Electrodynamic Effects Research Articles

МОЛЕКУЛЯРНЫЙ ИОН ВОДОРОДА𝑯𝟐+. МАГНИТНЫЕ M1 ПЕРЕХОДЫ

The magnetic dipole transitions in the homonuclear molecular ion 𝐻2+are obtained for a range ofand L, vibrational and total orbital momentum quantum numbers, respectively. Calculations are performed in the nonrelativistic approximation. The effects of the ion spin structure on M1 transitions are also considered. Numerical calculations were carried out on the basis of “exponential” variational expansion. One of the simplest and most fully developed areas of application of quantum mechanics is the theory of atoms with one or two electrons. For hydrogen and hydrogen-like ions, calculations can be performed strictly in both Schrödinger's non-relativistic wave mechanics and Dirac's relativistic electron theory. The exact calculations are rigorous for an electron at a fixed Coulomb potential. Therefore, the hydrogen-like atom provides an excellent material for testing the validity of quantum mechanics. For such an atom, the correction terms that take into account the motion and structure of the atomic nucleus, as well as quantum electrodynamic effects, are small and can be calculated with great accuracy. Since the energy levels of hydrogen and hydrogen-like atoms can be experimentally studied with anamazing degree of accuracy, it turns out that it is possible to test the correctness of quantum electrodynamics to some extent accurately.

Optical coupling of individual air-suspended carbon nanotubes to silicon microcavities.

Carbon nanotubes are a telecom band emitter compatible with silicon photonics, and when coupled to microcavities, they present opportunities for exploiting quantum electrodynamical effects. Microdisk resonators demonstrate the feasibility of integration into the silicon platform. Efficient coupling is achieved using photonic crystal air-mode nanobeam cavities. The molecular screening effect on nanotube emission allows for spectral tuning of the coupling. The Purcell effect of the coupled cavity-exciton system reveals near-unity radiative quantum efficiencies of the excitons in carbon nanotubes.

Dielectronic recombination experiment of Na-like Kr<sup>25+</sup> at heavy ion storage ring CSRe

The experimental study of precision spectroscopy of dielectronic recombination (DR) of highly charged ions is not only important for astronomical plasma and fusion plasma, but also can be used as a new precision spectroscopy to test the strong-field quantum electrodynamic effect, measure isotope shift, and extract the radius of atomic nuclei. An specially designed electron beam energy detuning system for electron-ion recombination precision spectroscopy experiments has been installed on the heavy ion storage ring CSRe in Lanzhou, China, where the electron-ion collision energy in the center-of-mass system can be detuned to 1 keV, and an independently-developed plastic scintillator detector and multiwire proportional chamber detector have been installed downstream of the electron cooler of the CSRe for detecting recombined ions. The multiwire proportional chamber detector has the ability to non-destructively monitor the profile of the ion beam in real-time while acquiring the recombined ion counts, providing guidance for optimizing the ion beam. On this basis, the first test experiment on dielectronic recombination of Kr<sup>25+</sup> ions is carried out at the CSRe, and the dielectronic recombination rate coefficients in a range of 0–70 eV in the frame of center-of-mass are measured. In order to fully understand the experimental results, we calculate the dielectronic recombination rate coefficient of the Kr<sup>25+</sup> ion by using the flexible atomic code (FAC) and make a detailed comparison with the experimental result, showing that they are in good agreement with each other, and only the resonance energy values of the two resonance peaks at 1.695 eV and 2.573 eV are significantly different. In addition, the DR resonance energy values and intensities are obtained by fitting the experimental results in a range of 0–35 eV, and we find that the transition 3s→4l (∆<i>n</i> = 1) contributes significantly to the experimental spectral lines. Furthermore, we compare the plasma rate coefficients derived from the DR rate coefficients with those derived from the AUTOSTRUCTURE and FAC theories, which differ by 20 percent in a temperature range less than 10<sup>6</sup> K. The experimental results show that the DR experimental platform of the CSRe has very good stability and reproducibility, and can provide support for the future DR experiments of highly charged ion, i.e. for testing strong-field quantum electrodynamics effect and measuring the properties of atomic nuclei.

Large Casimir Flipping Torque in Quantum Trap.

Casimir torque between parallel plates, a macroscopic quantum electrodynamics effect, is known to be induced by dielectric anisotropy and related to the rotational degree of freedom. We here reveal a different type of Casimir torque generated on a Au plate suspended in a quantum trap without recourse to materials anisotropy. As the Au plate deflects from the equilibrium plane with a nonzero flipping angle, the regions departing from and approaching the Teflon-coated Au substrate are subjected to attractive and repulsive Casimir forces, respectively, resulting in a restoring torque about the axis of flipping. For a quantum trap with an equilibrium separation of ∼10 nm, the stiffness per unit area of the Casimir flipping torque can be an order of magnitude larger than those of previously reported dielectric anisotropy-induced rotational torques at the same separation. The large Casimir flipping torque provides the possibility of designing a mechanical oscillator completely dominated by quantum and thermal fluctuations.

ОГЛЯД ПРИНЦИПІВ СЕЛЕКТИВНОСТІ ЗАХИСТІВ В РОЗПОДІЛЬЧИХ МЕРЕЖАХ СПОЖИВАЧІВ НАПРУГОЮ 0,4 кВ

The analysis of existing principles of selectivity indicates the complexity and incompleteness of ensuring the coordination of the operation of protection devices in distribution networks of 0.4 kV consumers. Current selectivity is ensured only in the area of action of short-circuit currents. To ensure it, electromagnetic or electronic decouplers with a constant deceleration setting are required. This type of disconnectors is used to perform time selectivity and limit the thermal impact of short-circuit currents on the electrical installation and device. The use of devices with "pseudo-time" selectivity ensures the selectivity of the operation of automatic switches in the area of short-circuit currents. Selectivity "SELLIM" is provided with a speed of 0.01 s, but it is possible only in automatic circuit breakers "Schneider Electric". Logical selectivity requires a communication channel between switching devices and the presence of circuit breakers with appropriate communication ports. It is easiest to ensure selectivity by using switches from the same manufacturer using selectivity tables. But such a solution is not always found in practice. The method of energy selectivity allows, taking into account the ratio between ratings, to implement either partial selectivity or full selectivity up to the limit of the breaking capacity of automatic switches. To ensure energy selectivity between two or more current-limiting devices, it must be taken into account that depending on the location of the short circuit, a different number of circuit breakers will be involved in limiting the emergency current, and therefore, the value of the limited current will also be different. By using circuit breakers with a high level of current limitation and a tripping speed that is inversely related to the short-circuit current, full selectivity can be provided at several levels of the network. This makes it possible to simplify the analysis of selectivity, minimize electrodynamic and thermal effects and reduce the level of voltage drop due to the action of a short circuit. Improvement of electrical installation protection systems makes it possible to design power supply systems without excessive reserves of electrical equipment overload, which reduces their cost, dimensions and weight. On the other hand, in the event of malfunctions in the operation of electrical equipment, this limits emergency currents and prevents failure of the undamaged part of the electrical installation, which significantly reduces downtime. Key words: selectivity, relay protection devices, circuit breakers, electrical devices, 0.4 kV network.

Atomic structure calculations, and electron impact ionization cross-sections of W LXI

The present study provides a wide range of calculations of atomic structure data for the tungsten ion W LXI, that belongs to the silicon isoelectronic sequence. The fully relativistic Multi-configuration Dira-Hartree–Fock (MCDHF) method including configuration interaction (CI) is applied to the current ion. Calculated results of energy levels, oscillator strengths, and radiative rates of W LXI are presented. A set of two configuration state lists including the configurations of 3s23p2, 3s3p3, 3s23p3d, and 3p4 at different angular momenta (J) and parity (P) are considered in the configuration interaction calculations of level energies and oscillator strengths. To increase the accuracy of the results, the electronic correlations from higher orbitals, i.e., 7l orbitals are included in the calculations. Quantum electrodynamics effects such as vacuum polarization and self-energy are recalled in the CI calculations. Many more transitions in the soft x-ray region (between 20 and 200 angstroms) have been identified. The flexible atomic code package has been used to compute the electron impact ionization cross-sections of 3s23p2 3P0,1, 1D2 levels in silicon-like tungsten. The cross-sections of the transitions from the ground level in W LXI to the first levels in the 61st ionization of tungsten have been computed using FAC code. The total ionization cross-sections of the 3s23p2 at electron energy range from 5–35 keV are evaluated as well.

Singly-excited resonant open quantum system Tavis-Cummings model with quantum circuit mapping

Tavis-Cummings (TC) cavity quantum electrodynamical effects, describing the interaction of N atoms with an optical resonator, are at the core of atomic, optical and solid state physics. The full numerical simulation of TC dynamics scales exponentially with the number of atoms. By restricting the open quantum system to a single excitation, typical of experimental realizations in quantum optics, we analytically solve the TC model with an arbitrary number of atoms with linear complexity. This solution allows us to devise the Quantum Mapping Algorithm of Resonator Interaction with N Atoms (Q-MARINA), an intuitive TC mapping to a quantum circuit with linear space and time scaling, whose N+1 qubits represent atoms and a lossy cavity, while the dynamics is encoded through 2N entangling gates. Finally, we benchmark the robustness of the algorithm on a quantum simulator and superconducting quantum processors against the quantum master equation solution on a classical computer.

Unveiling the combined effects of neutral dynamics and electrodynamic forcing on dayside ionosphere during the 3–4 February 2022 “SpaceX” geomagnetic storms

Geomagnetic storms of G1-class were observed on 3 and 4 February 2022, which caused the loss of 38 out of 49 SpaceX satellites during their launch due to enhanced neutral density. The effects of storm-time neutral dynamics and electrodynamics over the American sector during this minor storm have been investigated using Global Positioning System—total electron content (TEC) and Global‐scale Observations of the Limb and Disk (GOLD) mission measured thermospheric composition and temperature. Results revealed an unexpected feature in terms of increase in O/N2 and depletion in TEC over the American low-latitudes. This feature is in addition to the classic storm time ionospheric variations of enhancement in ionospheric electron density in presence of enhanced O/N2 and an intense equatorial electrojet (EEJ). Further, significant morning-noon electron density reductions were observed over the southern mid-high latitudes along the American longitudes. Results from Multiscale Atmosphere-Geospace Environment (MAGE) model simulations elucidated storm-induced equatorward thermospheric wind which caused the strong morning counter electrojet by generating the disturbance dynamo electric field. This further explains the morning TEC depletion at low-latitudes despite an increase in O/N2. Sub-storm related magnetospheric convection resulted in significant noon-time peak in EEJ on 4 February. Observation and modelling approaches together suggested that combined effects of storm-time neutral dynamic and electrodynamic forcing resulted in significant ionospheric variations over the American sector during minor geomagnetic storms.

A high-resolution asymmetric von Hamos spectrometer for low-energy X-ray spectroscopy at the CRYRING@ESR electron cooler

We present research program and project for high-resolution wavelength-dispersive spectrometer dedicated to low-energy X-ray spectroscopy at the electron cooler of the CRYRING@ESR storage ring, which is a part of the international Facility for Antiproton and Ion Research (FAIR) currently being built in Darmstadt. Due to the unique shape of the electorn-ion recombination X-ray source, resulting from the overlapping of the electron and ion beams in the electron cooler, the spectrometer can work in the specific asymmetric von Hamos (AvH) geometry. In order to completely eliminate the influence of Doppler effect on the measured X-ray energies, two asymmetric von Hamos spectrometers will be installed next to the dipole magnets on both sides of the electron cooler to detect blue/red (0°/180°) shifted X-rays, e.g. emitted in the radiative recombination (RR) process. The X-ray-tracing Monte-Carlo simulations show that the proposed AvH spectrometer will allow to determine with sub-meV precision, the low-energy X-rays (5–10 keV) emitted from stored bare or few-electron heavy ions interacting with cooling electrons. This experimental precision will enable accurate studies of the quantum electrodynamics (QED) effects in mid-Z H- and He-like ions.

Formation of SiV centers by doping in bottom-up grown HPHT nanodiamonds and its implication for optical nanosensig

We investigate doping and formation of luminescent point defects in nanodiamond at high pressures and high temperatures (HPHT) in fluorine-containing hydrocarbon growth systems with an excessive content of dopant organosilicon component. It is shown experimentally that the average concentration of silicon-vacancy centers (SiV-) tends to increase proportionally to the diameter of the nanocrystals. Respectively, the local concentration of the dopant in a crystal linearly increases with the distance from the crystal center. This phenomenon is explained by competition between growth of a perfect crystal and doping. The kinetics of the crystal growth are determined by the diffusion of carbon containing precursors to the surface of the crystal and the doping takes place at a very high concentration of the dopant in the growth mixture and that is defined by the rate of the chemical reaction on the crystal surface. Electrodynamic effects in the nanocrystals affecting the observed intensity of the photoluminescence are also considered. Although these results are obtained using important for applications SiV- photo luminescent centers, they have much wider implications.

Plasma modes in QED super-strong magnetic fields of magnetars and laser plasmas

Ultra-magnetized plasmas, where the magnetic field strength exceeds the Schwinger field of about BQ≈4×1013 G, become of great scientific interest, thanks to the current advances in laser-plasma experiments and astrophysical observations of magnetar emission. These advances demand better understanding of how quantum electrodynamics (QED) effects influence collective plasma phenomena. In particular, Maxwell's equations become nonlinear in the strong-QED regime. Here we present the “QED plasma framework,” which will allow one to systematically explore collective phenomena in a QED-plasma with arbitrary strong magnetic field. Further, we illustrate the framework by exploring low-frequency modes in the ultra-magnetized, cold, electron-positron plasmas. We demonstrate that the classical picture of five branches holds in the QED regime; no new eigenmodes appear. The dispersion curves of all the modes are modified. The QED effects include the overall modification to the plasma frequency, which becomes field-dependent. They also modify resonances and cutoffs of the modes, which become both field- and angle-dependent. The strongest effects are (i) the field-induced transparency of plasma for the O-mode via the dramatic reduction of the low-frequency cutoff well below the plasma frequency, (ii) the Alfvén mode suppression in the large-k regime via the reduction of the Alfvén mode resonance, and (iii) the O-mode slowdown via strong angle-dependent increase in the index of refraction. These results should be important for understanding of a magnetospheric pair plasma of a magnetar and for laboratory laser-plasma experiments in the QED regime.

Thermodynamics under the impact of thermal fluctuations and quasi-normal modes of Euler-Heisenberg AdS BH in the framework of NLED

We study the impact of thermal fluctuations on the thermodynamics, quasi-normal modes, and phase transitions of an anti-de Sitter Euler-Heisenberg black hole (BH) with a nonlinear electrodynamic field. An anti-de Sitter Euler-Heisenberg BH with a nonlinear electrodynamic field is composed of four parameters: the mass, electric charge, cosmological constant, and Euler-Heisenberg parameter. We calculate thermodynamic variables such as Hawking temperature, entropy, volume, and specific heat, which comply with the first law of thermodynamics. First, we use this BH to determine the thermodynamics and thermal fluctuations with the Euler-Heisenberg parameter to distinguish their effect on uncorrected and corrected thermodynamical quantities. We derive the expression for corrected entropy to study the impact of thermal fluctuation with simple logarithmic corrections on unmodified thermodynamical potentials, including Helmholtz energy, pressure, Gibbs free energy, and enthalpy. The Euler-Heisenberg parameter improves BH stability at large radii. Second, we analyze the local stability of the proposed BH, and the phase shifts of the BH are also investigated using temperature and specific heat. When there is a decrease in charge and an increase in and α, the temperature shifts from an unstable region to a stable one. Similarly, increases in local stability are observed with each of these parameters. Third, we use null geodesics to deal with the effects of nonlinear electrodynamics on the quasi-normal modes of the Euler-Heisenberg anti-de Sitter BH. The null geodesics provide the angular velocity and Lyapunov exponent of the photon sphere, which are the same as the real and imaginary parts of the quasi-normal modes in the eikonal limit.

Significant Mid‐ and Low‐Latitude Ionospheric Disturbances Characterized by Dynamic EIA, EPBs, and SED Variations During the 13–14 March 2022 Geomagnetic Storm

AbstractThis work investigates mid‐ and low‐latitude ionospheric disturbances over the American sector during a moderate but geo‐effective geomagnetic storm on 13–14 March 2022 (π‐Day storm), using ground‐based Global Navigation Satellite System total electron content data, ionosonde observations, and space‐borne measurements from the Global‐scale Observations of Limb and Disk (GOLD), Swarm, the Defense Meteorological Satellite Program (DMSP), and the Ionospheric Connection Explorer (ICON) satellites. Our results show that this modest but geo‐effective storm created a number of large ionospheric disturbances, especially the dynamic multi‐scale electron density gradient features in the storm main phase as follows: (a) The low‐latitude equatorial ionization anomaly (EIA) exhibited a dramatic storm‐time deformation and reformation, where the EIA crests evolved into a bright equatorial band for 1–2 hr and then quickly separated back into the typical double‐crest structure with a broad crest width and deep equatorial trough. (b) Strong equatorial plasma bubbles (EPBs) occurred with an abnormally high latitude/altitude extension, reaching the geomagnetic latitude of ∼30°, corresponding to an Apex height of 2,600 km above the dip equator. (c) The midlatitude ionosphere experienced a conspicuous storm‐enhanced density (SED) plume structure associated with the subauroral polarization stream (SAPS). This SED/SAPS feature showed an unusual temporal variation that intensified and diminished twice. These distinct mid‐ and low‐latitude ionospheric disturbances could be attributed to the storm‐time electrodynamic effect of electric field perturbation, along with contributions from neutral dynamics and thermospheric composition change.

Energy levels and radiative transition properties of the 2s2p double K-shell vacancy state in He-like ions ([formula omitted

The energy levels of 1s2, 1s2s, and 2s2p configurations for He-like ions (4≤Z≤54) are calculated using the multi-configuration Dirac–Hartree–Fock​ methods. The transition energies, transition rates, and oscillator strengths of 2s2p→1s2 and 2s2p→1s2s are also calculated. A parallel calculation based on the Dirac–Fock–Slater method with a local central potential is performed using the Flexible Atomic Code to cross-check the accuracy of the data. The Breit interaction and quantum electrodynamics effects, including self-energy and vacuum polarization, are included as perturbations in these calculations. The average relative standard deviation of the energy levels from the available NIST data is about 0.2% for both methods. The transition energies and rates are in reasonable agreement with other available theoretical and experimental data, and the consistency between the transition energies calculated by the two methods reaches 99.9%. These results are expected to help future investigations on double K-shell vacancy decays of He-like ions.

High-energy synchrotron flares powered by strongly radiative relativistic magnetic reconnection: 2D and 3D PIC simulations

ABSTRACT The time evolution of high-energy synchrotron radiation generated in a relativistic pair plasma energized by reconnection of strong magnetic fields is investigated with 2D and 3D particle-in-cell (PIC) simulations. The simulations in this 2D/3D comparison study are conducted with the radiative PIC code OSIRIS, which self-consistently accounts for the synchrotron radiation reaction on the emitting particles, and enables us to explore the effects of synchrotron cooling. Magnetic reconnection causes compression of the plasma and magnetic field deep inside magnetic islands (plasmoids), leading to an enhancement of the flaring emission, which may help explain some astrophysical gamma-ray flare observations. Although radiative cooling weakens the emission from plasmoid cores, it facilitates additional compression there, further amplifying the magnetic field B and plasma density n, and thus partially mitigating this effect. Novel simulation diagnostics utilizing 2D histograms in the n-B space are developed and used to visualize and quantify the effects of compression. The n-B histograms are observed to be bounded by relatively sharp power-law boundaries marking clear limits on compression. Theoretical explanations for some of these compression limits are developed, rooted in radiative resistivity or 3D kinking instabilities. Systematic parameter-space studies with respect to guide magnetic field, system size, and upstream magnetization are conducted and suggest that stronger compression, brighter high-energy radiation, and perhaps significant quantum electrodynamic effects such as pair production, may occur in environments with larger reconnection-region sizes and higher magnetization, particularly when magnetic field strengths approach the critical (Schwinger) field, as found in magnetar magnetospheres.

Proof-of-Principle Experiment for Testing Strong-Field Quantum Electrodynamics with Exotic Atoms: High Precision X-Ray Spectroscopy of Muonic Neon.

To test bound-state quantum electrodynamics (BSQED) in the strong-field regime, we have performed high precision x-ray spectroscopy of the 5g-4f and 5f- 4d transitions (BSQED contribution of 2.4 and 5.2eV, respectively) of muonic neon atoms in the low-pressure gas phase without bound electrons. Muonic atoms have been recently proposed as an alternative to few-electron high-Z ions for BSQED tests by focusing on circular Rydberg states where nuclear contributions are negligibly small. We determined the 5g_{9/2}- 4f_{7/2} transition energy to be 6297.08±0.04(stat)±0.13(syst) eV using superconducting transition-edge sensor microcalorimeters (5.2-5.5eV FWHM resolution), which agrees well with the most advanced BSQED theoretical prediction of 6297.26eV.

IXPE detection of polarized X-rays from magnetars and photon mode conversion at QED vacuum resonance

The recent observations of the anomalous X-ray pulsars 4U 0142+61 and 1RXS J170849.0-400910 by the Imaging X-ray Polarimetry Explorer (IXPE) opened up a new avenue to study magnetars, neutron stars endowed with superstrong magnetic fields (B ≳ 1014 G). The detected polarized X-rays from 4U 0142+61 exhibit a 90° linear polarization swing from low photon energies (E ≲ 4 keV) to high energies (E ≳ 5.5 keV). We show that this swing can be explained by photon polarization mode conversion at the vacuum resonance in the magnetar atmosphere; the resonance arises from the combined effects of plasma-induced birefringence and Quantum electrodynamics (QED)-induced vacuum birefringence in strong magnetic fields. This explanation suggests that the atmosphere of 4U 0142 is composed of partially ionized heavy elements and that the surface magnetic field is comparable to or less than 1014 G, consistent with the dipole field inferred from the measured spindown. It also implies that the spin axis of 4U 0142+61 is aligned with its velocity direction. The polarized X-rays from 1RXS J170849.0-400910 do not show such 90° swing, consistent with magnetar atmospheric emission with B ≳ 5 × 1014 G.

Move Aside Pentacene: Diazapentacene-Doped para-Terphenyl, a Zero-Field Room-Temperature Maser with Strong Coupling for Cavity Quantum Electrodynamics.

Masers can deliver ultralow-noise amplification of microwave signals in medical imaging and deep-space communication, with recent research being rekindled through the discovery of gain media operating at room-temperature, eschewing bulky cryogenics that hindered their use. This work shows the discovery of 6,13-diazapentacene doped in para-terphenyl (DAP:PTP) as a maser gain medium that can operate at room-temperature, without an external magnetic field. With a maser output power of -10 dBm, it is on par with pentacene-doped para-terphenyl in masing power, while possessing compelling advantages such as faster amplification startup times, being pumped by longer wavelength light at 620 nm and greater chemical stability from nitrogen groups. Furthermore, the maser bursts from DAP:PTP allow one to reach the strong coupling regime for cavity quantum electrodynamics, with a highcooperativity of 182. The optical and microwave spin dynamics of DAP:PTP are studied in order to evaluate its capabilities as a maser gain medium, where it features fast intersystem crossing and an advantageously higher triplet quantum yield. The results pave the way for the future discovery of similar maser materials and help designate them as promising candidates for quantum sensors, optoelectronic devices and the study of cavity quantum electrodynamic effects atroom-temperature.

On heat properties of charged AdS black holes in Gauss-Bonnet gravity coupled with nonlinear electrodynamics

We investigate the heat properties of charged AdS black holes in the Gauss-Bonnet gravity coupled with nonlinear electrodynamics. We consider the thermodynamics of black holes from the perspective of heat capacity and show that the nonlinear electrodynamics can be helpful to improve the thermodynamic stability of black holes. We perform a two-dimensional description in order to reproduce the Hawking temperature, which confirms that the Hawking temperature has an intrinsic topological nature and holds for a higher dimensional spherically symmetric spacetime. We also analyze the Maxwell equal area law and coexistence curve, and find the existence of van der Waals-like phase transitions based on critical exponents. Moreover, we deal with a charged AdS black hole in the Gauss-Bonnet gravity coupled with nonlinear electrodynamics as a working material to study holographic heat engines and obtain an exact expression for the efficiency of a rectangular engine cycle. We then discuss the effects of nonlinear electrodynamics and Gauss-Bonnet couplings on the rectangular engine cycle and compare the efficiency of this cycle with that of the Carnot cycle.

Radiation-reaction in the Effective Field Theory approach to Post-Minkowskian dynamics

We extend the Post-Minkowskian (PM) effective field theory (EFT) approach to incorporate conservative and dissipative radiation-reaction effects in a unified framework. This is achieved by implementing the Schwinger-Keldysh “in-in” formalism and separating conservative and non-conservative terms according to the formulation in [1], which we show promotes Feynman’s i0-prescription and cutting rules to a prominent role at the classical level. The resulting integrals, involving both Feynman and retarded propagators, can be bootstrapped to all orders in the velocity via differential equations with boundary conditions including potential and radiation modes. As a paradigmatic example we provide an ab initio derivation of the classical solution to the scattering problem in general relativity to mathcal{O} (G3). For the sake of completeness, we also reproduce the leading order radiation-reaction effects in classical electrodynamics.