Ultrarelativistic Regime Research Articles

A fresh look at the concept of a relativistic oscillator

The theory of a unidimensional relativistic oscillator is developed assuming a frame of reference fixed to the oscillator. This approach is at variance with conventional consideration of the same problem in an inertial frame of reference. It is shown that examination of a freely falling body by an observer sitting on the oscillator is advantageous because it permits to avoid introducing of any additional conditions required to ensure the Lorentz invariance of the theory. The time track of such a body in a rigid accelerated frame of reference is derived in a general manner. The effect of a systematic delay of time during vibrations is unveiled in the ultrarelativistic regime.

Photon emission and radiation reaction effects in surface plasma waves in ultra-high intensities

Manipulating and harnessing plasmonic phenomena in the ultra-relativistic regime reveal promising prospects for the use of surface plasma waves (SPW) to create high-energy particle and radiation sources in the next generation of multi-petawatt lasers. Indeed, relativistic high-charge electron bunches can be produced by SPW excited by ultra-high intensity femtosecond lasers impinging on a periodically modulated solid-density target. In this regime, there is good evidence that SPW excitation survives and that the produced electron bunches experience strong acceleration, thus emitting large amounts of electromagnetic radiation. Therefore, extending the study to ultra-high laser intensities (I>1021 W/cm2), the use of a resonant grating for SPW generation represents an interesting alternative to light sources, as the energy lost by electrons due to radiation emission is transferred to high-energy γ photons. In addition, we show that using a laser with wavefront rotation coupled with a tailored blazed grating improves photon emission in the ultra-relativistic regime of interaction.

Galileo Observation of Electron Spectra Dawn‐Dusk Asymmetry in the Middle Jovian Magnetosphere: Evidence for Convection Electric Field

AbstractIn Jupiter's middle magnetosphere, debate remains on the controlling physics of electron acceleration to the ultrarelativistic regime. Some local‐time asymmetric processes regulating MeV electrons may have their hold across electron spectra, leaving imprints down to 10–100s keV energies. Spectra at these lower energies can be measured with finite energy resolution, which is hardly achieved for MeV electrons. We investigate 10–100s keV electron spectra using Galileo measurements. We show that at 15–20 RJ, the power‐law exponents exhibit a previously unexpected dawn‐dusk asymmetry. This asymmetry is more prominent for 100s‐keV spectra, persistent but enhanced from 1996 to 2001. These match the theory of transport driven by a dawn‐to‐dusk electric field. Contrary to past expectations of dawn‐to‐dusk electric field at Io plasma torus (IPT) extending outward from 6 RJ, the origin of the field we infer may be completely different, despite its orientation and impacts on electron energization similar with the IPT one.

Energy enhancement of laser-driven ions by radiation reaction and Breit–Wheeler pair production in the ultra-relativistic transparency regime

Abstract The impact of radiation reaction and Breit–Wheeler pair production on the acceleration of fully ionized carbon ions driven by an intense linearly polarized laser pulse has been investigated in the ultra-relativistic transparency regime. Against initial expectations, the radiation reaction and pair production at ultra-high laser intensities are found to enhance the energy gained by the ions. The electrons lose most of their transverse momentum, and the additionally produced pair plasma of Breit–Wheeler electrons and positrons co-streams in the forward direction as opposed to the existing electrons streaming at an angle above zero degree. We discuss how these observations could be explained by the changes in the phase velocity of the Buneman instability, which is known to aid ion acceleration in the breakout afterburner regime, by tapping the free energy in the relative electron and ion streams. We present evidence that these non-classical effects can further improve the highest carbon ion energies in this transparency regime.

BMS3 (Carrollian) field theories from a bound in the coupling of current-current deformations of CFT2

Two types of Carrollian field theories are shown to emerge from finite current-current deformations of toroidal CFT2’s when the deformation coupling is precisely fixed, up to a sign. In both cases the energy and momentum densities fulfill the BMS3 algebra. Applying these results to the bosonic string, one finds that the electric-like deformation (positive coupling) reduces to the standard tensionless string. The magnetic-like deformation (negative coupling) yields to a new theory, still being relativistic, devoid of tension and endowed with an “inner Carrollian structure”. Classical solutions describe a sort of “self-interacting null particle” moving along generic null curves of the original background metric, not necessarily geodesics. This magnetic-like theory is also shown to be recovered from inequivalent limits in the tension of the bosonic string. Electric- and magnetic-like deformations of toroidal CFT2’s can be seen to correspond to limiting cases of continuous exactly marginal (trivial) deformations spanned by an SO(1,1) automorphism of the current algebra. Thus, the absolute value of the current-current deformation coupling is shown to be bounded. When the bound saturates, the deformation ceases to be exactly marginal, but still retains the full conformal symmetry in two alternative ultrarelativistic regimes.

Thermodynamics of a charged relativistic ideal Boltzmann gas

This paper presents a toy model of a charged relativistic classical gas in flat spacetime of an arbitrary number of dimensions equipped with some ``pair production'' mechanism. Working with the microcanonical ensemble, the charge is taken to be conserved in contrast with the total number of ``particles'' plus ``antiparticles'' which varies with temperature $T$. Thermodynamics of the classical gas is detailed studied in the nonrelativistic ($Mc^{2}\gg kT$) as well as in the ultrarelativistic ($Mc^{2}\ll kT$) regimes. It is shown that, although we are dealing with classical distributions, at the ultrarelativistic regime the behavior of the gas is Planckian. We also compare the thermodynamics of the toy model with that of quantum gases.

Giant orbital magnetic moments and paramagnetic shift in artificial relativistic atoms and molecules.

Materials such as graphene and topological insulators host massless Dirac fermions that enable the study of relativistic quantum phenomena. Single quantum dots and coupled quantum dots formed with massless Dirac fermions can be viewed as artificial relativistic atoms and molecules, respectively. Such structures offer a unique testbed to study atomic and molecular physics in the ultrarelativistic regime (particle speed close to the speed of light). Here we use a scanning tunnelling microscope to create and probe single and coupled electrostatically defined graphene quantum dots to unravel the magnetic-field responses of artificial relativistic nanostructures. We observe a giant orbital Zeeman splitting and orbital magnetic moment up to ~70 meV T-1 and ~600μB (μB, Bohr magneton) in single graphene quantum dots. For coupled graphene quantum dots, Aharonov-Bohm oscillations and a strong Van Vleck paramagnetic shift of ~20 meV T-2 are observed. Our findings provide fundamental insights into relativistic quantum dot states, which can be potentially leveraged for use in quantum information science.

The eikonal operator at arbitrary velocities I: the soft-radiation limit

Observables related to the real part of the gravitational eikonal, such as the deflection angle and time delay, have been found so far to have a smooth post-Minkowskian (PM) expansion whose validity extends from the non-relativistic to the most extreme ultra-relativistic (UR) regime, which smoothly connects with massless particle collisions. To describe gravitational radiation, the eikonal phase has to be promoted to a unitary operator for which we motivate a proposal and start discussing properties in the soft-radiation limit. A convergent PM expansion is found to only hold below an UR bound (discussed in the GR literature in the seventies) above which a different expansion is instead needed implying, in general, some non-analyticity in Newton’s constant. In this extreme UR regime soft radiative observables receive contributions only from gravitons and are therefore universal. This generalises the pattern discussed in [1] beyond the elastic case.

Electron spin- and photon polarization-resolved probabilities of strong-field QED processes

A derivation of fully polarization-resolved probabilities is provided for high-energy photon emission and electron-positron pair production in ultrastrong laser fields. The probabilities resolved in both electron spin and photon polarization of incoming and outgoing particles are indispensable for developing QED Monte Carlo and QED-particle-in-cell codes, aimed at the investigation of polarization effects in nonlinear QED processes in ultraintense laser-plasma and laser-electron beam interactions, and other nonlinear QED processes in external ultrastrong fields, which involve multiple elementary processes of a photon emission and pair production. The quantum operator method introduced by Baier and Katkov is employed for the calculation of probabilities within the quasiclassical approach and the local constant field approximation. The probabilities for the ultrarelativistic regime are given in a compact form and are suitable to describe polarization effects in strong laser fields of arbitrary configuration, rendering them very well suited for applications.

B-field induced mixing between Langmuir waves and axions

We present an analytic study of the dispersion relation for an isotropic magnetized plasma interacting with axions. We provide a quantitative picture of the electromagnetic plasma oscillations in both the ultrarelativistic and nonrelativistic regimes and considering both non-degenerate and degenerate media, accounting for the dispersion curves as a function of the plasma temperature and the ratio of the plasma phase velocity to the characteristic velocity of particles. We include the modifications on the Landau damping of plasma waves induced by the presence of the axion field, and we comment on the effects of damping on subluminal plasma oscillations.

Neutrino–(anti)neutrino forward scattering potential for massive neutrinos at low energies

In this work, we calculate the expression for the potential due to neutrino–(anti)neutrino forward scattering at low energies [Formula: see text] for ultra-relativistic massive neutrinos [Formula: see text], a representative regime within astrophysical scenarios. There is a broadly used expression for this potential in the literature, which, however, lacks an explicit derivation from basic principles of quantum field theory. Therefore, this paper has an intention to guide the reader through the steps and concepts to derive this potential, trying to be clear and pedagogical. Moreover, we used a rigorous approach concerning the massive nature of the neutrinos, using massive quantized neutrino fields throughout the entire process, while the usual approach is to consider massless neutrino fields at the interaction. In this context, we explicitly show the validity of the massless neutrino fields approximation at the ultra-relativistic regime, as expected. As the last step, we connect the potential expression to the density matrix formalism, which is a usual framework for works considering neutrino–neutrino interactions. We also discuss some theoretical details through the paper such as the normal ordering of quantum operators and the implications of massive fields in the neutrino state at its production.

Radiative pulsar magnetospheres: oblique rotators

ABSTRACT Pulsar magnetospheres are filled with relativistic pairs copiously emitting photons detected from the radio wavelengths up to high and very high energies in the GeV and sometimes in the TeV range. Efficient particle acceleration converts the stellar rotational kinetic energy into radio, X-ray, and gamma-ray photons. Force-free magnetospheres, being dissipationless, cannot operate this conversion. Some non-ideal plasma effects must set in within the magnetosphere. In this paper, we compute numerical solutions of pulsar radiative magnetospheres in the radiation reaction limit, where radiation fully balances single particle acceleration. Using an appropriate Ohm’s law, the dissipation is only controlled by the pair multiplicity factor κ. Moreover, we allow for either a minimal radiative region where dissipation is added only where required or for a force-free inside radiative outside model. This approach naturally and self-consistently connects the particle dynamics to its radiation field in the ultra-relativistic regime. Our solutions tend to the force-free limit for moderately large multiplicities, κ ≫ 1, decreasing the spin-down energy conversion into radiation. Nevertheless, for sufficiently low multiplicity κ ≲ 1, a significant fraction of the spin-down energy flows into radiation via particle acceleration. The work done by the electromagnetic field on the plasma mainly occurs in the current sheet of the striped wind, right outside the light-cylinder. Nevertheless the impact on the magnetic topology is negligible whatever the model. Therefore, the associated sky maps and light curves are only weakly impacted as shown.

Theoretical approaches for hard electron bremsstrahlung and their scaling properties in the ultrarelativistic regime

Bremsstrahlung angular and frequency distributions from 35-MeV electrons colliding with lead are calculated within the Dirac partial-wave (DW) theory. These benchmark results are compared with the Dirac-asymptotic Sommerfeld-Maue approach, with an analytical approximation to this DaSM model, and with the Sommerfeld-Maue (SM) theory, in order to investigate the validity of these simpler theories for photons with frequencies beyond 25 MeV. Scaling properties with respect to the collision energy, the photon emission angle, and the energy of the scattered electron are used to extend the predictions at 35 MeV to higher collision energies. For the angle-integrated photon spectrum a Green's-function-based theory by Milstein and coworkers [J. Exp. Theor. Phys. 100, 1 (2005)] serves as a complement to the DW theory at the lower photon frequencies. Earlier conjectures are confirmed that, for the singly differential cross section, the SM theory is applicable for frequencies at least some 5 MeV below the short-wavelength limit.

Retrieving Transient Magnetic Fields of Ultrarelativistic Laser Plasma via Ejected Electron Polarization.

Interaction of an ultrastrong short laser pulse with nonprepolarized near-critical density plasma is investigated in an ultrarelativistic regime, with an emphasis on the radiative spin polarization of ejected electrons. Our particle-in-cell simulations show explicit correlations between the angle resolved electron polarization and the structure and properties of the transient quasistatic plasma magnetic field. While the magnitude of the spin signal is the indicator of the magnetic field strength created by the longitudinal electron current, the asymmetry of electron polarization is found to gauge the islandlike magnetic distribution which emerges due to the transverse current induced by the laser wave front. Our studies demonstrate that the spin degree of freedom of ejected electrons could potentially serve as an efficient tool to retrieve the features of strong plasma fields.

Single particle entanglement in the mid- and ultra-relativistic regime

In this work we analyse the amount of entanglement associated with the spin and momentum degrees of freedom of a single massive spin- particle from a relativistic perspective. The effect of a Lorentz boost introduces a Wigner rotation that correlates the spin and momentum degrees of freedom. We show that the natural basis to discuss the geometrical effects of the boost are the helicity eigenstates in the rest frame. In the mid-relativistic regime (where the Wigner rotation angle is limited by ) we prove for states with equal helicity that the entanglement with respect to the Wigner rotation angle is monotonically decreasing, however, in the ultra-relativistic regime () the entanglement is increasing. If the states are prepared as a superposition of unequal helicity eigenstates, the monotonic behaviour is inverted. This implies that in the ultra-relativistic regime a geometrical setup can be found such that the amount of entanglement exhibits local maxima or minima. This shows a counter-intuitive behaviour of the relative amount of entanglement, an effect due to the internal and external geometrical configuration space, and points towards the difficulties in achieving a Lorentz invariant formulation of entanglement in general.

Effect of relativistically degenerate electrons on linear and nonlinear structures in ion temperature gradient driven pure drift mode

Low frequency, electrostatic, pure drift mode is investigated in dense magnetized electron-ion plasma in the presence of relativistically degenerate electrons using quantum magnetohydrodynamic model (QMHD). Ions are considered as warm classical particles. Inhomogeneities in background ion density, ion temperature and external magnetic field are taken into account. In the linear regime, dispersion relation is obtained and plotted for both non-relativistic and ultra-relativistic regimes. Parametric study shows that for both non-relativistic and ultra-relativistic cases, growth rate of the wave increases by increasing, , which is the ratio of background ion temperature to density. In the nonlinear case, solitary solutions are obtained by using the functional variable method. Graphical illustrations are used to show the effect of relativistically degenerate electrons and other parameters like electron and ion number densities, magnetic field and ion temperature on nonlinear structures in both non relativistic and relativistic regimes. This work may be helpful to understand low frequency phenomena in dense inhomogeneous plasmas like neutron stars, white dwarfs and next generation lasers.

The eikonal approach to gravitational scattering and radiation at mathcal{O} (G3)

Using mathcal{N} = 8 supergravity as a theoretical laboratory, we extract the 3PM gravitational eikonal for two colliding massive scalars from the classical limit of the corresponding elastic two-loop amplitude. We employ the eikonal phase to obtain the physical deflection angle and to show how its non-relativistic (NR) and ultra-relativistic (UR) regimes are smoothly connected. Such a smooth interpolation rests on keeping contributions to the loop integrals originating from the full soft region, rather than restricting it to its potential sub-region. This task is efficiently carried out by using the method of differential equations with complete near-static boundary conditions. In contrast to the potential-region result, the physical deflection angle includes radiation-reaction contributions that are essential for recovering the finite and universal UR limit implied by general analyticity and crossing arguments. We finally discuss the real emission of massless states, which accounts for the imaginary part of the 3PM eikonal and for the dissipation of energy-momentum. Adopting a direct approach based on unitarity and on the classical limit of the inelastic tree-level amplitude, we are able to treat mathcal{N} = 8 and General Relativity on the same footing, and to complete the conservative 3PM eikonal in Einstein’s gravity by the addition of the radiation-reaction contribution. We also show how this approach can be used to compute waveforms, as well as the differential and integrated spectra, for the different radiated massless fields.

Scalar Radiation in Interaction of Cosmic String with Point Charge

We consider the scalar bremsstrahlung of the spinless relativistic particle, which interacts with infinitely thin cosmic string by linearized gravity. With the iterational scheme, based on the Perturbaion Theory with respect to the Newtonian constant, we compute the radiation amplitude and the emitted energy due to collision. The general phenomenon of mutual cancellation of the leading terms on the local and non-local amplitude, known in the ultrarelativistic regime for several types of collision, also takes place here. Remarkably, this cancellation (destructive interference) is complete, and takes place for any particle’s velocity. We compute the spectral and angular distributions of the emitted waves. Particular attention is paid to the ultrarelativistic case. Due to the radiation emission, a string may lose its energy and decrease the tension; it may affect all field effects, including the vacuum polarization and the Casimir effect, in terms of physical problems with the real cosmic strings.

Radiation reaction from soft theorems

Radiation reaction (RR) terms at the third post-Minkowskian (3PM) order have recently been found to be instrumental in restoring smooth continuity between the non-relativistic, relativistic, and ultra-relativistic (including the massless) regimes. Here we propose a new and intriguing connection between RR and soft (bremsstrahlung) theorems which short-circuits the more involved conventional loop computations. Although first noticed in the context of the maximally supersymmetric theory, unitarity and analyticity arguments support the general validity of this 3PM-order connection that we apply, in particular, to Einstein's gravity and to its Jordan-Brans-Dicke extension. In the former case we find full agreement with a recent result by Damour obtained through a very different reasoning.

Freeze-in produced dark matter in the ultra-relativistic regime

When dark matter particles only feebly interact with plasma constituents in the early universe, they never reach thermal equilibrium. As opposed to the freeze-out mechanism, where the dark matter abundance is determined at T ≪ M, the energy density of a feebly interacting state builds up and increases over T ≳ M. In this work, we address the impact of the high-temperature regime on the dark matter production rate, where the dark and Standard Model particles are ultra-relativistic and nearly light-like. In this setting, multiple soft scatterings, as well as 2 → 2 processes, are found to give a large contribution to the production rate. Within the model we consider in this work, namely a Majorana fermion dark matter of mass M accompanied by a heavier scalar — with mass splitting Δ M — which shares interactions with the visible sector, the energy density can be dramatically underestimated when neglecting the high-temperature dynamics. We find that the overall effective 1 ↔ 2 and 2 →2 high-temperature contributions to dark-matter production give \U0001d4aa(10) (20%) corrections for Δ M /M =0.1 (Δ M /M =10) to the Born production rate with in-vacuum masses and matrix elements. We also assess the impact of bound-state effects on the late-time annihilations of the heavier scalar, in the context of the super-WIMP mechanism.