Radiation from a Uniformly Accelerated Charge

The emission of radiation by a uniformly accelerated charge is analyzed. According to the standard approach, a radiation is observed whenever there is a relative acceleration between the charge and the observer. Analyzing difficulties that arose in the standard approach, we propose that a radiation is created whenever a relative acceleration between the charge and its own electric field exists. The electric field induced by a charge accelerated by an external (nongravitational) force is not accelerated with the charge. Hence the electric field is curved in the instantaneous rest frame of the accelerated charge. This curvature gives rise to a stress force, and the work done to overcome the stress force is the source of the energy carried by the radiation. In this way, the energy balance paradox finds its solution.     

Equation of Motion of an Electric Charge

The appearance of the time derivative of the acceleration in the equation of motion (EOM) of an electric charge is studied. It is shown that when an electric charge is accelerated, a stress force exists in the curved electric field of the accelerated charge, and in the case of a constant linear acceleration, this force is proportional to the acceleration. This stress force acts as a reaction force which is responsible for the creation of the radiation (instead of the radiation reaction force that actually does not exist at low velocities). Thus the initial acceleration should be supplied as an initial condition for the solution of the EOM of an electric charge.     

Origin of Radiation Reaction

The emission of radiation from an accelerated charge is analyzed. It is foundthat at zero velocity, the radiation emitted from the charge imparts no countermomentum to the emitting charge, and no radiation reaction force is created bythe radiation. A reaction force is created by the stress force that exists in thecurved electric field of the charge, and the work done in overcoming this forceis the source of the energy carried by the radiation.     

Transition radiation measurements at distances from the transition point comparable to the formation length

The spatial distribution of the electromagnetic field excited by a relativistic particle crossing the surface of a metal is studied. It is shown that the field of the uniformly moving charge must also be taken into account during measurements at distances comparable to the path length for formation of the radiation. Expressions describing the effect of the self-field of the charge on the transition radiation field are derived. Zh. Tekh. Fiz. 67, 89–93 (September 1997)     

Length measurement in accelerated systems

We investigate the limitations of length measurements by accelerated observers in Minkowski spacetime brought about via the hypothesis of locality, namely, the assumption that an accelerated observer at each instant is equivalent to an otherwise identical momentarily comoving inertial observer. We find that consistency can be achieved only in a rather limited neighborhood around the observer with linear dimensions that are negligibly small compared to the characteristic acceleration length of the observer.     

Self-force of a charge in a real current

The analysis of the EM radiation from a single charge shows that the radiated power depends on the retarded acceleration of the charge. Therefore for consistency, an accelerated charge, free from the influence of external forces, should gradually lose its acceleration, until its total energy is radiated. Calculations show that the self force of a charge, which compensates for its radiation, is proportional to the derivative of the acceleration. However, when using this self force in the equation of motion of the charge, one gets a diverging solution, for which the acceleration runs away to infinity. This means that there is an inconsistency in the solution of the single charge problem. However, in the construction of the conserved Maxwell charge density, there is implicitly an integral over the corresponding world line which corresponds to a collection of charged spacetime events. One may therefore consistently think of the “self force” as the force on a charge due to another charge at the retarded position. From this point of view, the energy is evidently conserved and the radiation process appears as an absorbing resistance to the feeding source. The purpose of this work is to learn about the behavior of single charges from the behavior of a real current, corresponding to the set of charges moving on a world line, and to study the analog of the self force of a charge associated with the radiation resistance of a continuum of charges.     

The Equivalence Principle and an Electric Charge in a Gravitational Field II. A Uniformly Accelerated Charge Does Not Radiate

The electromagnetic field of a charge supported in a uniform gravitational field is examined from the viewpoint of an observer falling freely in the gravitational field. It is argued that such a charge, which from the principle of equivalence is moving with a uniform acceleration with respect to the (inertial) observer, could not be undergoing radiation losses at a rate implied by Larmor's formula. It is explicitly shown that the total energy in electromagnetic fields, including both velocity and acceleration fields, of a uniformly accelerated charge, at any given instant of the inertial observer's time, is just equal to the self-energy of a non-accelerated charge moving with a velocity equal to the instantaneous present velocity of the accelerated charge. At any given instant of time, and as seen with respect to the present position of the uniformly accelerated charge, although during the acceleration phase there is a radially outward component of the Poynting vector, there is throughout a radially inward Poynting flux component during the deceleration phase, and a null Poynting vector at the instant of the turn around. From Poynting's theorem, defined for any region of space strictly in terms of fixed instants of time, it is shown that a uniformly accelerated charge does not emit electromagnetic radiation, in contrast to what is generally believed. Contrary to some earlier suggestions in the literature, there is no continuous passing of electromagnetic radiation from a uniformly accelerated charge into the region inaccessible to a co-accelerating observer.     

Electrodynamics of hyperbolically accelerated charges V. The field of a charge in the Rindler space and the Milne space

We describe the electromagnetic field of a uniformly accelerated charge in its co-moving Rindler frame. It is shown that the electrical field lines coincide with the trajectories of photons. The self force of a charged particle at rest in Rindler space, and the increase of its weight due to its charge, is calculated. The general case of an accelerated charge in Rindler space is also considered. It is shown that the electrical field inside a uniformly charged spherical shell can be used as a measure of it 4-acceleration. A result that has earlier been deduced in a different way by Fugmann and Kretzschmar is confirmed, namely that the intensity of radiation from a point charge instantaneously at rest in an accelerated frame is proportional to the square of the relative acceleration of the charge and the observer. In particular it is shown that a freely falling charge in Rindler space radiates in accordance with Larmor’s formula. In this case the radiation energy is taken from the Schott energy. The energy of the electromagnetic field is analysed from the point of view of the Hirayama-separation, which generalizes the Teitelboim-separation to non-inertial frames, of the field in a bound part and an unbound part. A detailed account, with reference to the Rindler frame, of the field energy and particle energy is given for the case of a charge entering and leaving a region with hyperbolic motion. We also consider the electromagnetic field of a uniformly accelerated charge with reference to the Milne frame, which covers a different part of spacetime than the Rindler frame. The radiating part of the electromagnetic field is found in the Milne sector of spacetime.     

Laser-induced ion acceleration at ultra-high laser intensities

Ion acceleration by ultrashort laser pulses of very high intensities of the order 10²²?W/cm² is studied by two-dimensional Particle-In-Cell simulations. We show that laser normal incidence is preferred for such high intensities. For linearly polarized laser radiation, higher maximum proton/ion energies are achieved than for circular polarization. For linear polarization, the transition from the target normal sheath acceleration to the acceleration on the target front side by the radiation pressure is analyzed in detail. The transition intensity is increasing with the target thickness. The radiation pressure dominated regime leads to considerably higher number of accelerated protons and thus to a higher acceleration efficiency.     

Spontaneous excitation of a circularly accelerated atom coupled to electromagnetic vacuum fluctuations

We study, using the formalism proposed by Dalibard, Dupont-Roc and Cohen-Tannoudji, the contributions of the vacuum fluctuation and radiation reaction to the rate of change of the mean atomic energy for a circularly accelerated multilevel atom coupled to vacuum electromagnetic fields in the ultrarelativistic limit. We find that the balance between vacuum fluctuation and radiation reaction is broken, which causes spontaneous excitations of accelerated ground state atoms in vacuum. Unlike for a circularly accelerated atom coupled to vacuum scalar fields, the contribution of radiation reaction is also affected by acceleration, and this term takes the same form as that of a linearly accelerated atom coupled to vacuum electromagnetic fields. For the contribution of vacuum fluctuations, we find that in contrast to the linear acceleration case, terms proportional to the Planckian factor are replaced by those proportional to a non-Planck exponential term, and this indicates that the radiation perceived by a circularly orbiting observer is no longer thermal as is in the linear acceleration case. However, for an ensemble of two-level atoms, an effective temperature can be defined in terms of the atomic transition rates, which is found to be dependent on the transition frequency of the atom. Specifically, we calculate the effective temperature as a function of the transition frequency and find that in contrast to the case of circularly accelerated atoms coupled to the scalar field, the effective temperature in the current case is always larger than the Unruh temperature.     

Radiation From an Electric Charge

The conditions in which electromagnetic radiation is formed are discussed. It is found that the main condition for the emission of radiation by an electric charge is the existence of a relative acceleration between the charge and its electric field. Such a situation exists both for a charge accelerated in a free space, and for a charge supported at rest in a gravitational field. Hence, in such situations, the charges radiate. It is also shown that relating radiation to the relative acceleration between a charge and its electric field, solves several difficulties that existed in earlier approaches, like the energy balance paradox, and the relativistic nature of the observation of the emitted radiation.     

Depth distribution of vacancies generated by irradiating a solid surface with a flux of accelerated ions

Kinetic transport theory is used to find analytical expressions for the absorbed doses of the primary-particle flux and primary-particle energy as functions of distance into a solid with finite or semi-infinite thickness when the surface of the latter is irradiated by a flux of accelerated ions (atoms) in the direction normal to the surface. The theory was compared with experiments in which solid silicon films with thicknesses 50, 100, and 400 nm were irradiated by a flux of accelerated boron atoms with energies from 10 to 20 keV. These expressions were used to calculate the depth distribution of vacancies generated in a solid whose surface is irradiated by a flux of accelerated ions. The method developed can be used to determine the depth distribution of vacancies created by fluxes of accelerated electrons, neutrons, or photons. Zh. Tekh. Fiz. 68, 60–65 (April 1998)     

Electret mechanism of electron beam capture by the magnetic field of a betatron

The mechanism of electron capture into acceleration that takes into account the electret properties of the accelerating chamber shell is described. The electron capture into acceleration is a self-consistent problem. It is demonstrated that the electron capture into acceleration is caused by the interaction of the injected electrons with the electric field of the charge created on the side interior wall of the chamber by electrons dropped out of the acceleration. The spectrum of the captured electrons is not normal. A large number of low-energy electrons are presented in the spectrum. Two and more peaks previously unknown are revealed in the dependence of the captured charge on the injected charge for large values of the injected charge. The results obtained are in agreement with the data of previous experimental studies. The captured charge and the dose rate of bremsstrahlung from a target correspond to their actual values for betatrons with accelerated electron energies of 6 and 10 MeV. Results of simulation can be used to design accelerating chambers and electron injection systems of betatrons and other cyclic accelerators. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 35–45, December, 2006.     

Femtosecond laser-induced dynamic alignment in Coulomb explosion of CO: Roles of laser wavelength, intensity and pulse duration

Dependences of dynamic alignment of CO molecules induced by intense femtosecond laser fields on laser wavelength, intensity and pulse duration are investigated by numerical simulations. A counting approach and a fourth-order Runge-Kutta algorithm are used to calculate the angular distribution and the time evolution of molecules. A two-step Coulomb explosion model of diatomic molecules in intense laser fields is used to determine the instant that CO molecular dynamic alignment is over. Our calculating results show that the linear polarizability and the damping force play an important role in the angular rotation of CO molecule in conditions of 800 nm laser wavelength and 10¹⁵ W/cm² laser intensity. The contributions of the second-order field-induced dipole moment and the higher-order correction term to molecular rotation acceleration comparing to the linear polarizability and damping force are negligible. The extent of dynamic alignment of CO molecules reduces with the increasing of laser intensity. The dynamic alignment time of CO molecules is tightly connected to the laser pulse duration. The angular distributions of CO molecules as the laser pulse length varied from 50 to 250 fs at laser intensity of 3×10¹⁴ W/cm² are shown and discussed.     

Rarefaction wave and gravitational equilibrium in a two-phase liquid-vapor medium

The problems studied in this paper involve the action of laser radiation or a particle beam on a condensed material. Such an interaction produces a hot corona, and the recoil momentum accelerates the cold matter. In the coordinate frame tied to the accelerated target, the acceleration is equivalent to the acceleration of gravity. For this reason, the density distribution ρ is hydrostatic in the zeroth approximation. In this paper the structure of such a flow is studied for a two-phase equation of state. It is shown that instead of a power-law density profile, which obtains for a constant specific-heat ratio, a complicated distribution containing a region with a sharp variation of ρ arises. Similar characteristics of the density profile arise with isochoric heating of matter by an ultrashort laser pulse and the subsequent expansion of the heated layer. The formation of a rarefaction wave and the interaction of oppositely propagating rarefaction waves in a two-phase medium are studied. It is very important to take account of the two-phase nature of the material, since conditions (p _a ∼1 Mbar) are often realized under which the foil material comes after expansion into the two-phase region of the phase diagram. Zh. éksp. Teor. Fiz. 115, 2091–2105 (June 1999)     

Laser acceleration of light impurity from an ultrathin foil of complex ionic composition

The model of acceleration of light impurity particles from a planar ultrathin foil of complex ionic composition under an ultrashort high-power high-contrast laser pulse is proposed. Both the mode of pure Coulomb acceleration of ions, characteristic of extremely high electron energies, and acceleration under conditions of spatial charge separation controlled by a finite characteristic electron temperature are studied. Accurate and approximate analytical approaches for describing impurity particle acceleration are formulated. Spatial and spectral characteristics of accelerated particles are determined. Particle dynamics is studied in both the approximation of test impurity particles and taking into account their intrinsic electrostatic field, depending on the relative charge density of light particles.     

Radiation from a Charge Supported in a Gravitational Field

We examine whether a charge supported statically in a gravitational field radiates, and find the answer to this question to be positive. Based on our earlier results we find that the important condition for the creation of radiation is the existence of a relative acceleration between the charge and its electric field, where such an acceleration causes the curving of the electric field and the creation of a stress force due to this curvature. This stress force is the reaction force, which creates the radiation. Later we find that this condition do exist for a charge supported statically in a gravitational field, where the electric field of the charge falls in the gravitational field, it curves, and the stress force raised in this curved field, creates electromagnetic radiation.     

A symmetry relating certain processes in 2-and 4-dimensional space-times and the value α0 = 1/4π of the bare fine structure constant

The symmetry manifests itself in exact relations between the Bogoliubov coefficients for processes induced by an accelerated point mirror in 1 + 1 dimensional space and the current (charge) densities for the processes caused by an accelerated point charge in 3 + 1 dimensional space. The spectra of pairs of Bose (Fermi) massless quanta emitted by the mirror coincide with the spectra of photons (scalar quanta) emitted by the electric (scalar) charge up to the factor e ²/ħc. The integral relation between the propagator of a pair of oppositely directed massless particles in 1 + 1 dimensional space and the propagator of a single particle in 3 + 1 dimensional space leads to the equality of the vacuum-vacuum amplitudes for the charge and the mirror if the mean number of created particles is small and the charge e = √ħc. Due to the symmetry, the mass shifts of electric and scalar charges (the sources of Bose fields with spin 1 and 0 in 3 + 1 dimensional space) for the trajectories with a subluminal relative velocity β₁₂ of the ends and the maximum proper acceleration w ₀ are expressed in terms of the heat capacity (or energy) spectral densities of Bose and Fermi gases of massless particles with the temperature w ₀/2π in 1 + 1 dimensional space. Thus, the acceleration excites 1-dimensional oscillation in the proper field of a charge, and the energy of oscillation is partly deexcited in the form of real quanta and partly remains in the field. As a result, the mass shift of an accelerated electric charge is nonzero and negative, while that of a scalar charge is zero. The symmetry is extended to the mirror and charge interactions with the fields carrying spacelike momenta and defining the Bogoliubov coefficients α^B,F. The traces trα^B,F, which describe the vector and scalar interactions of the accelerated mirror with a uniformly moving detector, were found in analytic form for two mirror trajectories with subluminal velocities of the ends. The symmetry predicts one and the same value e ₀ = √ħc for the electric and scalar charges in 3 + 1 dimensional space. Arguments are adduced in favor of the conclusion that this value and the corresponding value α₀ = 1/4π of the fine structure constant are the bare, nonrenormalized values. The text was submitted by the author in English.     

Vacuum electron acceleration by coherent dipole radiation

The validity of the concept of laser-driven vacuum acceleration has been questioned, based on an extrapolation of the well-known Lawson-Woodward theorem, which stipulates that plane electromagnetic waves cannot accelerate charged particles in vacuum. To formally demonstrate that electrons can indeed be accelerated in vacuum by focusing or diffracting electromagnetic waves, the interaction between a point charge and coherent dipole radiation is studied in detail. The corresponding four-potential exactly satisfies both Maxwell's equations and the Lorentz gauge condition everywhere, and is analytically tractable. It is found that in the far-field region, where the field distribution closely approximates that of a plane wave, we recover the Lawson-Woodward result, while net acceleration is obtained in the near-field region. The scaling of the energy gain with wave-front curvature and wave amplitude is studied systematically.     

Photographic observation of aluminum micropellet ablation in theMT-1M tokamak plasma

Laser beam accelerated aluminum micropellets were injected into the MT-1M tokamak plasma, and the distribution of characteristic line radiation of aluminum atoms and ions of different charge state was detected. The investigations are focused on the visualization of the pellet cloud, on the bending of the pellet path, and on the striation occurring in the radiation of different charge state along the pellet path in the plasma