Non-relativistic Velocities Research Articles

Electrodynamics of Balanced Charges

We introduce here a new “neoclassical” electromagnetic (EM) theory in which elementary charges are represented by wave functions and individual EM fields to account for their EM interactions. We call so defined charges balanced or “b-charges”. We construct the EM theory of b-charges (BEM) based on a relativistic field Lagrangian and show that: (i) the elementary EM fields satisfy the Maxwell equations; (ii) the Newton equations with the Lorentz forces hold approximately when b-charges are well separated and move with non-relativistic velocities. When the BEM theory is applied to atomic scales it yields a hydrogen atom model with a frequency spectrum matching the Schrodinger model with desired accuracy. An important feature of the theory is a mechanism of elementary EM energy absorption established for retarded potentials.

Quantum radiation reaction force on a one-dimensional cavity with two relativistic moving mirrors

We consider a real massless scalar field inside a cavity with two moving mirrors in a two-dimensional spacetime, satisfying the Dirichlet boundary condition at the instantaneous position of the boundaries, for arbitrary and relativistic laws of motion. Considering vacuum as the initial field state, we obtain formulas for the exact value of the energy density of the field and the quantum force acting on the boundaries, which extend results found in previous papers [D. T. Alves, E. R. Granhen, H. O. Silva, and M. G. Lima, Phys. Rev. D 81, 025016 (2010); L. Li and B.-Z. Li, Phys. Lett. A 300, 27 (2002); L. Li and B.-Z. Li, Chin. Phys. Lett. 19, 1061 (2002); L. Li and B.-Z. Li, Acta Phys. Sin. 52, 2762 (2003); C. K. Cole and W. C. Schieve, Phys. Rev. A 64, 023813 (2001)]. For the particular cases of a cavity with just one moving boundary, nonrelativistic velocities, or in the limit of infinity length of the cavity (a single mirror), our results coincide with those found in the literature.

High frequency electromagnetic modes in a weakly magnetized relativistic electron plasma

Using the linearized Vlasov-Maxwell model, the polarization tensor for a weakly magnetized electron plasma is derived. For isotropic relativistic Maxwellian velocity distribution function, dispersion relations are obtained for both parallel and perpendicular propagations. The integrals (called Meijer G functions) that arise due to relativistic effects are examined in various limits and dispersion relations are derived for the nonrelativistic, weakly, strongly, and ultrarelativistic Maxwellian velocity distributions. It is generally observed that the propagation domains of the modes are enlarged as one proceeds from the nonrelativistic to the highly relativistic regime. Resultantly, due to the relativistic effects, the Whistler mode is suppressed in the R-wave, the nonpropagation band of X-mode is reduced, and the X-mode itself approaches the O-mode. Further, the results derived in the ultra- and nonrelativistic limits found to be in agreement with the earlier calculations [G. Abbas et al. Phys. Scr. 76, 649 (2007); F. F. Chen, Introduction to Plasma Physics and Controlled Fusion (Plenum, New York, 1984), Vol. 1].

Relativistic warm plasma theory of nonlinear laser-driven electron plasma waves

A relativistic, warm fluid model of a nonequilibrium, collisionless plasma is developed and applied to examine nonlinear Langmuir waves excited by relativistically intense, short-pulse lasers. Closure of the covariant fluid theory is obtained via an asymptotic expansion assuming a nonrelativistic plasma temperature. The momentum spread is calculated in the presence of an intense laser field and shown to be intrinsically anisotropic. Coupling between the transverse and longitudinal momentum variances is enabled by the laser field. A generalized dispersion relation is derived for Langmuir waves in a thermal plasma in the presence of an intense laser field. Including thermal fluctuations in three-velocity-space dimensions, the properties of the nonlinear electron plasma wave, such as the plasma temperature evolution and nonlinear wavelength, are examined and the maximum amplitude of the nonlinear oscillation is derived. The presence of a relativistically intense laser pulse is shown to strongly influence the maximum plasma wave amplitude for nonrelativistic phase velocities owing to the coupling between the longitudinal and transverse momentum variances.

Conservative—dissipative interaction forces and heating caused by a fluctuation electromagnetic field: Two plates in a nonrelativistic relative motion

The heating rate and conservative—dissipative forces in a system of two parallel plates moving at a nonrelativistic velocity with respect to each other have been calculated in terms of the fluctuation electromagnetic electrodynamics for the first time. It has been demonstrated that the recently proposed relativistic theory of fluctuation electromagnetic interactions in the configuration under consideration offers fundamental disadvantages.

Quantum radiation force on the moving mirror of a cavity, with Dirichlet and Neumann boundary conditions for a vacuum, finite temperature, and a coherent state

We consider a real massless scalar field inside a cavity with a moving mirror in a two-dimensional spacetime, satisfying the Dirichlet or Neumann boundary condition at the instantaneous position of the boundaries, for an arbitrary and relativistic law of motion. Considering an arbitrary initial field state, we show that the exact value of the energy density in the cavity can be obtained by tracing back a sequence of null lines, connecting the value of the energy density at the given spacetime point to a certain known value of the energy density at a point in the region where the initial field modes are not affected by the boundary motion. We obtain the particular formulas for the energy density of the field and the quantum force acting on the boundaries for a vacuum, thermal, and a coherent state. We thus generalize a previous result in literature [17], where this problem is approached for only one mirror. For the particular cases of vacuum and Dirichlet boundary condition, nonrelativistic velocities, or in the limit of large length of the cavity, our results coincide with those found in the literature.

Conservative–dissipative forces and heating mediated by fluctuation electromagnetic field: Two plates in relative nonrelativistic motion

We calculate heating rate, attractive conservative and tangential dissipative fluctuation electromagnetic forces felt by a thick plate moving with nonrelativistic velocity parallel to a closely spaced another plate in rest using relativistic fluctuation electrodynamics. We argue that recently developed relativistic out of equilibrium theory of fluctuation electromagnetic interactions [A.I. Volokitin, B.N.J. Persson, Phys. Rev. B78 (2008) 155437; arXiv:/cond-mat.other/0807.1004v1, 2008] has serious drawbacks.

Electric field generation by the electron beam filamentation instability: filament size effects

The filamentation instability (FI) of counter-propagating beams of electrons is modelled with a particle-in-cell simulation in one spatial dimension and with a high statistical plasma representation. The simulation direction is orthogonal to the beam velocity vector. Both electron beams have initially equal densities, temperatures and moduli of their non-relativistic mean velocities. The FI is electromagnetic in this case. A previous study of a small filament demonstrated that the magnetic pressure gradient force (MPGF) results in a nonlinearly driven electrostatic field. The probably small contribution of the thermal pressure gradient to the force balance implied that the electrostatic field performed undamped oscillations around a background electric field. Here, we consider larger filaments, which reach a stronger electrostatic potential when they saturate. The electron heating is enhanced and electrostatic electron phase space holes form. The competition of several smaller filaments, which grow simultaneously with the large filament, also perturbs the balance between the electrostatic and magnetic fields. The oscillations are damped but the final electric field amplitude is still determined by the MPGF.

Wave-Corpuscle Mechanics for Electric Charges

It is well known that the concept of a point charge interacting with the electromagnetic (EM) field has a problem. To address that problem we introduce the concept of wave-corpuscle to describe spinless elementary charges interacting with the classical EM field. Every charge interacts only with the EM field and is described by a complex valued wave function over the 4-dimensional space time continuum. A system of many charges interacting with the EM field is defined by a local, gauge and Lorentz invariant Lagrangian with a key ingredient—a nonlinear self-interaction term providing for a cohesive force assigned to every charge. An ideal wave-corpuscle is an exact solution to the Euler-Lagrange equations describing both free and accelerated motions. It carries explicitly features of a point charge and the de Broglie wave. Our analysis shows that a system of well separated charges moving with nonrelativistic velocities are represented accurately as wave-corpuscles governed by the Newton equations of motion for point charges interacting with the Lorentz forces. In this regime the nonlinearities are “stealthy” and don’t show explicitly anywhere, but they provide for the binding forces that keep localized every individual charge. The theory can also be applied to closely interacting charges as in hydrogen atom where it produces discrete energy spectrum.

Conservative-dissipative forces and heat exchange between moving plates caused by fluctuational electromagnetic field: Relativistic case

Expressions for the conservative-dissipative interaction forces and heat exchange between two parallel plates separated by a vacuum gap and moving at a nonrelativistic relative velocity are obtained for the first time within the framework of relativistic fluctuation electrodynamics.

The limits of the validity of the theory of a spherical diode and the problem of calculation of dense electron beams with substantially different scales

The limits of the validity of the theory of a spherical diode are discussed in the case of nonrelativistic and relativistic velocities. This theory is considered a tool for mathematical and physical testing of trajectory analysis programs applied for calculation of flows that have substantially different scales (convergent and divergent flows). The effect of the self-magnetic field determining these limits is analyzed.

VERY-LONG-BASELINE INTERFEROMETRY OBSERVATIONS OF SN 2008D

We report on two epochs of very-long-baseline interferometry (VLBI) observations of the Type Ib/c supernova, SN 2008D, which was associated with the X-ray outburst XRF 080109. At our first epoch, at t = 30 days after the explosion, we observed at 22 and 8.4 GHz, and at our second, at t = 133 days, at 8.4 and 5.0 GHz. The VLBI observations allow us to accurately measure the source's size and position at each epoch, and thus constrain its expansion velocity and proper motion. We find the source at best marginally resolved at both epochs, allowing us to place a 3σ upper limit of ~ 0.75 c on the expansion velocity of a circular source. For an elongated source, our measurements are compatible with mildly relativistic expansion. However, our 3σ upper limit on the proper motion is 4 μas day–1, corresponding to an apparent velocity of less than 0.6 c, and is consistent with a stationary flux centroid. This limit rules out a relativistic jet such as a gamma-ray burst jet away from the line of sight, which would be expected to show apparent proper motion of greater than c. Taken together, our measurements argue against the presence of any long-lived relativistic outflow in SN 2008D. On the other hand, our measurements are consistent with the nonrelativistic expansion velocities of less than 30,000 km s–1 and small proper motions (< 500 km s–1) seen in typical supernovae.

Finite difference time domain algorithm for electromagnetic problems involving material movement

The finite difference time domain (FDTD) method, adapted for magnetic field diffusion problems, is used to study the electromagnetic induction in moving materials by including motional emf in standard FDTD electromagnetic equations. The material movement is implemented by continuously changing material properties in each computational cell consistent to material advection. The flux corrected transport (FCT) algorithm is used to transport magnetic field in a fixed eulerian cell. A higher time-step is achieved by artificially increasing permittivity of the medium. This new approach is validated with standard analytical solutions for planar magnetic flux compression system and magnetic field diffusion in moving conductors with a non-relativistic velocity. To our knowledge, this is the first approach to use FDTD method for electromagnetic problems involving material motion.

Testing cosmological structure formation using redshift-space distortions

Observations of redshift-space distortions in spectroscopic galaxy surveys offer an attractive method for observing the build-up of cosmological structure. In this paper, we develop and test a new statistic based on anisotropies in the measured galaxy power spectrum, which is independent of galaxy bias and matches the matter power spectrum shape on large scales. The amplitude provides a constraint on the derivative of the linear growth rate through fσ8(mass). This demonstrates that spectroscopic galaxy surveys offer many of the same advantages as weak lensing surveys, in that they both use galaxies as test particles to probe all matter in the Universe. They are complementary as redshift-space distortions probe non-relativistic velocities and therefore the temporal metric perturbations, while weak lensing tests the sum of the temporal and spatial metric perturbations. The degree to which our estimator can be pushed into the non-linear regime is considered and we show that a simple Gaussian damping model, similar to that previously used to model the behaviour of the power spectrum on very small scales, can also model the quasi-linear behaviour of our estimator. This enhances the information that can be extracted from surveys for Λ cold dark matter (ΛCDM) models.

Self-spin-controlled rotation of spatial states of a Dirac electron in a cylindrical potential via spin–orbit interaction

Solution of the Dirac equation predicts that when an electron with nonzero orbital angular momentum (OAM) propagates in a cylindrically symmetric potential, its spin and orbital degrees of freedom interact, causing the electron's phase velocity to depend on whether its spin angular momentum (SAM) and OAM vectors are oriented parallel or anti-parallel with respect to each other. This spin–orbit splitting of the electronic dispersion curves can result in a rotation of the electron's spatial state in a manner controlled by the electron's own spin z-component value. These effects persist at non-relativistic velocities. To clarify the physical origin of this effect, we compare solutions of the Dirac equation to perturbative predictions of the Schrödinger–Pauli equation with a spin–orbit term, using the standard Foldy–Wouthuysen Hamiltonian. This clearly shows that the origin of the effect is the familiar relativistic spin–orbit interaction.

Correlated stopping power of a chain of N charges

AbstractWe evaluate the correlated stopping power of a swift chain of N charges aligned with its (non-relativistic) velocity. We find that the distance required between two charges for the chain to act as a separated set of isolated charges is much larger than the dynamical screening length because the wake effect is very important when the chain elements are situated close to each other.

Gravitational radiation from approaching neutron stars and the rotational explosion mechanism for collapsing supernovae

We consider the evolution of a neutron star binary system under the effect of two factors: gravitational radiation and mass transfer between the components. Gravitational radiation is specified under the justified assumption of a circular orbit and point masses and in the approximation of a weak gravitational field at nonrelativistic velocities of the binary components. During the first evolutionary phase determined only by gravitational radiation, the neutron stars approach each other according to a simple analytical solution. The second evolutionary phase begins at the time of Roche-lobe filling by the low-mass component, when the second factor, mass transfer as a result of mass loss by the latter, also begins to affect the evolution. Under the simplest assumptions of conservative mass transfer and exact equality between the Roche-lobe radius and the radius of the low-mass neutron star, it is still possible to extend the analytical solution of the problem of evolution to its second phase. We present this complete solution at both phases and, in particular, give theoretical light curves of gravitational radiation that depend only on two dimensionless parameters (mt and δ0). Based on the solution found, we analyze the theoretical gravitational signals from SN 1987A; this analysis includes the hypothesis about the rotational explosion mechanism for collapsing supernovae.

An interpretation of the energy conservation law for a point charge moving in a uniform electric field

The standard interpretation of the energy conservation law accepted in the theory of electromagnetism maintains that a change in the field energy occurring in a volume is the sum of the energy increment in the volume due to the Poynting vector flow and the energy dissipated as heat in the interaction of charge carriers with the medium in which these carriers move. We show that the work done by an external electric field on a moving point charge is due to two sources: the energy arriving at the charge with the Poynting vector flow and a specific channel of energy supply to the charge originating from the interaction of the charge's field with the external field. Interestingly, at nonrelativistic charge velocities (v ≪ c), 2/3 of the energy is supplied by the Poynting vector flow and 1/3 by the second channel. In the ultrarelativistic case (v c), all of the energy comes with the Poynting vector flow.

Color-transfer enhancement for heavy quarkonium production

We study the transfer of color between a heavy quark pair and an unpaired heavy quark or antiquark moving at a nonrelativistic velocity with respect to the pair. We find that the open heavy quark or antiquark can catalyze the transformation of the pair from octet representation at short distances to singlet at long distances. This process is infrared sensitive in general, and we exhibit double poles in dimensional regularization at next-to-next-to-leading order in the transition probability. Because of their dependence on kinematic variables, these poles cannot be matched to the nonperturbative matrix elements of effective field theories based on a single heavy quark pair.

Stopping of ions based on semiclassical phase shifts

We develop a semiclassical theory of the stopping of ions in matter, aiming at a wide validity range in terms of ion energies and mass number. The excitation of a target electron is described as a binary ion-electron interaction governed by a screened-Coulomb potential. The energy loss is expressed in terms of the transport cross section for electron-ion scattering which is calculated in a semiclassical approximation to the scattering phase shifts. Exact numerical integrations of the Schroedinger equation are used for quantitative tests of the derived results. This approach provides a nonperturbative representation of the energy loss which bridges the gap between classical and quantal descriptions. It applies to nonrelativistic velocities for light and heavy ions with arbitrary charge states, and it reproduces typical quantum phenomena such as the oscillatory atomic-number dependence of stopping cross sections at low energies. Calculated results have been compared with predictions from linear and nonlinear stopping theory, in particular for stopping in the electron gas and by a quantum harmonic oscillator. Moreover, attention has been paid to the Bloch correction which, in the present scheme, approaches Bloch's well-known expression but does not blow up at low projectile speed. We have also determined a generalized Blochmore » correction which depends on the ion charge. Particular attention has been given to the description of static and dynamic screening of a dressed ion.« less