Electron Mass Ratio Research Articles

Physics beyond the Standard Model from hydrogen spectroscopy

Spectroscopy of hydrogen can be used for a search into physics beyond the Standard Model. Differences between the absorption spectra of the Lyman and Werner bands of H2 as observed at high redshift and those measured in the laboratory can be interpreted in terms of possible variations of the proton–electron mass ratio μ=mp/me over cosmological history. Investigation of ten such absorbers in the redshift range z=2.0–4.2 yields a constraint of |Δμ/μ|<5×10-6 at 3σ. Observation of H2 from the photospheres of white dwarf stars inside our Galaxy delivers a constraint of similar magnitude on a dependence of μ on a gravitational potential 104 times as strong as on the Earth’s surface. While such astronomical studies aim at finding quintessence in an indirect manner, laboratory precision measurements target such additional quantum fields in a direct manner. Laser-based precision measurements of dissociation energies, vibrational splittings and rotational level energies in H2 molecules and their deuterated isotopomers HD and D2 produce values for the rovibrational binding energies fully consistent with quantum ab initio calculations including relativistic and quantum electrodynamical (QED) effects. Similarly, precision measurements of high-overtone vibrational transitions of HD+ ions, captured in ion traps and sympathetically cooled to mK temperatures, also result in transition frequencies fully consistent with calculations including QED corrections. Precision measurements of inter-Rydberg transitions in H2 can be extrapolated to yield accurate values for level splittings in the H2+-ion. These comprehensive results of laboratory precision measurements on neutral and ionic hydrogen molecules can be interpreted to set bounds on the existence of possible fifth forces and of higher dimensions, phenomena describing physics beyond the Standard Model.

Light-by-light-type corrections to the muon anomalous magnetic moment at four-loop order

The numerically dominant QED contributions to the anomalous magnetic moment of the muon stem from Feynman diagrams with internal electron loops. We consider such corrections and present a calculation of the four-loop light-by-light-type corrections where the external photon couples to a closed electron or muon loop. We perform an asymptotic expansion in the ratio of electron and muon mass and reduce the resulting integrals to master integrals which we evaluate using analytical and numerical methods. We confirm the results present in the literature which are based on different computational methods.

Distinguishing modified gravity models

Modified gravity models with screening in local environments appear in three different guises: chameleon, K-mouflage and Vainshtein mechanisms. We propose to look for differences between these classes of models by considering cosmological observations at low redshift. In particular, we analyse the redshift dependence of the fine structure constant and the proton to electron mass ratio in each of these scenarios. When the absorption lines belong to unscreened regions of space such as dwarf galaxies, a time variation would be present for chameleons. For both K-mouflage and Vainshtein mechanisms, the cosmological time variation of the scalar field is not suppressed in both unscreened and screened environments, therefore enhancing the variation of constants and their detection prospect. We also consider the time variation of the redshift of distant objects using their spectrocopic velocities. We find that models of the K-mouflage and Vainshtein types have very different spectroscopic velocities as a function of redshift and that their differences with the Λ-CDM template should be within reach of the future ELT-HIRES observations.

The electron forewake: Shadowing and drift-energization as flowing magnetized plasma encounters an obstacle

Flow of magnetized plasma past an obstacle creates a traditional wake, but also a forewake region arising from shadowing of electrons. The electron forewakes resulting from supersonic flows past insulating and floating-potential obstacles are explored with 2D electrostatic particle-in-cell simulations, using a physical ion to electron mass ratio. Drift-energization is discovered to give rise to modifications to the electron velocity-distribution, including a slope-reversal, providing a novel drive of forewake instability. The slope-reversal is present at certain locations in all the simulations, and appears to be quite robustly generated. Wings of enhanced electron density are observed in some of the simulations, also associated with drift-energization. In the simulations with a floating-potential obstacle, the specific potential structure behind that obstacle allows fast electrons to cross the wake, giving rise to a more traditional shadowing-driven two-stream instability. Fluctuations associated with such instability are observed in the simulations, but this instability-mechanism is expected to be more sensitive to the plasma parameters than that associated with the slope-reversal.

Orientation of X lines in asymmetric magnetic reconnection—Mass ratio dependency

AbstractUsing fully kinetic simulations, we study the X line orientation of magnetic reconnection in an asymmetric configuration. A spatially localized perturbation is employed to induce a single X line, which has sufficient freedom to choose its orientation in three‐dimensional systems. The effect of ion to electron mass ratio is investigated, and the X line appears to bisect the magnetic shear angle across the current sheet in the large mass ratio limit. The orientation can generally be deduced by scanning through the corresponding 2‐D simulations to find the reconnection plane that maximizes the peak reconnection electric field. The deviation from the bisection angle in the lower mass ratio limit is consistent with the orientation shift of the most unstable linear tearing mode in an electron‐scale current sheet.

Scaling behavior of circular colliders dominated by synchrotron radiation

The scaling formulas in this paper — many of which involve approximation — apply primarily to electron colliders like CEPC or FCC-ee. The more abstract “radiation dominated” phrase in the title is intended to encourage use of the formulas — though admittedly less precisely — to proton colliders like SPPC, for which synchrotron radiation begins to dominate the design in spite of the large proton mass. Optimizing a facility having an electron–positron Higgs factory, followed decades later by a p, p collider in the same tunnel, is a formidable task. The CEPC design study constitutes an initial “constrained parameter” collider design. Here the constrained parameters include tunnel circumference, cell lengths, phase advance per cell, etc. This approach is valuable, if the constrained parameters are self-consistent and close to optimal. Jumping directly to detailed design makes it possible to develop reliable, objective cost estimates on a rapid time scale. A scaling law formulation is intended to contribute to a “ground-up” stage in the design of future circular colliders. In this more abstract approach, scaling formulas can be used to investigate ways in which the design can be better optimized. Equally important, by solving the lattice matching equations in closed form, as contrasted with running computer programs such as MAD, one can obtain better intuition concerning the fundamental parametric dependencies. The ground-up approach is made especially appropriate by the seemingly impossible task of simultaneous optimization of tunnel circumference for both electrons and protons. The fact that both colliders will be radiation dominated actually simplifies the simultaneous optimization task. All GeV scale electron accelerators are “synchrotron radiation dominated”, meaning that all beam distributions evolve within a fraction of a second to an equilibrium state in which “heating” due to radiation fluctuations is canceled by the “cooling” in RF cavities that restore the lost energy. To the contrary, until now, the large proton to electron mass ratio has caused synchrotron radiation to be negligible in proton accelerators. The LHC beam energy has still been low enough that synchrotron radiation has little effect on beam dynamics; but the thermodynamic penalty in cooling the superconducting magnets has still made it essential for the radiated power not to be dissipated at liquid helium temperatures. Achieving this has been a significant challenge. For the next generation p, p collider this will be even more true. Furthermore, the radiation will effect beam distributions on time scales measured in minutes, for example causing the beams to be flattened, wider than they are high. In this regime scaling relations previously valid only for electrons will be applicable also to protons.

Physical processes in an electron current layer causing intense plasma heating and formation of x-lines

We study the evolution of an electron current layer (ECL) through its several stages by means of three-dimensional particle-in-cell (PIC) simulations with ion to electron mass ratio M/me = 400. An ECL evolves through the following stages: (i) Electrostatic (ES) current-driven instability (CDI) soon after its formation with half width w about 2 electron skin depth (de), (ii) current disruption in the central part of the ECL by trapping of electrons and generation of anomalous resistivity, (iii) electron tearing instability (ETI) with significantly large growth rates in the lower end of the whistler frequency range, (iv) widening of the ECL and modulation of its width by the ETI, (v) gradual heating of electrons by the CDI-driven ES ion modes create the condition that the electrons become hotter than the ions, (vi) despite the reduced electron drift associated with the current disruption by the CDI, the enhanced electron temperature continues to favor a slow growth of the ion waves reaching nonlinear amplitudes, (vii) the nonlinear ion waves undergo modulation and collapse into localized density cavities containing spiky electric fields like in double layers (DLs), (viii) such spiky electric fields are very effective in further rapid heating of both electrons and ions. As predicted by the electron magnetohydrodynamic (EMHD) theories, the ETI growth rate maximizes at wave numbers in the range 0.4 < kxW < 0.8 where kx is the wave number parallel to the ECL magnetic field and w is the evolving half width of the ECL. The developing ETI generates in-plane currents that support out-of-plane magnetic fields around the emerging x-lines. The ETI and the spiky electrostatic structures are accompanied by fluctuations in the magnetic fields near and above the lower-hybrid (ion plasma) frequency, including the whistler frequency range. We compare our results with experimental results and satellite observation.

H2 Lyman and Werner band lines and their sensitivity for a variation of the proton–electron mass ratio in the gravitational potential of white dwarfs

Recently an accurate analysis of absorption spectra of molecular hydrogen, observed with the Cosmic Origins Spectrograph aboard the Hubble Space Telescope, in the photosphere of white dwarf stars GD133 and GD29-38 was published in a Letter [Phys. Rev. Lett. 113, 123002 (2014)], yielding a constraint on a possible dependence of the proton-electron mass ratio on a gravitational field of strength 10,000 times that at the Earth's surface. In the present paper further details of that study are presented, in particular a re-evaluation of the spectrum of the $B^1\Sigma_u^+ - X^1\Sigma_g^+ (v',v'')$ Lyman bands relevant for the prevailing temperatures (12,000 - 14,000 K) of the photospheres. An emphasis is on the calculation of so-called $K_i$-coefficients, that represent the sensitivity of each individual line to a possible change in the proton-electron mass ratio. Such calculations were performed by semi-empirical methods and by ab initio methods providing accurate and consistent values. A full listing is provided for the molecular physics data on the Lyman bands (wavelengths $\lambda_i$, line oscillator strengths $f_i$, radiative damping rates $\Gamma_i$, and sensitivity coefficients $K_i$) as required for the analyses of H$_2$-spectra in hot dwarf stars. A similar listing of the molecular physics parameters for the $C^1\Pi_u - X^1\Sigma_g^+ (v',v'')$ Werner bands is provided for future use in the analysis of white dwarf spectra.

Fidelity of reduced and realistic electron mass ratio multi-scale gyrokinetic simulations of tokamak discharges

The first study using multi-scale (coupled ITG/TEM/ETG) gyrokinetic simulations at both reduced and realistic electron mass ratios, μ = (mD/me).5 = 20.0, 40.0 and 60.0, has been performed on a standard, Alcator C-Mod, L-mode discharge. Ion-scale (kθρs ∼ 1.0) and multi-scale (up to kθρe ∼ 0.8) gyrokinetic simulations are compared at different simulated mass ratios to investigate the fidelity of reduced electron mass ratio, multi-scale simulation through direct comparison with realistic mass ratio, multi-scale simulation. Detailed description of both the numerical setup and the turbulent scales required to obtain meaningful coupled ITG/TEM/ETG simulation is presented. Significant high-k driven (TEM/ETG) heat flux is found to exist at scales of approximately kθρe ∼ 0.1 at all mass ratios but can only be obtained by simulation capturing turbulence up to kθρe ∼ 1.0. At slightly reduced mass ratio, μ = 40.0, qualitative agreement with realistic mass simulation can be obtained in the studied discharge, consistent with intuition obtained from linear stability analysis. However, realistic electron mass is required for any robust quantitative comparison with experimental heat fluxes for the condition studied, as significant differences are observed at even slightly reduced electron mass ratio. The details of this numerical study are presented to provide a basis for future studies utilizing coupled ITG/TEM/ETG gyrokinetic simulation.

Kinetic electron and ion instability of the lunar wake simulated at physical mass ratio

The solar wind wake behind the moon is studied with 1D electrostatic particle-in-cell (PIC) simulations using a physical ion to electron mass ratio (unlike prior investigations); the simulations also apply more generally to supersonic flow of dense magnetized plasma past non-magnetic objects. A hybrid electrostatic Boltzmann electron treatment is first used to investigate the ion stability in the absence of kinetic electron effects, showing that the ions are two-stream unstable for downstream wake distances (in lunar radii) greater than about three times the solar wind Mach number. Simulations with PIC electrons are then used to show that kinetic electron effects can lead to disruption of the ion beams at least three times closer to the moon than in the hybrid simulations. This disruption occurs as the result of a novel wake phenomenon: the non-linear growth of electron holes spawned from a narrow dimple in the electron velocity distribution. Most of the holes arising from the dimple are small and quickly leave the wake, approximately following the unperturbed electron phase-space trajectories, but some holes originating near the center of the wake remain and grow large enough to trigger disruption of the ion beams. Non-linear kinetic-electron effects are therefore essential to a comprehensive understanding of the 1D electrostatic stability of such wakes, and possible observational signatures in ARTEMIS data from the lunar wake are discussed.

The effects of ion mass variation and domain size on octupolar out-of-plane magnetic field generation in collisionless magnetic reconnection

Graf von der Pahlen and Tsiklauri [Phys. Plasmas 21, 060705 (2014)] established that the generation of octupolar out-of-plane magnetic field structure in a stressed X-point collapse is due to ion currents. The field has a central region, comprising of the well-known quadrupolar field (quadrupolar components), as well as four additional poles of reversed polarity closer to the corners of the domain (octupolar components). In this extended work, the dependence of the octupolar structure on domain size and ion mass variation is investigated. Simulations show that the strength and spatial structure of the generated octupolar magnetic field is independent of ion to electron mass ratio; thus showing that ion currents play a significant role in out-of-plane magnetic structure generation in physically realistic scenarios. Simulations of different system sizes show that the width of the octupolar structure remains the same and has a spacial extent of the order of the ion inertial length. The width of the structure thus appears to be independent on boundary condition effects. The length of the octupolar structure, however, increases for greater domain sizes, prescribed by the external system size. This was found to be a consequence of the structure of the in-plane magnetic field in the outflow region halting the particle flow and thus terminating the in-plane currents that generate the out-of-plane field. The generation of octupolar magnetic field structure is also established in a tearing-mode reconnection scenario. The differences in the generation of the octupolar field and resulting qualitative differences between X-point collapse and tearing-mode are discussed.

Constraint on a varying proton-electron mass ratio 1.5 billion years after the big bang.

A molecular hydrogen absorber at a lookback time of 12.4 billion years, corresponding to 10% of the age of the Universe today, is analyzed to put a constraint on a varying proton-electron mass ratio, μ. A high resolution spectrum of the J1443+2724 quasar, which was observed with the Very Large Telescope, is used to create an accurate model of 89 Lyman and Werner band transitions whose relative frequencies are sensitive to μ, yielding a limit on the relative deviation from the current laboratory value of Δμ/μ=(-9.5 ± 5.4(stat)± 5.3(syst))×10(-6).

Constraints on changes in the proton–electron mass ratio using methanol lines

Abstract We report Karl G. Jansky Very Large Array (VLA) absorption spectroscopy in four methanol (CH3OH) lines in the z = 0.885 82 gravitational lens towards PKS1830−211. Three of the four lines have very different sensitivity coefficients Kμ to changes in the proton–electron mass ratio μ; a comparison between the line redshifts thus allows us to test for temporal evolution in μ. We obtain a stringent statistical constraint on changes in μ by comparing the redshifted 12.179 and 60.531 GHz lines, [Δμ/μ] ≤ 1.1 × 10−7 (2σ) over 0 &amp;lt; z ≤ 0.885 82, a factor of ≈2.5 more sensitive than the best earlier results. However, the higher signal-to-noise ratio (by a factor of ≈2) of the VLA spectrum in the 12.179 GHz transition also indicates that this line has a different shape from that of the other three CH3OH lines (at &amp;gt;4σ significance). The sensitivity of the above result, and that of all earlier CH3OH studies, is thus likely to be limited by unknown systematic errors, probably arising due to the frequency-dependent structure of PKS1830−211. A robust result is obtained by combining the three lines at similar frequencies, 48.372, 48.377 and 60.531 GHz, whose line profiles are found to be in good agreement. This yields the 2σ constraint [Δμ/μ] ≲ 4 × 10−7, the most stringent current constraint on changes in μ. We thus find no evidence for changes in the proton–electron mass ratio over a lookback time of ≈7.5 Gyr.

Electron vortex magnetic holes: A nonlinear coherent plasma structure

We report the properties of a novel type of sub-proton scale magnetic hole found in two dimensional particle-in-cell simulations of decaying turbulence with a guide field. The simulations were performed with a realistic value for ion to electron mass ratio. These structures, electron vortex magnetic holes (EVMHs), have circular cross-section. The magnetic field depression is associated with a diamagnetic azimuthal current provided by a population of trapped electrons in petal-like orbits. The trapped electron population provides a mean azimuthal velocity and since trapping preferentially selects high pitch angles, a perpendicular temperature anisotropy. The structures arise out of initial perturbations in the course of the turbulent evolution of the plasma, and are stable over at least 100 electron gyroperiods. We have verified the model for the EVMH by carrying out test particle and PIC simulations of isolated structures in a uniform plasma. It is found that (quasi-)stable structures can be formed provided that there is some initial perpendicular temperature anisotropy at the structure location. The properties of these structures (scale size, trapped population, etc.) are able to explain the observed properties of magnetic holes in the terrestrial plasma sheet. EVMHs may also contribute to turbulence properties, such as intermittency, at short scale lengths in other astrophysical plasmas.

Photon momentum sharing between an electron and an ion in photoionization: from one-photon (photoelectric effect) to multiphoton absorption.

We investigate photon-momentum sharing between an electron and an ion following different photoionization regimes. We find very different partitioning of the photon momentum in one-photon ionization (the photoelectric effect) as compared to multiphoton processes. In the photoelectric effect, the electron acquires a momentum that is much greater than the single photon momentum ℏω/c [up to (8/5) ℏω/c] whereas in the strong-field ionization regime, the photoelectron only acquires the momentum corresponding to the photons absorbed above the field-free ionization threshold plus a momentum corresponding to a fraction (3/10) of the ionization potential Ip. In both cases, due to the smallness of the electron-ion mass ratio, the ion takes nearly the entire momentum of all absorbed N photons (via the electron-ion center of mass). Additionally, the ion takes, as a recoil, the photoelectron momentum resulting from mutual electron-ion interaction in the electromagnetic field. Consequently, the momentum partitioning of the photofragments is very different in both regimes. This suggests that there is a rich, unexplored physics to be studied between these two limits which can be generated with current ultrafast laser technology.

A study on aberrations in energy band gap of quantum confined gallium arsenide spherical nanoparticles

The present paper reports the energy band gap behaviour in quantum confined gallium arsenide (GaAs) nanoparticles. GaAs spherical nanoparticles were formed by highly energetic and high fluence ions of GaAs in argon plasma generated in a modified dense plasma focus device. The energy band gaps of these nanoparticles having size in the range of 6-13nm were obtained from optical absorption spectra experimentally and then compared with the theoretically expected values of band gap. A deviation in energy band gap has been observed. This deviation has been attributed to non-spherical shape of nanoparticles in the literature. Instead, we have found that for spherical nanoparticles the observed deviation is because of change in effective mass ratio of electrons and holes.

Electron heating during magnetic reconnection: A simulation scaling study

Electron bulk heating during magnetic reconnection with symmetric inflow conditions is examined using kinetic particle-in-cell simulations. Inflowing plasma parameters are varied over a wide range of conditions, and the increase in electron temperature is measured in the exhaust well downstream of the x-line. The degree of electron heating is well correlated with the inflowing Alfvén speed cAr based on the reconnecting magnetic field through the relation ΔTe=0.033 mi cAr2, where ΔTe is the increase in electron temperature. For the range of simulations performed, the heating shows almost no correlation with inflow total temperature Ttot=Ti+Te or plasma β. An out-of-plane (guide) magnetic field of similar magnitude to the reconnecting field does not affect the total heating, but it does quench perpendicular heating, with almost all heating being in the parallel direction. These results are qualitatively consistent with a recent statistical survey of electron heating in the dayside magnetopause (Phan et al., Geophys. Res. Lett. 40, 4475, 2013), which also found that ΔTe was proportional to the inflowing Alfvén speed. The net electron heating varies very little with distance downstream of the x-line. The simulations show at most a very weak dependence of electron heating on the ion to electron mass ratio. In the antiparallel reconnection case, the largely parallel heating is eventually isotropized downstream due a scattering mechanism, such as stochastic particle motion or instabilities. The simulation size is large enough to be directly relevant to reconnection in the Earth's magnetosphere, and the present findings may prove to be universal in nature with applications to the solar wind, the solar corona, and other astrophysical plasmas. The study highlights key properties that must be satisfied by an electron heating mechanism: (1) preferential heating in the parallel direction; (2) heating proportional to mi cAr2; (3) at most a weak dependence on electron mass; and (4) an exhaust electron temperature that varies little with distance from the x-line.

Suppression of AC Stark shift in Raman spectroscopy of optically trapped molecules

The variation of proton–electron mass ratio can be tested through precise measurements of the transition frequency of ultracold diatomic molecules confined in an optical trap. We propose to measure resonant frequency via the Raman transition induced by an intense trapping laser beam and a weak probe laser beam. By tuning the trap laser to a specific frequency at which the AC Stark shift is cancelled, the relative frequency shift on the Raman transition can be reduced to below 10−16.

Synergistic cross-scale coupling of turbulence in a tokamak plasma

For the first time, nonlinear gyrokinetic simulations spanning both the ion and electron spatio-temporal scales have been performed with realistic electron mass ratio ((mD∕me)1∕2 = 60.0), realistic geometry, and all experimental inputs, demonstrating the coexistence and synergy of ion (kθρs∼O(1.0)) and electron-scale (kθρe∼O(1.0)) turbulence in the core of a tokamak plasma. All multi-scale simulations utilized the GYRO code [J. Candy and R. E. Waltz, J. Comput. Phys. 186, 545 (2003)] to study the coupling of ion and electron-scale turbulence in the core (r/a = 0.6) of an Alcator C-Mod L-mode discharge shown previously to exhibit an under-prediction of the electron heat flux when using simulations only including ion-scale turbulence. Electron-scale turbulence is found to play a dominant role in setting the electron heat flux level and radially elongated (kr ≪ kθ) “streamers” are found to coexist with ion-scale eddies in experimental plasma conditions. Inclusion of electron-scale turbulence in these simulations is found to increase both ion and electron heat flux levels by enhancing the transport at the ion-scale while also driving electron heat flux at sub-ρi scales. The combined increases in the low and high-k driven electron heat flux may explain previously observed discrepancies between simulated and experimental electron heat fluxes and indicates a complex interaction of short and long wavelength turbulence.

EXCITATION OF KINETIC ALFVÉN WAVES BY FAST ELECTRON BEAMS

Energetic electron beams, which are ubiquitous in a large variety of active phenomena in space and astrophysical plasmas, are one of the most important sources that drive plasma instabilities. In this paper, taking account of the return-current effect of fast electron beams, kinetic Alfven wave (KAW) instability driven by a fast electron beam is investigated in a finite-beta plasma of Q < beta < 1 (where beta is the kinetic-to-magnetic pressure ratio and Q = m(e)/m(i) is the mass ratio of electrons to ions). The results show that the kinetic resonant interaction of beam electrons is the driving source for KAW instability, unlike the case driven by a fast ion beam, where both the kinetic resonant interaction of beam ions and the return-current are the driving source for the KAW instability. KAW instability has a nonzero growth rate in the range of the perpendicular wave number, 0 < k(perpendicular to) < k(perpendicular to)(u), and the maximum growth rate, gamma(m), occurs between 0.5k(perpendicular to)(u) < k(perpendicular to)(m) < 0.8k(perpendicular to)(u). Both the maximal growing perpendicular wave number k(perpendicular to)(m) and the maximal growth rate gamma(m) depend sensitively on the velocity of electron beam upsilon(b), and the most favorable beam velocity occurs between 8 upsilon(A) < upsilon(b) < 10 upsilon(A). On the other hand, the excited KAWs are weakly dispersive with k(perpendicular to) rho(i) < 1 and have the maximum growth rate at relatively low perpendicular wave numbers in the range 0.3 < k(perpendicular to)(m) rho(i) < 0.6 for a beam velocity upsilon(b) < 10 upsilon(A). A possible application to the upward electron beams in the terrestrial magnetosphere is briefly discussed.