Electron Mass Ratio Research Articles

Author Correction: Proton–electron mass ratio by high-resolution optical spectroscopy of ion ensembles in the resolved-carrier regime

Author Correction: Proton–electron mass ratio by high-resolution optical spectroscopy of ion ensembles in the resolved-carrier regime

Fast correlation heating in moderately coupled electron–ion plasmas

If the electrons in a plasma are suddenly heated, the resulting change in Debye shielding causes the ion kinetic energy to quickly increase. For the first time, this correlation heating, which is much faster than collisional energy exchange, is rigorously derived for a moderately coupled, electron–ion plasma. The electron–ion mass ratio is taken to be the smallest parameter in the Bogoliubov–Born–Green–Kirkwood–Yvon hierarchy, smaller even than the reciprocal of the plasma parameter. This ordering differs from conventional kinetic theory by making the electron collision rates faster than the ion plasma frequency, which allows stronger coupling and makes the ion heating a function only of the total energy supplied to the electrons. The calculation uses known formulae for correlations in a two-temperature plasma, for which a new, elementary derivation is presented. Suprathermal ions may be created more rapidly by this mechanism than by ion–electron Coulomb collisions. This means that the use of a femtosecond laser pulse could potentially help to achieve ignition in certain fast ignition approaches to inertial confinement fusion.

Particle-in-cell simulations – ion beam instabilities and the generation of Alfvén and whistler waves in low β plasma

ABSTRACT Ion beam-driven instabilities in a collisionless space plasma with low β, i.e. low plasma and magnetic pressure ratio, are investigated using particle-in-cell (PIC) simulations. Specifically, the effects of different ion drift velocities on the development of Buneman and resonant electromagnetic (EM) right-handed (RH) ion beam instabilities are studied. Our simulations reveal that both instabilities can be driven when the ion beam drift exceeds the theoretical thresholds. The Buneman instability, which is weakly triggered initially, dissipates only a small fraction of the kinetic energy of the ion beam while causing significant electron heating, owing to the small electron-ion mass ratio. However, we find that the ion beam-driven Buneman instability is quenched effectively by the resonant EM RH ion beam instability. Instead, the resonant EM RH ion beam instability dominates when the ion drift velocity is larger than the Alfvén speed, leading to the generation of RH Alfvén waves and RH whistler waves. We find that the intensity of Alfvén waves decreases with decrease of ion beam drift velocity, while the intensity of whistler waves increases. Our results provide new insights into the complex interplay between ion beams and plasma instabilities in low β collisionless space plasmas.

Larmor Electric Field in Symmetric Magnetic Reconnection

The Larmor electric field (LEF) was previously suggested as a signature to identify the diffusion region in asymmetry reconnection. Using 2.5D particle-in-cell simulations, we show that the LEF also exists in symmetric reconnection, manifested as a transient structure upstream of the Hall electric field. The LEF emerges during the rapid growth phase of the reconnection rate and has opposite polarity to the Hall field. The half-width of the current sheet spontaneously decreases to the electron scale as the evolution of reconnection, which gives rise to the LEF. The current sheet later thickens to maintain the fast reconnection rate, which causes the disappearance of the LEF. We further find that the magnitude of LEF is sensitive to the initial half-width current sheet, the background plasma temperature and density, the guide-field strength, and the ion–electron mass ratio. Our results provide new insight into the dynamics around the diffusion region. The LEF can help satellites not only locate the diffusion region but also identify the onset phase of reconnection in the magnetotail.

The force balance of electrons during kinetic anti-parallel magnetic reconnection

Fully kinetic simulations are applied to the study of 2D anti-parallel reconnection, elucidating the dynamics by which the electron fluid maintains force balance within both the ion diffusion region (IDR) and the electron diffusion region (EDR). Inside the IDR, magnetic field-aligned electron pressure anisotropy (pe∥≫pe⊥) develops upstream of the EDR. Compared to previous investigations, the use of modern computer facilities allows for simulations at the natural proton to electron mass ratio mi/me=1836. In this high-mi/me-limit, the electron dynamics change qualitatively, as the electron inflow to the EDR is enhanced and mainly driven by the anisotropic pressure. Using a coordinate system with the x-direction aligned with the reconnecting magnetic field and the y-direction aligned with the central current layer, it is well known that for the much studied 2D laminar anti-parallel and symmetric scenario the reconnection electric field at the X-line must be balanced by the ∂pexy/∂x and ∂peyz/∂z off-diagonal electron pressure stress components. We find that the electron anisotropy upstream of the EDR imposes large values of ∂pexy/∂x within the EDR, and along the direction of the reconnection X-line, this stress cancels with the stress of a previously determined theoretical form for ∂peyz/∂z. The electron frozen-in law is instead broken by pressure tensor gradients related to the direct heating of the electrons by the reconnection electric field. The reconnection rate is free to adjust to the value imposed externally by the plasma dynamics at larger scales.

A non-neutral generalized Ohm's law model for magnetohydrodynamics in the two-fluid regime

A new non-neutral generalized Ohm's law (GOL) model for atomic plasmas is presented. This model differs from previous models of this type in that quasi-neutrality is not assumed at any point. Collisional effects due to ionization, recombination, and elastic scattering are included, and an expression for the associated plasma conductivity is derived. An initial set of numerical simulations are considered that compare the GOL model to a two-fluid model in the ideal (collisionless) case. The results demonstrate that solutions obtained from the two models are essentially indistinguishable in most cases when the ion–electron mass ratio is within the range of physical values for atomic plasmas. Additionally, some limitations of the model are discussed.

The Bulk van der Waals Layered Magnet CrSBr is a Quasi-1D Material.

Correlated quantum phenomena in one-dimensional (1D) systems that exhibit competing electronic and magnetic order are of strong interest for the study of fundamental interactions and excitations, such as Tomonaga-Luttinger liquids and topological orders and defects with properties completely different from the quasiparticles expected in their higher-dimensional counterparts. However, clean 1D electronic systems are difficult to realize experimentally, particularly for magnetically ordered systems. Here, we show that the van der Waals layered magnetic semiconductor CrSBr behaves like a quasi-1D material embedded in a magnetically ordered environment. The strong 1D electronic character originates from the Cr-S chains and the combination of weak interlayer hybridization and anisotropy in effective mass and dielectric screening, with an effective electron mass ratio of mXe/mYe ∼ 50. This extreme anisotropy experimentally manifests in strong electron-phonon and exciton-phonon interactions, a Peierls-like structural instability, and a Fano resonance from a van Hove singularity of similar strength to that of metallic carbon nanotubes. Moreover, because of the reduced dimensionality and interlayer coupling, CrSBr hosts spectrally narrow (1 meV) excitons of high binding energy and oscillator strength that inherit the 1D character. Overall, CrSBr is best understood as a stack of weakly hybridized monolayers and appears to be an experimentally attractive candidate for the study of exotic exciton and 1D-correlated many-body physics in the presence of magnetic order.

Effect of substitution doping and surface adsorption of Al atoms on photocatalytic decomposition of water and oxygen from BiVO<sub>4</sub> (010) crystal surface

Using solar photoelectrochemical decomposition of water to produce hydrogen and oxygen is one of the most feasible approaches to obtaining renewable energy. Compared with hydrogen-evolution reaction (HER), the oxygen-evolution reaction (OER) is very complex, there are four sluggish proton-coupled electron transfer processes. It is critical to improve OER performance. The BiVO<sub>4</sub> (010) facet possesses low surface energy, strong visible absorption, and good activity for OER, and is considered as one of the most suitable PEC catalysts. However, its poor electron conductivity, low charge carrier mobility, and high charge recombination rates significantly limit its practical applications. To achieve highly active OER photocatalysts, we modify BiVO<sub>4</sub> (010) facet by substitutial doping with Al atom and surface adsorption with Al atom. According to density functional theory calculations, we compare OER performances of these two modified BiVO<sub>4</sub> (010) facets. The results show that both approaches can effectively regulate the electronic structure of BiVO<sub>4</sub> and then tune OER activity resulting from the change of the structure. Though Al substitutional doping reduces the band gap of the (010) facet and enhances the visible light absorption, the improvement of OER performance is not significant because the doping site is inside and has little influence on the surface active site. Importantly, the surface adsorption of Al atom is considered as an efficient means to improve the OER activity on BiVO<sub>4</sub> (010) facet due to the combined action between surface adsorbed Al and active site Bi atoms. Al adsorbed (010) facet exhibits excellent OER catalytic activity: 1) the induction of localized states and the reduction of band gap are conducive to the electronic transition, optical absorption, thus increasing the electrical conductivity; 2) there is lower hole effective mass, and thus effectively enhancing the ability to transfer from anode surface to electrolyte surface, thereby increasing the difference between the effective mass ratio of electron−hole pairs and 1 and effectively reducing the electron-hole recombination; 3) the nteraction between the active sites and oxygen-containing intermediates is reinforced in the OER process, therefore the potential determining step of OER decreases effectively. This work provides an important reference for designing efficient and stable two-dimensional semiconductor-based photocatalysts for OER. We believe that it will arouse great interest of the BiVO<sub>4</sub> community and motivate numerous experimental researches.

Mid-IR frequency laser control with a comb for H2+ spectroscopy

We will report our recent progress toward H2+ spectroscopy by use of a SI-referenced Mid-IR source laser. H2+ molecular ions are very interesting candidates to improve the determination of fundamental constants, such as the proton to electron mass ratio mp/me and search for new physics beyond the standard model. At LKB, an erbium fibered frequency comb is phase locked to the LNE-SYRTE frequency standards thanks to the T-REFIMEVE network. By sum frequency generation in a AgGaSe2 crystal between a CO2 laser and an output of the comb at 1895 nm, a shifted frequency comb centered at 1560 nm is generated. The latter is then mixed with the original one to generate a beatnote used to stabilise the Mid-IR laser. As a first application, a narrow saturated absorption line in formic acid has been extensively studied. Pressure, power and modulation depth shifts and broadenings have been evaluated, leading to a determination of its central frequency at a sub ppt (10-12) resolution, high enough for H2+ spectroscopy and fundamental constant determination.

Precision Spectroscopy of the Hydrogen Molecular Ions: Present Status of Theory and Experiment

We review recent experiments on HD$^+$ spectroscopy. The reduced proton-deuteron mass to electron mass ratio, $\mu_{pd}/m_e$, is inferred from the comparison of theory and experiment. Theoretical issues related to the calculations of the spin structure, which are currently the main limiting factor of theoretical accuracy, are discussed.

Ion Acoustic Shock Wave Formation and Ion Acceleration in the Interactions of Pair Jets with Electron–ion Plasmas

Astrophysical jets are ubiquitous in the universe and often associated with compact objects, and their interactions with the ambient medium not only dissipate their own energy but also provide ideal circumstances for particle acceleration. By means of theoretical analysis and particle-in-cell simulations, here we study the ion acoustic shock wave (IASW) formation and consequent ion acceleration when electron–positron (e − e +) jets are injected into ambient electron–ion plasmas. It is found that the Buneman instability can be excited first, which induces the formation of an ion acoustic wave (IAW). As the amplitude of the IAW increases, its waveform is steepened and subsequently an IASW is formed. Some ions in the ambient plasmas will be reflected when they encounter the IASW, and thus can be accelerated to form an energetic ion beam. For an initial e − e + jet with the Lorentz factor γ 0 = 100 and the ion–electron mass ratio m i /m e = 1836, the ions can be accelerated up to 580 MeV. This study deepens our understanding of the fireball model of gamma-ray bursts, the shock model of pulsar wind nebulae, the origin of cosmic rays, and other related astrophysical processes.

Sheath collapse at critical shallow angle due to kinetic effects

The Debye sheath is known to vanish completely in magnetised plasmas for a sufficiently small electron gyroradius and small angle between the magnetic field and the wall. This angle depends on the current onto the wall. When the Debye sheath vanishes, there is still a potential drop between the wall and the plasma across the magnetic presheath. The magnetic field angle corresponding to the predicted sheath collapse is shown to be much smaller than previous estimates, scaling with the electron-ion mass ratio and not with the square root of the mass ratio. This is shown to be a consequence of the kinetic electron and finite ion orbit width effects, which are not captured by fluid models. The wall potential with respect to the bulk plasma at which the Debye sheath vanishes is calculated. Above this wall potential, it is possible that the Debye sheath will invert.

Kinetic simulation study of magnetized collisionless shock formation on a terawatt laser system

Perpendicular, magnetized, collisionless shocks in hydrogen and neon plasmas are studied with 2D particle-in-cell simulations for parameters accessible to experiments on OMEGA EP [Maywar et al., J. Phys.: Conf. Ser. 112, 032007 (2008)]. The simulations are performed with realistic ion-electron mass ratios by which the relative importance of different micro-instabilities can be accurately captured. The dispersion relation of the modified two-stream instability (MTSI), the main dissipation mechanism for these shocks, is used to find suitable parameters for upcoming experiments. Simulations show that magnetized collisionless shocks can be readily formed within a few tenths of an ion gyro-period in both hydrogen and neon gases, with a background magnetic field of 50 T, achievable using the magneto-inertial fusion electrical discharge system [Barnak et al., Rev. Sci. Instrum. 89, 033501 (2018)]. A portion of the ions are reflected to the upstream region and accelerated in both shock normal and tangential directions, indicating the formation of a supercritical shock. Shock front reformation is seen in longer time 1D simulations. The results show that the formation time and width of these shocks are determined by MTSI.

Proton–electron mass ratio by high-resolution optical spectroscopy of ion ensembles in the resolved-carrier regime

Optical spectroscopy in the gas phase is a key tool to elucidate the structure of atoms and molecules and of their interaction with external fields. The line resolution is usually limited by a combination of first-order Doppler broadening due to particle thermal motion and of a short transit time through the excitation beam. For trapped particles, suitable laser cooling techniques can lead to strong confinement (Lamb-Dicke regime, LDR) and thus to optical spectroscopy free of these effects. For non-laser coolable spectroscopy ions, this has so far only been achieved when trapping one or two atomic ions, together with a single laser-coolable atomic ion [1,2]. Here we show that one-photon optical spectroscopy free of Doppler and transit broadening can also be obtained with more easily prepared ensembles of ions, if performed with mid-infrared radiation. We demonstrate the method on molecular ions. We trap approximately 100 molecular hydrogen ions (HD$^{+}$) within a Coulomb cluster of a few thousand laser-cooled atomic ions and perform laser spectroscopy of the fundamental vibrational transition. Transition frequencies were determined with lowest uncertainty of 3.3$\times$10$^{-12}$ fractionally. As an application, we determine the proton-electron mass ratio by matching a precise ab initio calculation with the measured vibrational frequency.

Magnetized current filaments as a source of circularly polarized light

We show that the Weibel or current filamentation instability can lead to the emission of circularly polarized radiation. Using particle-in-cell simulations and a radiation post-processing numerical algorithm, we demonstrate that the level of circular polarization increases with the initial plasma magnetization, saturating at ${\sim }13\,\%$ when the magnetization, given by the ratio of magnetic energy density to the electron kinetic energy density, is larger than 0.05. Furthermore, we show that this effect requires an ion–electron mass ratio greater than unity. These findings, which could also be tested in currently available laboratory conditions, show that the recent observation of circular polarization in gamma-ray burst afterglows could be attributed to the presence of magnetized current filaments driven by the Weibel or current filamentation instability.

Unity Formula that connect the Fine Structure constant and the Proton to Electron Mass Ratio

In this paper will be presented the unity Formulas that connect the Fine Structure constant α and the Proton to Electron Mass Ratio μ. The equations are simple,elegant and symmetrical in a great physical meaning. At the beginning we will make a review of the last works. We will suggest the exact formula for the Fine Structure constant α with the Golden Angle and the Fifth Power of the Golden Mean and αlso we propose a simple and accurate expression for the Fine Structure constant α in terms of the Archimedes constant π. After we propose two exact mathematical expressions for the Proton to Electron Mass Ratio. It will be presented the mathematical Formula that connects the Proton to Electron Mass Ratio μ,the Fine-structure constant α,the ratio Ν1 of electric force to gravitational force between electron and proton,the Avogadro number NA,the Gravitational coupling constant αG for the electron and the gravitational coupling constant of proton αG(p). Also we will find a new formula for the Avogadro number NA and a new formula for Gravitational Constant G. Ιt will be explained that the product μ⋅α-1 is one of the roots of the following trigonometric equation: 2·102⋅cos(μ⋅α-1)+132=0 (1) It will also be shown that another way to show this equation is the following exponential form of the equation: 102⋅(eiμ/α+e-iμ/α)+132=0 (2) This exponential form can also be written with the form: 102⋅(eiμ/α+e-iμ/α)=132⋅eiπ (3) So the beautiful formula that connect the Fine Structure constant,the Proton to Electron Mass Ratio and the Fifth Power of the Golden Mean is: 52⋅(5∙φ-2+φ-5)2⋅(eiμ/α+e-iμ/α)+(5∙φ2-φ-5)2=0 (4) Also the formula that connect the Fine Structure constant,the Proton to Electron Mass Ratio and Mathematical constants π,φ,e,i is: 102⋅(eiμ/α+e-iμ/α)=(5∙φ2-φ-5)2⋅eiπ (5) Also the unity Formula can also be written in the form: 10⋅(eiμ/α+e-iμ/α)1/2=13⋅i (6) Finally we will show that the radio ω=(c/υs)2 of the speed of light and the maximum speed of sound depends only from the Fine Structure constant α and not from the Proton to Electron Mass Ratio μ: 102⋅(eiωα/2+e-iωα/2)+132=0 (7) All these equations are simple,elegant and symmetrical in a great physical meaning.

Exact Mathematical Expressions of the Proton to Electron Mass Ratio with Symmetrical Shape and Physical Meaning

We present 26 exact mathematical expressions of the Proton to Electron Mass Ratio with exact value μ=1.836,15267343. Also we present exact mathematical expressions between the Proton to Electron Mass Ratio and mathematical constants and also exact mathematical expressions between the Proton to Electron Mass Ratio and the Fine Structure constant α.

Structure-preserving electromagnetic–kinetic simulations of lower hybrid-wave injection and current drive

In this article, we present a first-principles electromagnetic–kinetic simulation of the slow-wave branch of the lower hybrid waves (LHWs) in electron–deuterium plasmas with real ion–electron mass ratios. Several models of two-dimensional slab configuration containing a grill antenna are constructed using different plasma parameters. Based on our recently developed fully kinetic charge-conservative electromagnetic non-canonical symplectic particle-in-cell method, we studied the coupling, propagation, absorption and current driving effect of LHWs in hot plasmas. The results for the coupling coefficient of the grill antenna, accessibility condition, and electron Landau damping rate show good agreement with theory and previous simulation. The long-term non-linear energy and current deposition of propagating LHWs are also presented, which show a decrement of heating and current-driving efficiency compared with the linear theoretical prediction. The collision effect between electrons and ions is shown to be important for actually driving the current. The relation between the density of the current generated and the amplitude of the LHW is given, which shows a qualitative agreement with the 1D theoretical prediction.

SI-traceable molecular transition frequency measurements at the 10−12 relative uncertainty level

Accurate and spectroscopic measurements of molecular transition frequencies are increasingly being employed in a variety of rigorous tests of physics, including the validity of quantum electrodynamics, the proton–electron mass ratio, and the dipole moment of the electron. Near-infrared molecular transitions may also underpin secondary frequency standards for length metrology and provide convenient wavelength standards for telecommunication and spectroscopy. To report progress in this field, we describe measurements of near-infrared Doppler-broadened carbon dioxide line positions. Our experiment uses cavity ring-down spectroscopy in the linear domain and provides an accurate International System of Units (SI)-traceable frequency axis via active locking of the probe laser and ring-down cavity to a Cs-clock-referenced optical frequency comb. The approach has several key attributes: the ability to rapidly scan the probe laser while maintaining a phase lock to the optical frequency comb, continuously tunable spectrum frequency axes that are not limited by the cavity mode spacing, and high signal-to-noise-ratio spectra resulting in stationary statistics amenable to long-term averaging. This performance is achieved by phase locking a single-mode probe laser to the optical frequency comb, coherent electro-optical phase modulation for rapid cavity mode-to-mode shifting of the probe laser, and sub-kilohertz-level frequency stabilization of the ring-down cavity relative to the probe laser. We report vacuum transition frequencies of five transitions in the ( 30012 ) ← ( 00001 ) vibrational band of 12 C 16 O 2 near 1.57 µm and achieve combined standard uncertainties as low as 212 Hz, corresponding to a relative combined standard uncertainty near 10 − 12 .

Finite spatial-grid effects in energy-conserving particle-in-cell algorithms

Finite-grid (or aliasing) instabilities are pervasive in particle-in-cell (PIC) plasma simulation algorithms, and force the modeler to resolve the smallest (Debye) length scale in the problem regardless of dynamical relevance. These instabilities originate in the aliasing of interpolation errors between mesh quantities and particles (which live in the space–time continuum). Recently, strictly energy-conserving PIC (EC-PIC) algorithms have been developed that promise enhanced robustness against aliasing instabilities. In this study, we confirm by analysis that EC-PIC is stable against aliasing instabilities for stationary plasmas. For drifting plasmas, we demonstrate by analysis and numerical experiments that, while EC-PIC algorithms are not free from these instabilities in principle, they feature a benign stability threshold for finite-temperature plasmas that make them usable in practice for a large class of problems (featuring ambipolarity and realistic ion-electron mass ratios) without the need to consider the size of the Debye length. We also demonstrate that this threshold is absent for the popular momentum-conserving PIC algorithms, which are therefore unstable for both drifting and stationary plasmas beyond a threshold in cell size compared to Debye length.