Search

10.1119/5.0218373.1 We describe a simplified experiment that can be used to verify the relativistic energy-momentum relationship for beta particles emitted from a 204Tl source. The experiment makes use of an exempt radioactive source and is therefore ideal for institutions that do not maintain a Nuclear Regulatory Commission (or state) license. The relativistic beta particles are injected into a uniform magnetic field and the maximum radius of the trajectories is determined. Comparing this radius to the relativistic and non-relativistic predictions demonstrates that only the relativistic equations are consistent with the data. The simplicity of the experiment and analysis makes this project ideal for inclusion in a sophomore-level modern physics course. [ABSTRACT FROM AUTHOR]

We show that the Connes–Rovelli thermal time associated with the quantum harmonic oscillator can be described as an (unsharp) observable, that is, as a positive operator valued measure. We furthermore present extensions of this result to the free massless relativistic particle in one dimension and to a hypothetical physical system whose equilibrium state is given by the noncommutative integral. [ABSTRACT FROM AUTHOR]

We present the development of a flexible tape-drive target system to generate and control secondary high-intensity laser-plasma sources. Its adjustable design permits the generation of relativistic MeV particles and x rays at high-intensity (i.e., ≥1 × 1018 W cm−2) laser facilities, at high repetition rates (>1 Hz). The compact and robust structure shows good mechanical stability and a high target placement accuracy (<4 μm RMS). Its compact and flexible design allows for mounting in both the horizontal and vertical planes, which makes it practical for use in cluttered laser-plasma experimental setups. The design permits ∼170° of access on the laser-driver side and 120° of diagnostic access at the rear. A range of adapted apertures have been designed and tested to be easily implemented to the targetry system. The design and performance testing of the tape-drive system in the context of two experiments performed at the COMET laser facility at the Lawrence Livermore National Laboratory and at the Advanced Lasers and Extreme Photonics (ALEPH) facility at Colorado State University are discussed. Experimental data showing that the designed prototype is also able to both generate and focus high-intensity laser-driven protons at high repetition rates are also presented. [ABSTRACT FROM AUTHOR]

Electromagnetic fields of relativistic charged particles have a broad frequency spectrum and a sophisticated spatial structure. Field lines offer a visual representation of this spatial structure. In this article, we derive a general set of equations for the field lines of any moving charged particle. The electric field lines are completely determined by the unit vector from the retarding point to the observation point. After proper transformations, the field line equations describe the rotation of this vector with an angular velocity coinciding with Thomas precession. In some cases, including all planar trajectories, the field line equations reduce to linear differential equations with constant coefficients. We present a detailed derivation of these equations and their general analytical solution. We then illustrate this method by constructing field lines for the "figure eight" motion of an electric charge moving under the influence of a plane wave, including complex field lines in three dimensions. [ABSTRACT FROM AUTHOR]

In this work, we present a combined experimental and theoretical study on the V L2,3-edge x-ray absorption (XAS) and x-ray magnetic circular dichroism (XMCD) spectra of VIVO(acac)2 and VIII(acac)3 prototype complexes. The recorded V L2,3-edge XAS and XMCD spectra are richly featured in both V L3 and L2 spectral regions. In an effort to predict and interpret the nature of the experimentally observed spectral features, a first-principles approach for the simultaneous prediction of XAS and XMCD spectra in the framework of wavefunction based ab initio methods is presented. The theory used here has previously been formulated for predicting optical absorption and MCD spectra. In the present context, it is applied to the prediction of the V L2,3-edge XAS and XMCD spectra of the VIVO(acac)2 and VIII(acac)3 complexes. In this approach, the spin-free Hamiltonian is computed on the basis of the complete active space configuration interaction (CASCI) in conjunction with second order N-electron valence state perturbation theory (NEVPT2) as well as the density functional theory (DFT)/restricted open configuration interaction with singles configuration state functions based on a ground state Kohn-Sham determinant (ROCIS/DFT). Quasi-degenerate perturbation theory is then used to treat the spin–orbit coupling (SOC) operator variationally at the many particle level. The XAS and XMCD transitions are computed between the relativistic many particle states, considering their respective Boltzmann populations. These states are obtained from the diagonalization of the SOC operator along with the spin and orbital Zeeman operators. Upon averaging over all possible magnetic field orientations, the XAS and XMCD spectra of randomly oriented samples are obtained. This approach does not rely on the validity of low-order perturbation theory and provides simultaneous access to the calculation of XMCD A, B, and C terms. The ability of the method to predict the XMCD C-term signs and provide access to the XMCD intensity mechanism is demonstrated on the basis of a generalized state coupling mechanism based on the type of the excitations dominating the relativistically corrected states. In the second step, the performance of CASCI, CASCI/NEVPT2, and ROCIS/DFT is evaluated. The very good agreement between theory and experiment has allowed us to unravel the complicated XMCD C-term mechanism on the basis of the SOC interaction between the various multiplets with spin S′ = S, S ± 1. In the last step, it is shown that the commonly used spin and orbital sum rules are inadequate in interpreting the intensity mechanism of the XAS and XMCD spectra of the VIVO(acac)2 and VIII(acac)3 complexes as they breakdown when they are employed to predict their magneto-optical properties. This conclusion is expected to hold more generally. [ABSTRACT FROM AUTHOR]

One of the most characteristic features of relativistic particle dynamics at cyclotron resonances is the stepwise dependence of energy and momentum on time [V. A. Buts and A. G. Zagorodny, Phys. Plasmas 28(2), 022311 (2021)]. The reason for these steps is the phase synchronization of charged particles and waves. To describe other features, we introduce new dependent variables in this paper. These variables allow us to find a convenient representation of the relativistic resonance that fits the numerical results and thus establish new expressions for the stationary phase, as well as analytically describe effects that were previously visible only in numerical experiment. In particular, the temporal width of the steps, the dynamics of particles on the steps, and, most importantly, the moments of random jumps of particles from one step to another are determined. Analysis of the obtained results opens the possibility to find the conditions for the unlimited acceleration of electrons by transverse electromagnetic waves in a vacuum without an external magnetic field. [ABSTRACT FROM AUTHOR]

We report the high gradient testing results of two single-cell off-axis coupled standing wave accelerating structures. Two brazed standing wave off-axis coupled structures with the same geometry were tested: one made of pure copper (Cu) and one made of a copper–silver (CuAg) alloy with a silver concentration of 0.08%. A peak surface electric field of 450 MV/m was achieved in the CuAg structure for a klystron input power of 14.5 MW and a 1 μs pulse length, which was 25% higher than the peak surface electric field achieved in the Cu structure. The superb high gradient performance was achieved because of the two major optimizations in the cavity's geometry: (1) the shunt impedance of the cavity was maximized for a peak surface electric field to accelerating gradient ratio of ∼2 for a fully relativistic particle, and (2) the peak magnetic field enhancement due to the input coupler was minimized to limit pulse heating. These tests allow us to conclude that C-band accelerating structures can operate at peak fields similar to those at higher frequencies while providing a larger beam iris for improved beam transport. [ABSTRACT FROM AUTHOR]

Nascent observations about the influence of kinetic instabilities on electron cyclotron emission (ECE) from runaway electrons (REs) have been detected and explored at the Aditya-Upgrade (Aditya-U) tokamak. The developed broadband ECE radiometer system offers wideband measurements by integrating several radio frequency units with a fixed intermediate frequency receiver with multiple channels, which is a novel approach to meet the needs of the localized measurements at various toroidal fields and extend the system dynamic range. The low density (ne ≤ 1 × 10−19 m−3) plasma discharges at Aditya-U are consistently accompanied by a 20%–40% increase in the ECE radiometer signal amplitude within 100 µs and sporadic step-like modulations. The Pitch Angle Scattering (PAS) of REs induced by kinetic instabilities is a potential candidate for their occurrence. This steep jump in the radiometer signals was detected due to its high temporal resolution of 10 µs. A "PREDICT" code that employs the relativistic test particle model validates these experimental findings of the radiometer diagnostic for the first time for Aditya-U tokamak. Preliminary observations of the ECE radiometer signals also show that additional gas puffs can be used to vary the trigger timings of such PAS events or even lead to their complete avoidance. [ABSTRACT FROM AUTHOR]

The "particle-in-a-box" problem is investigated for a relativistic particle obeying the Klein–Gordon equation. To find the bound states, the standard methods known from elementary non-relativistic quantum mechanics can only be employed for "shallow" wells. For deeper wells, when the confining potentials become supercritical, we show that a method based on a scattering expansion accounts for Klein tunneling (undamped propagation outside the well) and the Klein paradox (charge density increase inside the well). We will see that in the infinite well limit, the wave function outside the well vanishes, and Klein tunneling is suppressed: Quantization is, thus, recovered, similar to the non-relativistic particle in a box. In addition, we show how wave packets can be constructed semi-analytically from the scattering expansion, accounting for the dynamics of Klein tunneling in a physically intuitive way. [ABSTRACT FROM AUTHOR]

The motion of a relativistic charged particle in an external specified field of a planer single- and multifrequency circularly polarized electromagnetic wave of large amplitude in the presence of a constant uniform magnetic field (the Redmond field and the multifrequency Redmond field) when the relativistic consideration is required has been analyzed in detail. It is shown that the kinetic energy of a particle in the multi-frequency Redmond field depends not only on the intensity of the wave, and the frequencies of the carrier wave, but also on the direction of polarization of the wave (i.e., right- or left-handed), and the cyclotron frequency. The conditions required for autoresonant motion of a particle in an external field of a large-amplitude wave and the containment of a charged particle are considered. [ABSTRACT FROM AUTHOR]

Breaking of a plasma wave driven by a long beam of charged particles results in electron jets escaping from the plasma column and forming an electron halo. The halo is accompanied by a strong radial electric field around the plasma, which can distort the trajectories of relativistic charged particles that propagate near the plasma border or are injected into the plasma wave. We study the mechanisms of wave breaking and halo formation when the beam and plasma densities are comparable. If the plasma density is less than or of the order of the beam density, the wavebreaking is well described by a semi-analytical model, which agrees with simulations and allows us to calculate the position of wavebreaking points and determine the regions around the plasma column occupied by the halo. [ABSTRACT FROM AUTHOR]

Recently, in the context of Relativistic Quantum Information Theory (RQI) of massive spin-1/2 particles, it has been suggested that it is impossible to perform a momentum-independent spin measurement, showing the inadequacy of the spin reduced density matrix as a legitimate information resource. This is because there is an unavoidable ambiguity in the definition of the spin of a moving particle. In this paper, by introducing a vector bundle theoretic way to view the single-particle state space, we try to rule out this ambiguity. The discrete degree of freedom of the resulting representation space contains information about the Pauli–Lubanski four-vector of the particle instead of the ambiguous spin. Comparing this representation with the standard one used in the RQI literature, we show that the discrete degree of freedom of the standard representation space attains the meaning of the Newton–Wigner spin. In addition, using this viewpoint, we give a mathematical proof of why the spin reduced density matrix is meaningless, which is stronger than the previous claims in that it asserts that the matrix is void of any meaning at all, not just in terms of the impossibility of measurement or Lorentz non-covariance. We give a way (which turns out to be the only way) to modify it to obtain the Pauli–Lubanski reduced density matrix, which is covariant under Lorentz transformations. [ABSTRACT FROM AUTHOR]

A pairwise nuclear fusion algorithm for particle-in-cell simulations for arbitrarily weighted macro-particles at relativistic energies is proposed. When comparing with a recent study by Higginson et al. [J. Comput. Phys. 388, 439 (2019)], our method is also fitted with the widely used Coulomb scattering algorithm by Nanbu and Yonemura [J. Comput. Phys. 145, 639 (1998)] and Sentoku and Kemp [J. Comput. Phys. 227, 6846 (2008)] and can be implemented into a particle-in-cell simulation code with marginal efforts. The algorithm is benchmarked in situations with like-particles, unlike-particles, thermonuclear plasmas, and beam–target fusion. It is shown that only 50–100 macro-particles per cell are needed for the repeatability of fusion yields around 1%. [ABSTRACT FROM AUTHOR]

In this paper, we analyze trajectories of spacelike curves that are critical points of a Lagrangian depending on its total torsion. We focus on two important families of spacetimes, generalized Robertson–Walker and standard static spacetimes. For the former, we show that such trajectories are those with a constant curvature. For the latter, we also obtain a characterization in terms of the curvature of the trajectory but in this case measured with an appropriate conformal metric. [ABSTRACT FROM AUTHOR]

We have obtained the asymptotic velocity of a relativistic charged particle in static and uniform electric and magnetic fields with arbitrary orientations of the fields and with an arbitrary ratio of a = |E|/|B|, where the particle is assumed highly relativistic and has a constant velocity. The obtained solution corresponds to the relativistic E × B drift velocity of the guiding-center, which has features different from those of the non-relativistic drift velocity. The latter is given by v D/c = E × B/|B|2, but in the relativistic case, an additional drift motion exists in the direction that is perpendicular to both B and v D. The dependence of drift velocity on the angle between B and E is also modified substantially. [ABSTRACT FROM AUTHOR]

At short time scales, the inertia term becomes relevant for the magnetization dynamics of ferromagnets and leads to nutation for the magnetization vector. For the case of spatially extended magnetic systems, for instance, Heisenberg spin chains with the isotropic spin-exchange interaction, this leads to the appearance of a collective excitation, the "nutation wave," whose properties are elucidated by analytical arguments and numerical studies. The one-particle excitations can be identified as relativistic massive particles. These particles, the "nutatons," acquire their mass via the Brout–Englert–Higgs mechanism, through the interaction of the wave with an emergent topological gauge field. This spin excitation would appear as a peak in the spectrum of the scattering structure factor in inelastic neutron scattering experiments. The high frequency and speed of the nutation wave can open paths for realizing ultrafast spin dynamics. [ABSTRACT FROM AUTHOR]

In this paper, we consider the mean field limit and non-relativistic limit of the relativistic Vlasov–Maxwell particle system to the Vlasov–Poisson equation. With the relativistic Vlasov–Maxwell particle system being a starting point, we carry out the estimates (with respect to N and c) between the characteristic equation of both the Vlasov–Maxwell particle model and the Vlasov–Poisson equation, where the probabilistic method is exploited. In the last step, we take both a large N limit and a non-relativistic limit (meaning c tending to infinity) to close the argument. Deriving such a mean-field limit for interactions with Coulomb singularity is a difficult task; therefore, we introduce an N-dependent mollifier to smoothen the interactions. Note that the length scale of our mollifier is N−α for an α that can be chosen arbitrarily close to but smaller than 1/3, which improves previous results in the literature on deriving Vlasov–Maxwell in the non-relativistic setting. [ABSTRACT FROM AUTHOR]

We study the relativistic dynamics of a particle carrying a non-Abelian charge in the presence of a non-Abelian background electromagnetic field. To this end, we extract the non-Abelian Dirac Hamiltonian from a system describing the interaction between the Yang–Mills field and a spin-1/2 field. The dynamics of a particle with non-Abelian charge is quantized directly by analogy with its quantum theory. By choosing a suitable non-Abelian gauge field, we investigate the spectrum in two-dimensional space, paying particular attention to the role of the total angular momentum. Relativistic Landau levels are obtained explicitly by means of an analytical method. The wave functions of the system are obtained in terms of the generalized Laguerre polynomials. Interesting features of such models are discussed through the spectrum. [ABSTRACT FROM AUTHOR]

A new method to determine localized complex-valued one-electron functions in the occupied space is presented. The approach allows the calculation of localized orbitals regardless of their structure and of the entries in the spinor coefficient matrix, i.e., one-, two-, and four-component Kramers-restricted or unrestricted one-electron functions with real or complex expansion coefficients. The method is applicable to localization schemes that maximize (or minimize) a functional of the occupied spinors and that use a localization operator for which a matrix representation is available. The approach relies on the approximate joint diagonalization (AJD) of several Hermitian (symmetric) matrices which is utilized in electronic signal processing. The use of AJD in this approach has the advantage that it allows a reformulation of the localization criterion on an iterative 2 × 2 pair rotating basis in an analytical closed form which has not yet been described in the literature for multi-component (complex-valued) spinors. For the one-component case, the approach delivers the same Foster-Boys or Pipek-Mezey localized orbitals that one obtains from standard quantum chemical software, whereas in the multi-component case complex-valued spinors satisfying the selected localization criterion are obtained. These localized spinors allow the formulation of local correlation methods in a multi-component relativistic framework, which was not yet available. As an example, several heavy and super-heavy element systems are calculated using a Kramers-restricted self-consistent field and relativistic two-component pseudopotentials in order to investigate the effect of spin-orbit coupling on localization. [ABSTRACT FROM AUTHOR]

In this work we report very accurate variational calculations of the complete pure vibrational spectrum of the D2 molecule performed within the framework where the Born-Oppenheimer (BO) approximation is not assumed. After the elimination of the center-of-mass motion, D2 becomes a three-particle problem in this framework. As the considered states correspond to the zero total angular momentum, their wave functions are expanded in terms of all-particle, one-center, spherically symmetric explicitly correlated Gaussian functions multiplied by even non-negative powers of the internuclear distance. The nonrelativistic energies of the states obtained in the non-BO calculations are corrected for the relativistic effects of the order of α2 (where α = 1/c is the fine structure constant) calculated as expectation values of the operators representing these effects. [ABSTRACT FROM AUTHOR]

Electronic decay of the inner-valence Ar 3s-1 vacancy is energetically forbidden in an isolated argon atom and in all rare gas dimers where argon is present. However, if an argon atom has at least two suitable rare gas atoms in its neighborhood, the Ar 3s-1 vacancy may decay electronically via an electron transfer mediated decay (ETMD) mechanism. An ArXe2 cluster is considered in the present paper as an example of such systems. The single and double ionization spectra of different ArXe2 isomers as well as of homonuclear Ar2 and Xe2 and heteronuclear ArXe clusters have been calculated by means of propagator methods to reveal possible electronic decay channels. A four-component version of the one-particle propagator utilizing the Dirac–Coulomb Hamiltonian was employed to obtain the single ionization potentials of the clusters studied. Hereby electron correlation, scalar relativistic effects, and spin-orbit couplings are described in a consistent manner. A two-particle propagator in its one-component form, in conjunction with effective core potentials to account consistently for correlation and scalar relativistic effects, was used to calculate the double ionization potentials. ETMD is shown to be the only possible electronic decay process of the Ar 3s-1 vacancy in the ArXe2 cluster. In clusters with more Xe atoms, alternative electronic decay mechanisms may appear. [ABSTRACT FROM AUTHOR]

We presented a two-component relativistic quantum-chemical theory for magnetic shielding constants, which is based on the infinite-order Douglas–Kroll (IODK) transformation. Two-electron relativistic corrections were also generated using the IODK transformation, although negligibly small terms were discarded. The use of small-component basis functions was completely excluded from the present theory. We examined the combination of the levels of relativistic one- and two-electron terms and magnetic interaction terms using the first-order Foldy–Wouthuysen (FW1), the second-order Douglas–Kroll (DK2), and the infinite-order Douglas–Kroll (IODK) transformations, as well as the lowest-order (c-2) Breit–Pauli approximation. We calculated the magnetic shielding constants of several closed-shell atoms using the FW1, DK2, IODK, and Breit–Pauli Hamiltonians. The IODK Hamiltonian reproduced well the results calculated by the four-component Dirac–Fock–Coulomb theory: The maximum deviation is only about 2.2%. We found that the accuracy of the magnetic shielding constants is strongly affected by the relativistic treatments of one-electron magnetic interaction, while the effect of the two-component two-electron relativistic corrections is relatively small. We also discussed the picture change effect on magnetic operators. [ABSTRACT FROM AUTHOR]

The magnetic shielding σ of 3He is studied. The complete relativistic corrections of order O(α2), leading QED corrections of order O(α3 ln α), and finite nuclear mass effects of order O(m/mN) are calculated with high numerical precision. The resulting theoretical predictions for σ=59.967 43(10)×10-6 are the most accurate to date among all elements and support the use of 3He as a NMR standard. [ABSTRACT FROM AUTHOR]

It is shown that 2E states in tetrahedral systems exhibit a linear E×T Jahn–Teller effect which is of purely relativistic origin (that is, it arises from the spin-orbit-coupling operator). The electrostatic interactions give rise to a Jahn–Teller effect which is quadratic in the T displacements. The 4×4 Hamiltonian matrix in a diabatic spin-electron basis is derived by an expansion of the electrostatic electronic Hamiltonian and the Breit–Pauli spin-orbit operator in powers of the Jahn–Teller active normal mode and taking account of symmetry selection rules for the matrix elements. The adiabatic potential-energy functions of the 2E×T system are doubly degenerate (Kramers degeneracy). For small displacements from the tetrahedral reference geometry, the adiabatic potential-energy surfaces represent a double cone in four-dimensional space, which is a novel topography of Jahn–Teller potential-energy surfaces. The topological phases of the adiabatic electronic wave functions are discussed. [ABSTRACT FROM AUTHOR]

Different generalized Douglas-Kroll transformed Hamiltonians (DKn, n=1, 2,...,5) proposed recently by Hess et al. are investigated with respect to their performance in calculations of the spin–orbit splittings. The results are compared with those obtained in the exact infinite-order two-component (IOTC) formalism which is fully equivalent to the four-component Dirac approach. This is a comprehensive investigation of the ability of approximate DKn methods to correctly predict the spin–orbit splittings. On comparing the DKn results with the IOTC (Dirac) data one finds that the calculated spin–orbit splittings are systematically improved with the increasing order of the DK approximation. However, even the highest-order approximate two-component DK5 scheme shows certain deficiencies with respect to the treatment of the spin–orbit coupling terms in very heavy systems. The meaning of the removal of the spin-dependent terms in the so-called spin-free (scalar) relativistic methods for many-electron systems is discussed and a computational investigation of the performance of the spin-free DKn and IOTC methods for many-electron Hamiltonians is carried out. It is argued that the spin-free IOTC rather than the Dirac-Coulomb results give the appropriate reference for other spin-free schemes which are based on approximate two-component Hamiltonians. This is illustrated by calculations of spin-free DKn and IOTC total energies, r-1 expectation values, ionization potentials, and electron affinities of heavy atomic systems. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

A new approach for calculating relativistic corrections to the nuclear magnetic shieldings is presented. Starting from a full relativistic second order perturbation theory expression a two-component formalism is constructed by transforming matrix elements using the elimination of small component scheme and separating out the contributions from the no-virtual pair and the virtual pair part of the second order corrections to the energy. In this way we avoid a strong simplification used previously in the literature. We arrive at final expressions for the relativistic corrections which are equivalent to those of Fukui et al. [J. Chem Phys. 105, 3175 (1996)] and at some other additional terms correcting both the paramagnetic and the diamagnetic part of the nuclear magnetic shielding. Results for some relativistic corrections to the shieldings of the heavy and light nuclei in HX and CH[sub 3]X (X = Br, I) at both random phase and second order polarization propagator approach levels are given. [ABSTRACT FROM AUTHOR]

Propagation of short and ultraintense laser pulses in a semi-infinite space of overdense hydrogen plasma is analyzed via fully relativistic, real geometry particle-in-cell (PIC) simulations including radiation friction. The relativistic transparency and hole-boring regimes are found to be sensitive to the transverse plasma field, backward light reflection, and laser pulse filamentation. For laser intensities approaching I ∼ 1024 W/cm2, the direct laser acceleration of protons, along with ion Coulomb explosion, results in their injection into the acceleration phase of the compressed electron wave at the front of the laser pulses. The protons are observed to be accelerated up to 10–20 GeV with densities around a few times the critical density. The effect qualitatively depends on initial density and laser intensity, disappearing with the initial density increase or intensity decrease. [ABSTRACT FROM AUTHOR]

Constructing observables that describe the localization of relativistic particles is an important foundational problem in relativistic quantum field theory (QFT). The description of localization in terms of single-time observables leads to conflict with the requirement of causality. In this paper, we describe particle localization in terms of time-of-arrival observables, defined in terms of the interaction between a quantum field and a measuring apparatus. The resulting probabilities are linear functionals of QFT correlation functions. Specializing to the case of a scalar field, we identify several time-of-arrival observables differing on the way that the apparatus localizes particle-detection records. Maximum localization is obtained for a unique observable that is related to the Newton-Wigner position operator. Finally, we define a measure of localizability for relativistic particles in terms of a novel time-energy uncertainty relation for the variance of the time of arrival. [ABSTRACT FROM AUTHOR]

We develop a general 3-D relativistic test particle (TP) simulation code to examine the trajectories and pitch angle variations of test electrons. We investigate the conditions when the electrons transit broadband, parallel propagating H+ band electromagnetic ion cyclotron (EMIC) waves to find whether the classical quasilinear theory (QLT) can be applied to interactions between H+ band EMIC waves and radiation belt relativistic (and ultra-relativistic) electrons. We find that to reach good consistency between TP scattering coefficients and QLT calculations, the wave-particle resonant interaction time (which indicates the time of particles traveling in the wave fields and being resonant with the wave fields) must be carefully calculated to ensure the validity of the linear diffusion process. This wave-particle resonant interaction time depends largely on the wave amplitude, the bandwidth, and the initial parameters of electrons for TP simulations; once the time of electrons traveling in the wave fields becomes large enough when the pitch angles of electrons scattered by wave fields reach the maximal value limited by the resonance condition and cannot be diffused any longer, the linear diffusion process of particles defined by QLT will not be valid any longer. When the resonant electrons start to travel through the wave field, they undergo the linear diffusion process resulting from the pitch angle scattering by the H+ band EMIC wave field. As the time of traveling in the wave fields increases, the test electrons will suffer effective pitch angle scattering and the pitch angles of these electrons will reach the maximum value limited by the resonance condition, which is determined by the wave and electron parameters. These electrons are then reflected by the wave fields and the linear wave-particle interactions defined by QLT will not be valid anymore. This kind of wave-particle interaction subsequently introduces considerable deviation of TP diffusion coefficients from those predicted by QLT calculations. Our results demonstrate that the general validity of QLT in describing how broadband EMIC waves affect radiation belt relativistic electrons is highly related to the time of electron traveling in the wave fields, which tends to increase for smaller wave power and broader wave frequency spectra. [ABSTRACT FROM AUTHOR]

Offers information on a study which investigated relativistic sheet electron beams with periodic wiggler focusing. Theoretical background; Methodology; Results and discussion.

Presents information on a study which examined the interaction of a relativistic electron beam generation which is injected into a magnetized hydrogen plasma. Methodology of the study; Results and discussion; Conclusion.

The dispersion relation of relativistic rectilinear electron beam propagating along a guide magnetic field in a dielectric is investigated by cold fluid model. In such a system, due to anomalous Doppler effect, the instability occurs when the electron velocity exceeds the wave phase velocity. The growth rate and spatial growth rate are studied analytically and the nonlinear saturated efficiency is given analytically for the first time. Numerical results show that the saturated efficiency approaches about 10%–30%. The distinctive interaction mechanism is promising for the design of a new kind of compact high-power microwave generation devices. [ABSTRACT FROM AUTHOR]

We formulate a noncompact version of the Kuramoto model by replacing the invariance group SO(2) of the plane rotations by the noncompact group SO(1, 1). The N equations of the system are expressed in terms of hyperbolic angles αi and are similar to those of the Kuramoto model, except that the trigonometric functions are replaced by hyperbolic functions. Trajectories are generally unbounded, nevertheless synchronization occurs for any positive couplings κi, arbitrary positive multiplicative parameters λi and arbitrary exponents ωi. There are no critical values for the coupling constants. We measure the onset of synchronization by means of several order and disorder parameters. We show numerically and by means of exact solutions for N = 2 that solutions can develop singularities if the coupling constants are negative, or if the initial values are not suitably restricted. We describe a physical interpretation of the system as a cluster of interacting relativistic particles in 1 + 1 dimensions, subject to linear repulsive forces with space-time trajectories parametrized by the rapidity αi. The trajectories synchronize provided that the particle separations remain predominantly time-like, and the synchronized cluster can be viewed as a bound state of N relativistic particle constituents. We extend the defining equations of the system to higher dimensions by means of vector equations which are covariant with respect to SO(p, q). [ABSTRACT FROM AUTHOR]

Drive particle beams in linear or weakly nonlinear regimes of the plasma wakefield accelerator quickly reach a radial equilibrium with the wakefield, which is described in detail for the first time. The equilibrium beam state and self-consistent wakefields are obtained by combining analytical relationships, numerical integration, and first-principles simulations. In the equilibrium state, the beam density is strongly peaked near the axis, the beam radius is constant along most of the beam, and longitudinal variation of the focusing strength is balanced by varying beam emittance. The transverse momentum distribution of beam particles depends on the observation radius and is neither separable nor Gaussian. [ABSTRACT FROM AUTHOR]

We present a pedagogical discussion of the Coriolis field, emphasizing its not-so-well-understood aspects. We show that this field satisfies the field equations of the so-called Newton-Cartan theory, a generalization of Newtonian gravity that is covariant under changes of arbitrarily rotating and accelerated frames. Examples of solutions of this theory are given, including the Newtonian analogue of the Gödel universe. We discuss how to detect the Coriolis field by its effect on gyroscopes, of which the gyrocompass is an example. Finally, using a similar framework, we discuss the Coriolis field generated by mass currents in general relativity, and its measurement by the gravity probe B and LAGEOS/LARES experiments [ABSTRACT FROM AUTHOR]

We obtain the expressions for the energy and momentum of a relativistic particle by incorporating the equivalence of mass and energy into Newtonian mechanics. [ABSTRACT FROM AUTHOR]

A tunable hard x-ray source from intense laser interacting with overdense solid targets is proposed. It is shown that the incident angle of the laser plays an important role in influencing the radiation quality, including the spectrum of the radiation, the energy conversion efficiency from laser to radiation, and the angular distribution of the radiation. The two dimensional relativistic particle-in-cell simulations shows that, to get the highest energy conversion efficiency, the optimal incident angle for the present simulation parameters is 30°, and the energy conversion efficiency from laser to radiation in the optimal incident angle is about 5%, which is far more efficient than other incidence condition using the same laser pulse. The intensity of the laser used in the simulation is 1:34 × 1022W=cm². Detailed analysis shows that the vacuum heating radiation mechanism is the dominant mechanism responsible for hard x-ray emission, and the radiation frequency spectrum is tunable when the incident angle changes. [ABSTRACT FROM AUTHOR]

Numerical algorithms to load relativistic Maxwell distributions in particle-in-cell (PIC) and Monte- Carlo simulations are presented. For stationary relativistic Maxwellian, the inverse transform method and the Sobol algorithm are reviewed. To boost particles to obtain relativistic shifted- Maxwellian, two rejection methods are proposed in a physically transparent manner. Their acceptance efficiencies are ≈50% for generic cases and 100% for symmetric distributions. They can be combined with arbitrary base algorithms. [ABSTRACT FROM AUTHOR]