinite conductivity. Sen, Hari K. Abstract In the present paper, we have considered the meridional oscillations of Ferraro's model 1 of a homogeneous, incompressible spherical star of infinite conductivity in a central, monopole magnetic field, taking into account gravitational forces.2 This has led us to a modification of one of the boundary conditions used by Schwarzschild,3 Ferraro and Memory,1 for the purely magnetic oscillations, viz., that the pressure variation at the undisturbed surface of the star will not vanish but will be equal to the amount of matter supported after the oscillatory distortion. This pressure variation is of the same order as the radial amplitude of the oscillation and was correctly obtained by Miss Gjellestad4 in a paper in which she considered the gravitational oscillations of the Schwarzschild model. To estimate the comparative roles of the magnetic and the gravitational fields, we have considered, in particular, two limiting cases, viz., of small and large magnetic fields. For small fields we have used a perturbation method in which the non-dimensional constant 82 = H82/4irpX2a2 appears as a parameter; a is the radial distance from the center of an internal point in the star, H8 is the surface value of the permanent magnetic field, and 2ir/X is the periodic time of the harmonic vibrations of the star. For Babcock's star ~ (HD 125248), 82 ~ I0-~. To the first order in 82 we find that oscillations with the gravitational period only are possible and that it is necessary to postulate the existence of surface currents. For very large magnetic fields (82 oc) we find imaginary values for X, indicating either a building up or damping of the oscillation. Physically, the action of the magnetic field would be to damp rather than build up oscillations, and therefore we conclude that in our idealized case of infinite magnetic field the sphere has no (finite) period of oscillation. Ferraro S series solutions are poorly convergent for intermediate and large values of the variable. We have therefore used asymptotic series expansions of the solutions for intermediate magnetic fields and find again that no oscillations can exist except gravitational ones with surface currents. We conclude that no meridional oscillations are possible for the Ferraro model of a homogeneous, incompressible, spherical star of infinite conductivity in a central, monopole magnetic field, except the gravitational ones with surface currents. Miss Gjellestad4 reached a similar conclusion for Schwarzschild's model. The result seems to be independent of the model and may very well be true for any initial distribution of density and magnetic field. Further, it is hard to believe that non-meridional oscillations would occur in the absence of meridional ones. An investigation will be worth while on whether the negative result obtained in this paper is due to the assumption of infinite conductivity that inhibits any motion across the lines of magnetic force. Treatment of a reasonably simple model of finite conductivity and derivation of the asymptotic behavior of the model when the conductivity increases without limit will provide a most useful check. I.Ferraro and Memory, M. N. 112, 361, 1952. 2.Cf. Cowling, M. N. 112, 527, 1952. 3.Ann. Astroph. 12, 148, 1949. 4.Ann. Astroph. 15, 276, 1952. 5.Ap. J. "4, 1, 1951. National Bureau of Standards, Washington, D. C. Publication: The Astronomical Journal Pub Date: 1953 DOI: 10.1086/106904 Bibcode: 1953AJ.....58Q.227S full text sources ADS |

When magnetic monopoles are assumed to exist in plasma dynamics, the propagation of electromagnetic waves is modified as Maxwell equations acquire a symmetrical structure due to the existence of electric and magnetic charge and current densities. This work presents a theoretical exploration on how far we can push the limits of a plasma theory under the presence of magnetic monopoles. In particular, we study the modification of ponderomotive forces in a plasma composed by electric and magnetic charges. We show that the general ponderomotive force on this plasma depends non-trivially on the magnetic monopoles, through the slow temporal and spatial variations of the electromagnetic field amplitudes. The magnetic charges introduce corrections even if the plasma is unmagnetized. Also, it is shown that the magnetic monopoles also experience a ponderomotive force due to the electrons. This force is in the direction of propagation of the electromagnetic waves.

Helicity $H$, chirality $C$, and spin angular momentum $\mathbf{S}$ are three physical observables that play an important role in the study of optical fields. These quantities are closely related, but their connection is hidden by the use of four different vector fields for their representation, namely, the electric and magnetic fields $\mathbf{E}$ and $\mathbf{B}$, and the two transverse potential vectors $\mathbf{C}^\perp$ and $\mathbf{A}^\perp$. Helmholtz's decomposition theorem restricted to solenoidal vector fields, entails the introduction of a bona fide inverse curl operator, which permits one to express the above three quantities in terms of the observable electric and magnetic fields only. This yields clear expressions for $H, C$, and $\mathbf{S}$, which are automatically gauge-invariant and display electric-magnetic democracy.

The hydrodynamic theory of surface wave propagation in semi-infinite homogeneous isotropic plasma is considered. Explicit linear surface wave solutions are given for the electric and magnetic fields, charge and current densities. These solutions are used to obtain the well-known dispersion relations and, together with the general energy conservation equation, to find appropriate definitions for the energy and the energy flow densities of surface waves. These densities are associated with the dispersion relation and the group velocity by formulae similar to those for bulk waves in infinite plasmas. Both cases of high-frequency (HF) and low-frequency (LF) surface waves are considered.

Numerical methods for solving the ideal magnetohydrodynamic (MHD) equations in more than one space dimension must confront the challenge of controlling errors in the discrete divergence of the magnetic field. One approach that has been shown successful in stabilizing MHD calculations are constrained-transport (CT) schemes. CT schemes can be viewed as predictor-corrector methods for updating the magnetic field, where a magnetic field value is first predicted by a method that does not exactly preserve the divergence-free condition on the magnetic field, followed by a correction step that aims to control these divergence errors. In Helzel, Rossmanith, and Taetz [J. Comput. Phys., 230 (2011), pp. 3803--3829] the authors presented an unstaggered CT method for the MHD equations on three-dimensional Cartesian grids. In this approach an evolution equation for the magnetic potential is solved during each time step and a divergence-free update of the magnetic field is computed by taking the curl of the magnetic potential. The evolution equation for the vector potential is only weakly hyperbolic, which requires special numerical treatment. A key step in this method is the use of dimensional splitting in order to overcome these difficulties. In this work we generalize the method of Helzel, Rossmanith, and Taetz [J. Comput. Phys., 230 (2011), pp. 3803--3829] in three important ways: (1) we remove the need for operator splitting by switching to an appropriate method of lines discretization and coupling this with a nonconservative finite volume method for the magnetic vector potential equation; (2) we increase the spatial and temporal order of accuracy of the entire method to third order; and (3) we develop the method so that it is applicable on both Cartesian and logically rectangular mapped grids. The method-of-lines approach that is used in this work is based on a third-order accurate finite volume discretization in space coupled to a third-order strong stability preserving Runge--Kutta time-stepping method. The evolution equation for the magnetic vector potential is solved using a nonconservative finite volume method based on the approach of Castro et al. [Math. Comput., 79 (2010), pp. 1427--1472]. The curl of the magnetic potential is computed via a third-order accurate discrete operator that is derived from appropriate application of the divergence theorem and subsequent numerical quadrature on element faces. Special artificial resistivity limiters are used to control unphysical oscillations in the magnetic potential and field components across shocks. Several test computations are shown that confirm third-order accuracy for smooth test problems and high resolution for test problems with shock waves.

In this exploration, it is revealed for the first time that the full magnetic field gradient and current density distribution can be derived from two spacecraft magnetic field measurements under the assumptions that the magnetic field is approximately stationary and force‐free, conditions which are particularly relevant to low altitude regions of the Earth's magnetosphere and in the regions containing the field aligned current systems. The magnetic field gradients along the spacecraft line, spacecraft velocity direction and the normal direction can be defined so that the full magnetic field gradient tensor is determined, projected into any coordinate system. One test for an ideal situation has been made, which confirms the validity of this approach with very high accuracy. This method can be applied to the determination of the magnetic field gradient tensor and current density for the forthcoming multispacecraft Swarm mission.