Arbitrary Electromagnetic Field Research Articles

Tailoring light-induced charge transfer and intersystem crossing in FeCO using time-dependent spin-orbit configuration interaction.

Real-time (RT) electronic structure methods provide a natural framework for describing light-matter interactions in arbitrary time-dependent electromagnetic fields (EMF). Optically induced excited state transitions are of particular interest, which require tuned EMF to drive population transfer to and from the specific state(s) of interest. Intersystem crossing, or spin-flip, may be driven through shaped EMF or laser pulses. These transitions can result in long-lived "spin-trapped" excited states, which are especially useful for materials requiring charge separation or protracted excited state lifetimes. Time-dependent configuration interaction (TDCI) is unique among RT methods in that it may be implemented in a basis of eigenstates, allowing for rapid propagation of the time-dependent Schrödinger equation. The recent spin-orbit TDCI (TD-SOCI) enables a real-time description of spin-flip dynamics in an arbitrary EMF and, therefore, provides an ideal framework for rational pulse design. The present study explores the mechanism of multiple spin-flip pathways for a model transition metal complex, FeCO, using shaped pulses designed to drive controlled intersystem crossing and charge transfer. These results show that extremely tunable excited state dynamics can be achieved by considering the dipole transition matrix elements between the states of interest.

Geometric Visualization of the 3D Polarimetric Information of an Arbitrary Electromagnetic Field

The geometric visualization in this study concerns the three−dimensional (3D) polarimetric information of an arbitrary electromagnetic field. Based on previous research, a 3 × 3 coherency matrix Φ can be decomposed into an incoherent superposition of a totally 3D−polarized component Φ3D_p, a specific partially 3D−polarized component Φ3D_pp with a 3D degree of polarization (DoP) of 1/2, and a totally 3D−unpolarized component Φ3D_up. Combining the physical meaning of this decomposition, we mathematically construct three polarization purities, namely, P3D_p, P3D_pp, and P3D_up, for an arbitrary electromagnetic field to quantify the weight of the three 3D−polarized components. In order to show the proportion of the three polarized components of an electromagnetic field intuitively, we propose a geometric representation of a spatially quadric surface. Finally, two examples are cited to demonstrate the applicability of intuitively displaying the 3D polarimetric information of an arbitrary electromagnetic field.

Stuckelberg Particle in a Coulomb Field: A Non-Relativistic Approximation

We start with the Stuckelberg tensor system of equations for a boson with spin states S = 1 and S = 0 and fixed intrinsic parity, which is transformed to the matrix form, then generalize this matrix system to the generally covariant case with the use of the tetrad method. This equation is detailed in spherical coordinates in the presence of an external Coulomb field. After separation of the variables we derive the system of 11 radial equations. By diagonalizing the space reflection operator, this system is splitted into two system of four and seven equations for the states with the parities P = (−1) j+1 and P = (−1) j respectively. The system for the states with the parities P = (−1) j+1 leads to the known solution and energy spectrum. The system of seven equations for the states with the parities P = (−1) j is solved for the states with the total angular momentum j = 0 in terms of hypergeometric functions. The system of seven equations for the states with the total angular momenta j = 1, 2, 3, ... turns out to be very complicated, the only nonrelativistic approximation has been studied. The derived nonrelativistic equations are solved in terms of confluent hypergeometric functions, and the corresponding energy spectra are found. In addition, the general form of the nonrelativistic equations for the the Stuckelberg particle is derived in the presence of an arbitrary electromagnetic field.

High-order corrections to the radiation-free dynamics of an electron in the strongly radiation-dominated regime

A system of reduced equations is proposed for electron motion in the strongly radiation-dominated regime for an arbitrary electromagnetic field configuration. The approach developed here is used to analyze various scenarios of electron dynamics in this regime: motion in rotating electric and magnetic fields and longitudinal acceleration in a plane wave and in a plasma wakefield. The results obtained show that this approach is able to describe features of electron dynamics that are essential in certain scenarios, but cannot be captured in the framework of the original radiation-free approximation [Samsonov et al., Phys. Rev. A 98, 053858 (2018) and A. Gonoskov and M. Marklund, Phys. Plasmas 25, 093109 (2018)]. The results are verified by numerical integration of the nonreduced equations of motion with account taken of radiation reaction in both semiclassical and fully quantum cases.

Spin 2 Particle with Anomalous Magnetic Moment in Riemann Space−Time: A Massless Case with the Gauge Symmetry

The most of studies in the theory of spin 2 field were performed with the use of the 2-nd order equations. The spin 2 particle theory proposed by F.I. Fedorov is based on the first order equations requires a 30-component set of tensors. Besides, by him and coauthors was elaborated a more general theory, which is based on 50-component set of tensors. In the present paper, we consider this more general theory in presence of arbitrary electromagnetic fields and Riemannian space-time backgrounds. First we study the 50-component theory for a massive particle. In this case, there arises the non-minimal interaction with the curved space-time background through the Ricci and Riemann tensors. It is important that the theory under consideration allows for a new massless limit for the spin 2 field. This fact is of special interest, because the conventional Pauli - Fierz theory for the massless field does not possess gauge symmetry in the curved space-time, in particular, in models with the vanishing Ricci tensor. We show that the generalized theory possesses such a gauge symmetry in all space-time models for which the Ricci tensor vanishes.

Approximated analytical solution of the Landau–Lifshitz equation in tightly focused laser beams in the ultrarelativistic limit

The Landau–Lifshitz equation is widely considered as the equation, which correctly includes the effects of radiation reaction in the classical motion of an electric charge. Here, we provide an approximated analytical solution of the Landau–Lifshitz equation in the presence of a virtually arbitrary electromagnetic field by making the assumptions that the electron’s initial energy is the largest dynamical energy in the problem. We show that in a regime where radiation–reaction effects are a small correction of the Lorentz dynamics, the four-momentum of the electron can be determined perturbatively in the ultrarelativistic limit. We explicitly compute the electron four-momentum up to the first order and in the experimentally relevant case of an ultrashort, tightly focused laser beam as an external field.Graphical abstract

IMPEDANCE BOUNDARY CONDITION OF NON-UNIFORM ELECTROMAGNETIC FIELD PENETRATION INTO CONDUCTING HALF-SPACE

The influence of the non-uniformity of the external field to its distribution on the surface of the conducting half-space is investigated on the basis of exact analytical and approximate asymptotic calculation methods of an arbitrary three-dimensional electromagnetic field. The function that generalizes the impedance boundary condition for diffusion of non-uniform field into conducting body is proposed. On the basis of calculations results comparison by exact and approximate methods for concrete model of electromagnetic system the admissible value of the upper limit of the introduced small parameter is established. References 10, figures 5.

A Three-Dimensional Microwave Sparse Imaging Approach Using Higher-Order Basis Functions

This paper presents a novel method for three-dimensional microwave imaging based on sparse processing. To enforce the sparsity of the unknown function, we take advantage of the fact that arbitrary three-dimensional electromagnetic fields can be decomposed into two components with respect to the radial direction: one with transverse-magnetic polarization and the other with transverse-electric polarization. Each component can be further expressed as a sum of spherical harmonics, which provide the dictionary exploited by the sparse processing algorithm. Our measurement model relates the data and the parameters of the spherical harmonics’ sources, which are uniformly distributed on a grid sampling the imaging domain. By relying on the theory of degrees of freedom of electromagnetic fields, it can be shown that only a few harmonics are sufficient to accurately represent the measured scattered field from objects whose diameter is of the order of the wavelength, thus allowing reducing the dimension of the adopted dictionary. We analyze several imaging scenarios to assess the algorithm’s performance, including different object shapes, sensor orientations, and signal-to-noise ratios. Moreover, we compare the obtained results with other state-of-the-art linear imaging techniques. Notably, thanks to the adopted dictionary, the proposed algorithm can yield accurate images of both convex and concave objects.

Dirac quantum walks with conserved angular momentum

A quantum walk (QW) simulating the flat \((1 + 2)\)D Dirac equation on a spatial polar grid is constructed. Because fermions are represented by spinors, which do not constitute a representation of the rotation group \({\mathrm{SO}}(3)\), but rather of its double cover \({\mathrm{SU}}(2)\), the QW can only be defined globally on an extended spacetime where the polar angle extends from 0 to \(4 \pi \). The coupling of the QW with arbitrary electromagnetic fields is also presented. Finally, the cylindrical relativistic Landau levels of the Dirac equation are computed explicitly and simulated by the QW.

Dynamics of dipole in a stationary non-homogeneous electromagnetic field

The non-relativistic equations of motion for a dipole in a stationary non-homogeneous electromagnetic field are derived and analysed. It is shown that they are Hamiltonian with respect to a certain degenerated Poisson structure. Described by them dynamics is complex because the motion of the centre of mass of the dipole is coupled with its rotational motion. The problem of the existence of linear in momenta first integrals which can be useful for the separation of rotational motion is discussed. The presence of such first integral appears to be related with a linear symmetry of electric and magnetic fields. Also results of search of quadratic in momenta first integrals for uniform and stationary electromagnetic fields are reported. Deriving equations of motion of a dipole in arbitrary stationary electromagnetic fields and analysis of described by them dynamics is important for the construction of electromagnetic traps for polar particles.

Plasma dynamics and vacuum pair creation using the Dirac-Heisenberg-Wigner formalism.

We derive a system of coupled partial differential equations for the equal-time Wigner function in an arbitrary strong electromagnetic field using the Dirac-Heisenberg-Wigner formalism. In the electrostatic limit, we present a system of four coupled partial differential equations, which are completed by Ampères law. This electrostatic system is further studied for two different cases. In the first case, we consider linearized wave propagation in a plasma accounting for the nonzero vacuum expectation values. We then derive the dispersion relation and compare it with well-known limiting cases. In the second case, we consider Schwinger pair production using the local density approximation to allow for analytical treatment. The dependence of the pair production rate on the perpendicular momentum is investigated and it turns out that the spread of the produced pairs along with perpendicular momentum depends on the strength of the applied electric field.

Axial representation of external time-dependent electromagnetic fields for particle tracking in accelerators

We derive a power series representation of an arbitrary electromagnetic field near some axis through the coaxial field components on the axis. The obtained equations are compared with Fourier–Bessel series approach and verified by several examples. It is shown that for each azimuthal mode we need only two real functions on the axis in order to describe the field in a source free region near to it. The representation of dipole mode in a superconducting radio-frequency gun is analyzed.

Frequency analysis and dynamic aperture studies in a low energy antiproton ring with realistic 3D magnetic fields

We briefly present recent progress with our algorithm and its implementation called SIMPA described in a previous paper. The algorithm has a new and unique approach to long-term 4D tracking of charged particles in arbitrary static electromagnetic fields. Using the improvements described in this paper, we made frequency analysis and dynamic aperture studies in ELENA. The effect of the end fields and the perturbation introduced by the magnetic system of the electron cooler on dynamic aperture is shown. A special feature of this study is that we have not introduced any multipole errors into the model. The dynamic aperture calculated in this paper is the direct consequence of the geometry of the magnetic elements. Based on the results, we make a few suggestions to reduce the losses during the deceleration of the beam.

An energy-conserving and asymptotic-preserving charged-particle orbit implicit time integrator for arbitrary electromagnetic fields

We present a new implicit asymptotic preserving time integration scheme for charged-particle orbit computation in arbitrary electromagnetic fields. The scheme is built on the Crank-Nicolson integrator and continues to recover full-orbit motion in the small time-step limit, but also recovers all the first-order guiding center drifts as well as the correct gyroradius when stepping over the gyration time-scale. In contrast to previous efforts in this direction, the new scheme also features exact energy conservation. In the derivation of the scheme, we find that a new numerical time-scale is introduced. This scale is analyzed and the resulting restrictions on time-step are derived. Based on this analysis, we develop an adaptive time-stepping strategy the respects these constraints while stepping over the gyration scale when physically justified. It is shown through numerical tests on single-particle motion that the scheme's energy conservation property results in tremendous improvements in accuracy, and that the scheme is able to transition smoothly between magnetized and unmagnetized regimes as a result of the adaptive time-stepping.

Unified picture of electromagnetic and gravitational forces in two-spinor language

The well known Geodesic Equation of General Relativity is newly formulated in Weyl two-spinor language in a way susceptible of being generalized via a set of two-spinor equations, equivalent to the Lorentz Force of Electrodynamics, obtained in previous studies. General spinor equations of motion for a test charged spin 1/2 particle in arbitrary electromagnetic and gravitational fields are obtained describing not only spacetime trajectories but also spin precession. For the case of the Schwarzschild metric and radial trajectories, spinor equations unifying gravitational and electric forces are obtained and solved for a weak gravitational field (or long distance from the source).

Contribution to the Theory of Planar Wire Loop Antennas Used for Reception

Using “electromagnetic field” to designate an electric field and a magnetic field which satisfy Maxwell's equations, we define a decomposition of an arbitrary incident time-harmonic electromagnetic field into four elementary time-harmonic electromagnetic fields F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A</sub> , F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</sub> , F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</sub> , and F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</sub> . A formula, which gives the response of an arbitrary planar wire loop antenna used for reception, is based on this decomposition. This formula is applicable to any incident field configuration, and valid at any frequency at which the thin wire approximation applies. It separates the response of the antenna into three parts, one of which may be viewed as the intended response of the antenna. Our analysis teaches that F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</sub> and F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</sub> have no effect on the antenna and how F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A</sub> and F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</sub> excite the antenna. Thus, it allows us to better understand the characteristics and limitations of a planar wire loop antenna used as a measuring antenna or as a direction finder.

Efficient evaluation of arbitrary static electromagnetic fields with applications for symplectic particle tracking

This article describes a method devised for efficient evaluation of arbitrary static magnetic and electric fields in a source free region needed for long time tracking of charged particles. Field values given on the boundary of the region of interest are reproduced inside by an arrangement of hypothetical magnetic or electric monopoles surrounding the boundary surface. The vector and scalar potentials are obtained by summing the contributions of each monopole. The second step of the method improves the evaluation speed of the potentials and their derivatives by orders of magnitude. This comprises covering the region of interest by overlapping spheres, then calculating the spherical harmonic expansion of the potentials on each sphere. During tracking, field values are evaluated by calculating the solid harmonics and their derivatives inside a sphere containing the particle. Software has been developed to test and demonstrate the method on a small particle accelerator. To our knowledge, there is no other method of this kind, allowing long time symplectic integration in general static fields, without simplification.

Ultrarelativistic Electron-Beam Polarization in Single-Shot Interaction with an Ultraintense Laser Pulse.

Spin polarization of an ultrarelativistic electron beam head-on colliding with an ultraintense laser pulse is investigated in the quantum radiation-dominated regime. We develop a MonteCarlo method to model electron radiative spin effects in arbitrary electromagnetic fields by employing spin-resolved radiation probabilities in the local constant field approximation. Because of spin-dependent radiation reaction, the applied elliptically polarized laser pulse polarizes the initially unpolarized electron beam and splits it along the propagation direction into two oppositely transversely polarized parts with a splitting angle of about tens of milliradians. Thus, a dense electron beam with above 70% polarization can be generated in tensof femtoseconds with realistic laser pulses. The proposed method demonstrates a way for relativistic electron beam polarization with currently achievable laser facilities.

Dirac quantum walks on triangular and honeycomb lattices

In this paper, we present a detailed study on discrete-time Dirac quantum walks (DQWs) on triangular and honeycomb lattices. At the continuous limit, these DQWs coincide with the Dirac equation. Their differences in the discrete regime are analyzed through the dispersion relations, with special emphasis on Zitterbewegung. An extension which couples these walks to arbitrary discrete electromagnetic field is also proposed and the resulting Bloch oscillations are discussed.

Pulsar gamma-ray emission in the radiation reaction regime

Since the era of the Fermi/LAT and atmospheric Cerenkov telescopes, pulsars are known to emit high and very high-energy photons, in the MeV-GeV range and sometimes up to TeV. To date, it is still unclear where and how these photons are produced. Nevertheless gamma-ray photons require particle acceleration to ultra-relativistic speeds. In this paper, we compute single particle trajectories for leptons in an arbitrary strong electromagnetic field in the so-called radiation reaction limit. In this picture, particle velocity only depends on the local electromagnetic field which we assume to follow the vacuum dipole rotator. From this velocity field, we compute the curvature radiation spectrum and light-curves. Sky maps and phase-resolved spectra are then deduced accounting for realistic pulsar periods and magnetic field strengths. Emission sites within the pulsar magnetosphere where most of radiation emanates are then localized. For standard parameters of millisecond and normal pulsars, we show that a break in the spectrum occurs at several GeV in agreement with the Fermi/LAT second pulsar catalogue. A sample of representative phase-resolved spectra and sky-maps are shown. A pair multiplicity of several tenths to several thousands is required to account for the total gamma-ray luminosity. Moreover depending on the geometry, single or double-peaked light-curves are found. Our model shows that minimalist assumptions are already able to reproduce salient features of pulsar emission.