arXiv subjects

Hanno Essen

Publications and source records attributed to Hanno Essen.

18 recordsLinked to original sources

arXiv2013

Circulating electrons, superconductivity, and the Darwin-Breit interaction

The importance of the Darwin-Breit interaction between electrons in solids at low temperatures is investigated. The model problem of particles on a circle is used and applied to mesoscopic metal rings in their normal state. The London moment formula for a rotating superconducting sphere is used to calculate the number, $N$, of superconducting electrons on the sphere. This number is found to be three times the radius, $R$, of the sphere divided by the classical electron radius, i.e.\ $N=3R/r_{\rm e}$. The Darwin-Breit interaction gives a natural explanation for this relation from first principles. It also is capable of electron pairing. Collective effects of this interaction require a minimum of two dimensions but electron pairing is enhanced in one-dimensional systems.

cond-mat.supr-con↗

arXiv2013

The Darwin-Breit magnetic interaction and superconductivity

A number of facts indicating the relevance of the Darwin magnetic interaction energy in the superconducting phase are pointed out. The magnetic interaction term derived by Darwin is the same as the, so called, Breit term in relativistic quantum mechanics. While this term always is a small perturbation in few body systems it can be shown to be potentially dominating in systems of large numbers of electrons. It is therefore a natural candidate in the explanation of emergent phenomena---phenomena that only occur in sufficiently large systems. The dimensionless parameter that indicates the importance of the magnetic energy is the number of electrons times the classical electron radius divided by the size of the system. The number of electrons involved are only the electrons at the Fermi surface; electrons with lower energy cannot contribute to current density and thus not to the magnetic field. The conventional understanding of superconductivity has always been problematic and no really reductionistic derivation exists. The idea that the inductive inertia, due to magnetism, is important in the explanation of superconductivity was first advanced by Frenkel and later brought up by Welker before it was prematurely discarded. So were theories involving Wigner crystallization. We speculate that the answer requires the combination of a Wigner lattice and the Darwin interaction. We point out that the Darwin interaction can be shown to have the right order of magnitude to explain the energy scales involved in normal superconductors. The London magnetic moment of rotating superconductors and the Meissner effect and their connection are discussed next. The London moment is shown to indicate that the number of electrons involved in the superconducting condensate is such that the Darwin interaction cannot be neglected.

physics.gen-ph↗

arXiv2012

Mechanics, cosmology and Mach's principle

It is pointed out that recent cosmological findings seem to support the view that the mass/energy distribution of the universe defines the Newtonian inertial frames as originally suggested by Mach. The background concepts of inertial frame, Newton's second law, and fictitious forces are clarified. A precise definition of Mach's principle is suggested. Then an approximation to general relativity discovered by Einstein, Infeld, and Hoffmann is used and it is found that this precise formulation of Mach's principle is realized provided the mass/energy density of the universe has a specific value. This value turns out to be twice the critical density. The implications of this approximate result is put into context.

physics.class-ph↗

arXiv2011

Meissner effect, diamagnetism, and classical physics - a review

We review the literature on what classical physics has to say about the Meissner effect and the London equations. We first discuss the relevance of the Bohr-van Leeuwen theorem for the perfect diamagnetism of superconductors. The conclusion is that the theorem is based on assumptions that are not valid. We also point out results in the literature which prove that the magnetic flux expulsion from a sample cooled to superconductivity can be simply understood as an approach to the magnetostatic energy minimum. These results have been published several times but still many textbooks on magnetism claim that there is no classical diamagnetism, and virtually all books on superconductivity repeat Meissner's 1933 statement that flux expulsion has no classical explanation.

physics.class-ph↗

arXiv2011

Classical diamagnetism, magnetic interaction energies, and repulsive forces in magnetized plasmas

The Bohr-van Leeuwen theorem is often summarized as saying that there is no classical magnetic susceptibility, in particular no diamagnetism. This is seriously misleading. The theorem assumes position dependent interactions but this is not required by classical physics. Since the work of Darwin in 1920 it has been known that the magnetism due to classical charged point particles can only be described by allowing velocity dependent interactions in the Lagrangian. Legendre transformation to an approximate Hamiltonian can give an estimate of the Darwin diamagnetism for a system of charged point particles. Comparison with experiment, however, requires knowledge of the number of classically behaving electrons in the sample. A new repulsive effective many-body force, which should be relevant in plasmas, is predicted by the Hamiltonian.

physics.class-ph↗

arXiv2010

The comfortable roller coaster -- on the shape of tracks with constant normal force

A particle that moves along a smooth track in a vertical plane is influenced by two forces: gravity and normal force. The force experienced by roller coaster riders is the normal force, so a natural question to ask is: what shape of the track gives a normal force of constant magnitude? Here we solve this problem. It turns out that the solution is related to the Kepler problem; the trajectories in velocity space are conic sections.

math-ph↗

arXiv2010

Magnetic dynamics of simple collective modes in a two-sphere plasma model

A plasma blob is modeled as consisting of two homogeneous spheres of equal radius and equal but opposite charge densities that can move relative to each other. Relative translational and rotational motion are considered separately. Magnetic effects from the current density caused by the relative motion are included. Magnetic interaction is seen to cause an inductive inertia. In the relative translation case the Coulomb attraction, approximately a linear force for small amplitudes, causes an oscillation. For a large number of particles the corresponding oscillation frequency will not be the Langmuir plasma frequency, because of the large inductive inertia. For rotation an external magnetic field is included and the energy and diamagnetism of the plasma in the model is calculated. Finally it is noted how the neglect of resistivity is motivated by the results.

physics.plasm-ph↗

arXiv2010

New theorem of classical electromagnetism: equilibrium magnetic field and current density are zero inside ideal conductors

We prove a theorem on the magnetic energy minimum in a system of perfect, or ideal, conductors. It is analogous to Thomson's theorem on the equilibrium electric field and charge distribution in a system of conductors. We first prove Thomson's theorem using a variational principle. Our new theorem is then derived by similar methods. We find that magnetic energy is minimized when the current distribution is a surface current density with zero interior magnetic field; perfect conductors are perfectly diamagnetic. The results agree with currents in superconductors being confined near the surface. The theorem implies a generalized force that expels current and magnetic field from the interior of a conductor that loses its resistivity. Examples of solutions that obey the theorem are presented.

physics.class-ph↗

arXiv2010

Static deformation of heavy spring due to gravity and centrifugal force

The static equilibrium deformation of a heavy spring due to its own weight is calculated for two cases. First for a spring hanging in a constant gravitational field, then for a spring which is at rest in a rotating system where it is stretched by the centrifugal force. Two different models are considered. First a discrete model assuming a finite number of point masses connected by springs of negligible weight. Then the continuum limit of this model. In the second case the differential equation for the deformation is obtained by demanding that the potential energy is minimized. In this way a simple application of the variational calculus is obtained.

physics.class-ph↗

arXiv2009

Minimum magnetic energy theorem predicts Meissner effect in perfect conductors

A theorem on the magnetic energy minimum in a perfect, or ideal, conductor is proved. Contrary to conventional wisdom the theorem provides a classical explanation of the expulsion of a magnetic field from the interior of a conductor that loses its resistivity. It is analogous to Thomson's theorem which states that static charge distributions in conductors are surface charge densities at constant potential since these have minimum energy. This theorem is proved here using a variational principle. Then an analogous result for the magnetic energy of current distributions is proved: magnetic energy is minimized when the current distribution is a surface current density with zero interior magnetic field. The result agrees with currents in superconductors being confined near the surface and indicates that the distinction between superconductors and hypothetical perfect conductors is artificial.

cond-mat.supr-con↗

arXiv2009

From least action in electrodynamics to magnetomechanical energy -- a review

The equations of motion for electromechanical systems are traced back to the fundamental Lagrangian of particles and electromagnetic fields, via the Darwin Lagrangian. When dissipative forces can be neglected the systems are conservative and one can study them in a Hamiltonian formalism. The central concepts of generalized capacitance and inductance coefficients are introduced and explained. The problem of gauge independence of self-inductance is considered. Our main interest is in magnetomechanics, i.e. the study of systems where there is exchange between mechanical and magnetic energy. This throws light on the concept of magnetic energy, which according to the literature has confusing and peculiar properties. We apply the theory to a few simple examples: the extension of a circular current loop, the force between parallel wires, interacting circular current loops, and the rail gun. These show that the Hamiltonian, phase space, form of magnetic energy has the usual property that an equilibrium configuration corresponds to an energy minimum.

physics.class-ph↗

arXiv2008

On the nature of the plasma equilibrium

We calculate the energy of a homogeneous one component plasma and find that the energy is lower for correlated motions of the particles as compared to uncorrelated motion. Our starting point is the conserved approximately relativistic (Darwin) energy for a system of electromagnetically interacting particles that arises from the neglect of radiation. For the idealized model of a homogeneous one component plasma the energy only depends on the particle canonical momenta and the vector potential. The vector potential is then calculated in terms of the canonical momenta using recent theoretical advances and the plasma Hamiltonian is obtained. The result can be understood either as due to the energy lowering caused by the attraction of parallel currents or, alternatively, as due to the inductive inertia associated with the flow of net current.

physics.plasm-ph↗

arXiv2007

The exact Darwin Lagrangian

Darwin (1920) noted that when radiation can be neglected it should be possible to eliminate the radiation degrees-of-freedom from the action of classical electrodynamics and keep the discrete particle degrees-of-freedom only. Darwin derived his well known Lagrangian by series expansion in $v/c$ keeping terms up to order $(v/c)^2$. Since radiation is due to acceleration the assumption of low speed should not be necessary. A Lagrangian is suggested that neglects radiation without assuming low speed. It cures deficiencies of the Darwin Lagrangian in the ultra-relativistic regime.

physics.plasm-ph↗

arXiv2007

Electrostatic interaction energies of homogeneous cubic charge distributions

The starting point is the problem of finding the interaction energy of two coinciding homogeneous cubic charge distributions. The brute force method of subdividing the cube into $N^3$ sub-cubes and doing the sums results in slow convergence because of the Coulomb singularity. Using symmetry and algebra the Coulomb singularities can be eliminated. This leads to an accurate numerical algorithm as well as an interesting exact result relating the desired interaction energy to three other interaction energies, namely those of cubes touching each other at a face, at an edge, and at a corner, respectively. As an application a simple model illustrating Wigner crystallization is presented.

physics.atm-clus↗

arXiv2006

Catalyzing Fusion with Relativistic Electrons

The idea here is to use large relative velocities of electrons and nuclei in accelerator beams to increase the probability of fusion. The function of the electrons is to both screen the positive charge and to produce an increased parallel pinching current. The increase in reaction probability is estimated using the Darwin magnetic interaction energy approach.

physics.plasm-ph↗

arXiv2004

Connection between London moment and Meissner effect from classical electrodynamics

Theory and experiment on the London moment is reviewed. A simple mathematical model is motivated and then used to study the responses of a spherical superconductor to an external field and to rotation. It reveals a connection between perfect diamagnetism (Meissner effect) and the London moment. In the model neither of these are exact but the deviation from B=0 internal field in the former and from $B=(2mc/e)Ω$ in the latter case is described by the same dimensionless parameter. Apart from its pedagogical values the model might throw some light on the controversy surrounding the correction to the London moment.

cond-mat.supr-con↗

arXiv2004

The physics of rotational flattening and the point core model

A point mass at the center of an ellipsoidal homogeneous fluid is used as a simple model to study the effect of rotation on the shape and external gravitational field of planets and stars. Maclaurin's analytical result for a homogenous body is generalized to this model. The absence of a third order term in the Taylor expansion of the Maclaurin function leads to further simple but very accurate analytical results connecting the three observables: oblateness ($ε$), gravitational quadrupole ($J_{2}$), and angular velocity parameter ($q$). These are compared to observational data for the planets. The moments of inertia of the planets are calculated and compared to published values. The oblateness of the Sun is estimated. Oscillations near equilibrium are studied within the model.

astro-ph↗

arXiv2003

The pushing force of a propagating electromagnetic wave

The effect of the electrodynamic forces on a charged particle in a propagating plane electromagnetic wave is investigated. First it is pointed out that for constant fields fulfilling the radiation condition there will be an acceleration in the direction of the Poynting vector. When oscillating fields are considered the Lorentz force on the particle only causes a drift, with constant average velocity, in the direction of propagation of the wave, i.e.\ the direction of the Poynting vector. Finally, when the radiative reaction (radiation damping) force is added the result is again an acceleration in the direction of wave propagation. PACS classification numbers: 03.50.De, 41.60.-m, 41.75.Jv

physics.class-ph↗