Relativistic intermolecular forces, moderately long range.
Moderately long-range relativistic intermolecular forces, obtaining interaction energies
ANGULAR MOMENTUM↗
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Marginal stability constraint on runaway electron distribution
High-frequency kinetic instabilities of the strongly anisotropic runaway electrons (RE) can enhance the pitch-angle scattering of the runaways significantly. This wave-induced scattering can easily prevail over runaway scattering on high-Z impurities. In a steady state, collisional damping balances the kinetic drive of the unstable waves, keeping the RE distribution function at marginal stability. The marginal stability constraint limits the achievable RE densities and the shape of the RE distribution function. In this study, we consider whistler and compressional Alfvén waves as the primary source of enhanced elastic scattering of the runaways. By balancing the anomalous Doppler resonance drive with the collisional wave damping, we find the RE distribution function in the ultra-relativistic range of the phase space. We also derive an expression for the spectral energy density of the waves. We show that the power needed to compensate for the wave dissipation is negligible compared to the work of the electric field. The latter is in balance with the synchrotron losses of the runaway electrons.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
The FIREBIRD-II CubeSat Mission (Focused Investigations of Relativistic Electron Burst Intensity, Range, and Dynamics)
FIREBIRD-II is a National Science Foundation funded CubeSat mission designed to study the scale size and energy spectrum of relativistic electron microbursts. The mission consists of two identical 1.5 U CubeSats in a low earth polar orbit, each with two solid state detectors that differ only in the size of their geometric factors and fields of view. Having two spacecraft in close orbit allows the scale size of microbursts to be investigated through the intra-spacecraft separation when microbursts are observed simultaneously on each unit. Each detector returns high cadence (10 s of ms) measurements of the electron population from 200 keV to >1 MeV across six energy channels. The energy channels were selected to fill a gap in the observations of the Heavy Ion Large Telescope instrument on the Solar, Anomalous, and Magnetospheric Particle Explorer. FIREBIRD-II has been in orbit for 5 years and continues to return high quality data. After the first month in orbit, the spacecraft had separated beyond the expected scale size of microbursts, so the focus has shifted toward conjunctions with other magnetospheric missions. FIREBIRD-II has addressed all of its primary science objectives, and its long lifetime and focus on conjunctions has enabled additional science beyond the scope of the original mission. This paper presents a brief history of the FIREBIRD mission’s science goals, followed by a description of the instrument and spacecraft. The data products are then discussed along with some caveats necessary for proper use of the data.
47 OTHER INSTRUMENTATION↗
Stopping of relativistic heavy ions in various media
The residual ranges of (900 + or - 3)-MeV/amu gold nuclei accelerated at the Lawrence Berkeley Laboratory Bevalac have been measured in several different media. The energy of the beam of nuclei was measured directly using a new time-of-flight system. The ranges were measured by absorption in linear wedges of polyethylene, carbon, aluminum, copper, tin, and lead and in circular wedges of polystyrene, aluminum, and gold, and by total absorption in nuclear emulsion. The measured ranges were significantly different from those calculated from the best available theoretical estimates of the energy loss of highly charged nuclei. It is concluded that at present energy losses and residual ranges of relativistic heavy ions in an arbitrary medium cannot be predicted with better than an approximately 2 percent accuracy.
Waddington, C. J.↗
Relativistic Hartree–Fock chiral Lagrangians with confinement, nucleon finite size and short-range effects
A relativistic Hartree–Fock Lagrangian including a chiral potential and nucleon polarisation is investigated in hopes of providing a better description of dense nuclear matter. Here, we fully consider the contribution of the exchange Fock term to the energy and the self-energies, and in addition we investigate the nucleon’s compositeness and finite size effects (confinement and form factors) and short range correlations modeled by a Jastrow ansatz. These effects are added step by step, such that their impact on the dense matter properties can be analysed in details. The parameters of the model are adjusted to reproduce fundamental properties related to the QCD theory at low energy, such as the chiral symmetry breaking, nucleon’s quark substructure and Lattice-QCD predictions, as well as two empirical properties at saturation: the binding energy and the density. All other empirical parameters, e.g., symmetry energy and its slope, incompressibility modulus, effective mass, as well as spin–isospin Landau–Midgal parameter are predictions of the models and can be used to evaluate the gain of the different approximation schemes in describing nuclear properties. Bayesian statistics is employed in order to propagate parameter uncertainties into predictions for the nuclear matter properties. We show that the splitting of the effective Landau mass is largely influenced by the value of the ρ T coupling, and we show that the fit to the symmetry energy, which induces an increase of the coupling constant g ρ by about 20–25% compared to the case where it is fixed by the quark model, provides a very good EoS compatible with the present nuclear physics knowledge.
74 ATOMIC AND MOLECULAR PHYSICS↗
Relativistic Modeling Capabilities in Perseus Extended MHD Simulation Code for HED Plasmas
This project is submitted in response to DE-FOA-0001153, and will be carried out by Dr. Charles Seyler and Dr. Nathaniel Hamlin as post doc under the direction of Professor Seyler. The objectives are to enable PERSEUS to self-consistently model relativistic high-energy-density (HED) laboratory and astrophysical phenomena. Electrons and ions in a plasma are generally modeled either as fluids using a two-fluid code, like PERSEUS, or as particles using a Particle-In- Cell (PIC) code. Nonrelativistic PERSEUS solves the two-fluid equations, formulated in terms of a generalized Ohm’s law (GOL), so as to model about nine orders of magnitude in density variation using a local semi-implicit method. Relativistic PERSEUS preserves this structure and therefore retains these advantageous properties, enabling it to model a broader range of relativistic HED phenomena than previous codes. We have also overcome a major technical challenge associated with solving a relativistic system of equations relating conserved quantities (momentum, energy, etc.) to primitive variables (density, velocity, and pressure). We have thus far developed a relativistic version of PERSEUS and demonstrated that it recovers expected nonrelativistic results. We are currently using relativistic PERSEUS to model two HED phenomena, namely laser-plasma interactions and X-pinches, both of which show spectroscopic evidence of relativistic electrons. In an X-pinch, a section of wire carrying sufficiently large current forms a plasma column that pinches down to a point-like source, generating X-rays for use in radiographic imaging. Laser-plasma interactions have been simulated using PIC codes, and we use their results as a benchmark for comparison. However, neither PIC codes nor existing two-fluid schemes can simulate X-pinches, due to the broad range of densities which have thus far made such a simulation computationally prohibitive. In both laser-plasma interaction and Xpinch simulations, we have observed relativistic phenomena that PERSEUS could not previously model. This includes relativistic channeling of a laser into an over-dense deuterium gas (i.e. induced transparency), consistent with PIC simulation results, along with energetic electrons and ions following an X-pinch and likely accompanied by strong X-ray emission, consistent with experimental observations of energetic X-rays. This proposal includes our latest simulation results. We will improve computational efficiency with techniques that allow the use of a less refined numerical grid. This will enable extensions to three-dimensional geometries. We will improve modeling of laser-plasma interactions and X-pinches, including radiative transport processes, in order to improve comparisons with PIC simulations and experimental diagnostics. We will also model power loss through electrode surface plasmas in magnetically insulated transmission lines (MITLs). We will model relativistic astrophysical phenomena in both astrophysical and HED regimes, which could shed light on the validity of laboratory astrophysics for certain problems. These phenomena are currently modeled using PIC codes and existing relativistic two-fluid codes, neither of which can model the range of length scales of which relativistic PERSEUS is capable. There is strong potential for this project to have a broad impact on both the astrophysical and laboratory plasma communities. In the laboratory community, our work is applicable to those concerned with laser-plasma interactions such as laser-driven fusion, and those in the dense Z pinch community concerned with X-pinches and electrode surface plasmas. An improved understanding of the mechanisms of hard (i.e. high-energy) X-ray generation will likely make important contributions toward the use of X-pinches for radiography through the harnessing or mitigation of hard X-rays, depending on the application. The modeling of electrode surface plasmas, including vacuum electron flow, will improve our understanding of power loss to various loads.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Ultra-short pulse generation from mid-IR to THz range using plasma wakes and relativistic ionization fronts
In this work, we discuss numerical and experimental results on frequency downshifting and upshifting of a 10 μ m infrared (IR) laser to cover the entire wavelength (frequency) range from λ = 1 to 150 μ m ( ν = 300–2 THz) using two different plasma techniques. The first plasma technique utilizes frequency downshifting of the drive laser pulse in a nonlinear plasma wake. Based on this technique, we have proposed and demonstrated that in a tailored plasma structure, multi-millijoule energy, single-cycle, long-wavelength IR (3–20 μ m) pulses can be generated by using an 810 nm Ti:sapphire drive laser. Here, we extend this idea to the THz frequency regime. We show that sub-joule, terawatts, single-cycle terahertz (2–12 THz or 150–25 μ m) pulses can be generated by replacing the drive laser with a picosecond 10 μ m CO 2 laser and a different shaped plasma structure. The second plasma technique employs frequency upshifting by colliding a CO 2 laser with a rather sharp relativistic ionization front created by ionization of a gas in less than half cycle (17 fs) of the CO 2 laser. Even though the electrons in the ionization front carry no energy, the frequency of the CO 2 laser can be upshifted due to the relativistic Doppler effect as the CO 2 laser pulse enters the front. The wavelength can be tuned from 1 to 10 μ m by simply changing the electron density of the front. While the upshifted light with 5 < λ ( μ m ) < 10 propagates in the forward direction, that with 1 < λ ( μ m ) < 5 is back-reflected. These two plasma techniques seem extremely promising for covering the entire molecular fingerprint region.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Determination of astrodynamic constants and a test of the general relativistic time delay with S-band range and Doppler data from Mariners 6 and 7
Earth/moon mass ratio and Mars mass and ephemeris from Mariners range and Doppler tracking data, noting relativistic time delay measurement possibility
Anderson, J. D.↗
New results from a number operator interpretation of the compositeness of bound and resonant states
A novel theoretical approach to the problem of the compositeness (X) of a resonance or bound state is developed on the basis of the expectation values of the number operators of the free particles in the continuum. This formalism is specially suitable for effective field theories in which the bare elementary states are integrated out but that give rise to resonance and bound states when implemented in nonperturbative calculations. We demonstrate that X=1 for finite-range energy-independent potentials, either regular or singular. A non-trivial example for an energy-dependent potential is discussed where it is shown that X is independent of any type of cutoff regulator employed. The generalization of these techniques to relativistic states is developed. We also explain how to obtain a meaningful compositeness with respect to the open channels for resonances, even if it is complex in a first turn, by making use of suitable phase-factor transformations. Defining elementariness as X=0, we derive a new universal criterion for the elementariness of a bound state. Along the same lines, a necessary condition for a resonance to be qualified as elementary is given. The application of the formalism here developed might be of considerable practical interest.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Determination of astrodynamic constants and a test of general relativistic time delay with S-band range and Doppler data from Mariners 6 and 7
General relativistic time delay and moon-earth masses and Mars mass-ephemeris ratios from S-band range and Doppler tracking
Anderson, J. D.↗
Galaxy Cluster Contribution to the Diffuse Extragalactic Ultraviolet Background
The diffuse ultraviolet background radiation has been mapped over most of the sky with 2′ resolution using data from the Galaxy Evolution Explorer survey. We utilize this map to study the correlation between the UV background and clusters of galaxies discovered via the Sunyaev–Zeldovich effect in the Planck survey. We use only high Galactic latitude (|b|>60{sup ∘}) galaxy clusters to avoid contamination by Galactic foregrounds, and we only analyze clusters with a measured redshift. This leaves us with a sample of 142 clusters over the redshift range of 0.02 ≤ z ≤ 0.72, which we further subdivide into four redshift bins. In analyzing our stacked samples binned by redshift, we find evidence for a central excess of UV background light compared to local backgrounds for clusters with z < 0.3. We then stacked these z < 0.3 clusters to find a statistically significant excess of 12 ± 2.3 photon cm{sup −2} s{sup −1} sr{sup −1} Å{sup −1} over the median of ∼380 photon cm{sup −2} s{sup −1} sr{sup −1} Å{sup −1} measured around random blank fields. We measure the stacked radial profile of these clusters, and find that the excess UV radiation decays to the level of the background at a radius of ∼1 Mpc, roughly consistent with the maximum radial extent of the clusters. Analysis of possible physical processes contributing to the excess UV brightness indicates that non-thermal emission from relativistic electrons in the intracluster medium and faint, unresolved UV emission from cluster member galaxies and intracluster light are likely the dominant contributors.
79 ASTRONOMY AND ASTROPHYSICS↗
Collective Modes in BCS-Like Models
The Hamiltonian of the gapped modes in the BCS model of superconductivity is derived using the nilpotency expansion. It has the form of the Bogoliubov Hamiltonian of a boson superfluid. The gapped modes have a quadratic dispersion law. The smallest energy gap is smaller than twice the fermionic energy gap. The nilpotency expansion respects all the symmetries and it has been previously applied to nuclear physics and relativistic field theories including QCD. In particular, it reproduces exactly the bosonization occurring in a relativistic 4-fermion interaction model.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
From Hartree Dynamics to the Relativistic Vlasov Equation
We derive the relativistic Vlasov equation from quantum Hartree dynamics for fermions with relativistic dispersion in the mean-field scaling, which is naturally linked with an effective semiclassic limit. Similar results in the non-relativistic setting have been recently obtained in Benedikter et al. (Arch Rat Mech Anal 221(1): 273–334, 2016). The new challenge that we have to face here, in the relativistic setting, consists in controlling the difference between the quantum kinetic energy and the relativistic transport term appearing in the Vlasov equation.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Correction to: Heat Flux for a Relativistic Dilute Bidimensional Gas
The original version of this article unfortunately contained a mistake.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Polarisation non-reciprocity cancelling in Sagnac fibre ring interferometer: an attempt of realistic study
Polarisation non-reciprocity (PNR) of Sagnac fibre ring interferometer (FRI) is one the fundamental limits of its long term bias stability. PNR value, being huge initially, then was reduced strongly, but after that PNR problem was left far from PNR cancelling. The latter may be defined as PNR reducing up to 10{sup −10} deg/h when it does not prevent detecting the general relativistic Lense–Thirring effect. Clearly, such PNR cancelling may be treated only theoretically at this point. In this case, one has to model all practical defects of FRI. Present paper describes such kind of study for FRI of commercial fibre optic gyro implementing medium quality components. It is shown that for PNR cancelling, several meters fibre polariser is enough, despite of the stringent limitations of its standard polarisation extinction ratio. Also, a complete FRI configuration is treated for the first time in available literature, including an imperfect fibre coupler. This yields one more PNR component which is non-zero even for completely unpolarised light and which can be effectively suppressed by the fibre polariser too.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Self-focusing of cosh-Gaussian laser beam and its effect on the excitation of ion-acoustic wave and stimulated Brillouin backscattering in collisionless plasma
An analytical and numerical study has been carried out for self-focusing of an intense cosh-Gaussian laser beam in collisionless plasma and its impact on the excitation of ion-acoustic wave and stimulated Brillouin backscattering process. The analytical model has been developed under Wentzel–Kramers–Brillouin and paraxial ray approximations. The nonlinearities of ponderomotive force on electron and the relativistic oscillation of the electron mass have been used in this study. The nonlinear differential equations have been set up for the beam width parameters of the main beam, ion-acoustic wave, backscattered wave and back reflectivity of stimulated Brillouin scattering (SBS). These equations have been solved numerically for different values of decentred parameter (b), relative plasma density (ω{sub p0}/ω{sub 0}) and incident laser intensity (a). The results have been compared with only relativistic nonlinearity and Gaussian profile of laser beam. The focusing of laser beam, ion-acoustic wave and scattered wave are found to be strong under relativistic-ponderomotive regime compared to only relativistic regime. Further, it is observed that focusing/intensity of main laser beam, ion acoustic wave and SBS back reflectivity increases with increasing the values of b and ω{sub p0}/ω{sub 0}. Itis also found that back reflectivity of SBS process gets suppressed with the increase in the value of a. This study may be useful in laser induced fusion scheme where back scattering of SBS plays very important role.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Internal Structure of Charged Particles in a GRT Gravitational Model
With the help of an exact solution of the Einstein and Maxwell equations, the internal structure of a multiply connected space of wormhole type with two unclosed static throats leading out of it into two parallel vacuum spaces or into one space is investigated in GRT for a free electric field and dust-like matter. The given geometry is considered as a particle–antiparticle pair with fundamental constants arising in the form of first integrals in the solution of the Cauchy problem – electric charges ±e of opposite sign in the throats and rest mass m{sub 0} – the total gravitational mass of the inner world of the particle in the throat. With the help of the energy conservation law, the unremovable rotation of the internal structure is included and the projection of the angular momentum of which onto the rotation axis is identified with the z-projection of the spin of the charged particle. The radius of 2-Gaussian curvature of the throat R* is identified with the charge radius of the particle, and the z-projection of the magnetic moment and the g-factor are found. The feasibility of the given gravitational model is confirmed by the found condition of independence of the spin quantum number of the electron and the proton s = 1/2 of the charge radius R* and the relativistic rest mass m* of the rotating throat, which is reliably confirmed experimentally, and also by the coincidence with high accuracy of the proton radius calculated in the model R{sub *p} = 0.8412·10{sup –13} cm with the value of the proton charge radius obtained experimentally by measuring the Lamb shift on muonic hydrogen. The electron in the given model also turns out to be a structured particle with radius R{sub *e} = 3.8617·10{sup –11} cm.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Characteristics of a Two-Dimensional Hydrogen-like Atom
Using the customary and well-known representation of the radiation probability of a hydrogen-like atom in the three-dimensional case, a general expression for the probability of single-photon emission of a twodimensional atom has been obtained along with an expression for the particular case of the transition from the first excited state to the ground state, in the latter case in comparison with corresponding expressions for the three-dimensional atom and the one-dimensional atom. Arguments are presented in support of the claim that this method of calculation gives a value of the probability that is identical to the value given by exact methods of QED extended to the subspace {0, 1, 2}. Relativistic corrections ~ (Zα){sup 4} to the usual Schrödinger value of the energy (~ (Zα){sup 2}) are also discussed.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗