Free Electrons Compton Scattering Can Produce an Illusion of Expanding Universe

The high-precision measurements of the Hubble parameter make the theory of cosmic expansion more and more confusing, which bolsters the idea that new physics may be needed to explain the mismatch. Astronomical observations show that the Universe is expanding exponentially. Free electron Compton scattering (FEC) can produce the illusion of exponentially expanding Universe: FEC causes photons to redshift exponentially, and the photon beam exponentially expands along the propagation direction. Is this a coincidence? The redshift factor of the FEC is z = (1+z);the beam length stretch factor (time dilation of the supernova curve) of the FEC is z = (1+z);the expansion factor of the beam volume of the FEC is z = (1+z)3, and the FEC effect does not blur the image of distant galaxies. The reason for rejecting the “tired light” does not hold in FEC.

Nearly Free Electron State in Graphane Nanoribbon Superlattice

Nearly free electron （NFE） state has been widely studied in low dimensional systems. Based on first-principles calculations, we identify two types of NFE states in graphane nanoribbon superlattice, similar to those of graphene nanoribbons and boron nitride nanoribbons. Effect of electron doping on the NFE states in graphane nanoribbon superlattice has been studied, and it is possible to open a vacuum transport channel via electron doping.

Smith-Purcell free electron laser based on the semi-elliptical resonator

A novel Smith-Purcell （S-P） free electron laser composed of an electron gun, a semi-elliptical resonator, a metallic reflecting grating and a collector, is presented for the first time. This paper studies the characteristics of this device by theoretical analysis and particle-in-cell simulation method. Results indicate that tunable coherent S-P radiation with a high output peak power at millimeter wavelengths can be generated by adjusting the length of the grating period, or adjusting the voltage of the electron beam. The present scheme has the following advantages： the semi-elliptical resonator can reflect all radiation with the emission angle {？ and random azimuthal angles, back onto the electron beam with same-phase and causes the electrons to be modulated, so the output power and efficiency are improved.

First commissioning results of the coherent scattering and imaging endstation at the Shanghai soft X-ray free-electron laser facility

The Shanghai soft X-ray free-electron laser(SXFEL)user facility project started in 2016 and is expected to be open to users by 2022.It aims to deliver ultra-intense coherent femtosecond X-ray pulses to five endstations covering a range of 100–620 eV for ultrafast X-ray science.Two undulator lines are designed and constructed,based on different lasing modes:self-amplified spontaneous emission and echo-enabled harmonic generation.The coherent scattering and imaging(CSI)endstation is the first of five endstations to be commissioned online.It focuses on high-resolution single-shot imaging and the study of ultrafast dynamic processes using coherent forward scattering techniques.Both the single-shot holograms and coherent diffraction patterns were recorded and reconstructed for nanoscale imaging,indicating the excellent coherence and high peak power of the SXFEL and the possibility of‘‘diffraction before destruction’’experiments at the CSI endstation.In this study,we report the first commissioning results of the CSI endstation.

Infrared Spectroscopy of Neutral Clusters Based on a Vacuum Ultraviolet Free Electron Laseri

Spectroscopic characterization of clusters is crucial to understanding the structures and reaction mechanisms at the microscopic level,but it has been proven to be a grand challenge for neutral clusters because the absence of a charge makes it di伍cult for the size selection and detection.Infrared(IR)spectroscopy based on threshold photoionization using a tunable vacuum ultraviolet free electron laser(VUV-FEL)has recently been developed in the lab.The IR-VUV depletion and IR+VUV enhancement spectroscopic techniques open new avenues for size-selected IR spectroscopies of a large variety of neutral clusters without confinement(i.e.,an ultraviolet chromophore,a messenger tag,or a host matrix).The spectroscopic principles have been demonstrated by investigations of some neutral water clusters and some metal carbonyls.Here,the spectroscopic principles and their applications for neutral clusters are reviewed.

Application of Laser Dispersion Method in Apparatus Combining H Atom Rydberg Tagging Time-of-Flight Technique with Vacuum Ultraviolet Free Electron Laser

Photodissociation of H2S in the VUV region plays an important role in the atmospheric chemistry and interstellar chemistry.To date,however,few studies have been focused on this topic.In this article,we have described a laser dispersion method applied in the apparatus combining the high-n H atom Rydberg tagging time-of-flight technique with the vacuum ultraviolet free electron laser(VUV FEL).The Lyman-αlaser beam(121.6 nm)used in the H-atom detection was generated by the difference frequency four-wave mixing schemes in a Kr/Ar gas cell.After passing through an off-axis biconvex LiF lens,the 121.6 nm beam was dispersed from the 212.6 nm and 845 nm beams due to the different deflection angles experienced by these laser beams at the surfaces of the biconvex lens.This method can eliminate the background signal from the 212.6 nm photolysis.Combined with the VUV FEL,photodissociation of H2S at 122.95 nm was studied successfully.The TOF spectrum was measured and the derived total kinetic energy release spectrum was displayed.The results suggest that the experimental setup is a powerful tool for investigating photodissociation dynamics of molecules in the VUV region which involves the H-atom elimination processes.

Effects of self-fields on dispersion relation and growth rate in two-stream electromagnetically pumped free electron laser with axial guide magnetic field

A theory for a two-stream free-electron laser （FEL） with an electromagnetic wiggler （EMW） and axial guide magnetic field is developed. In the analysis, the effects of self-fields are taken into account. The growth rate is derived. The characteristics of the growth rate are studied numerically. The dependence of the normalized wave number, which corresponds to the maximum growth rate, on the cyclotron frequency is presented. The comparisons between the normalized maximum growth rate and its corresponding wave number normalized by employing the axial magnetic field, for the cases with and without self-fields in the two-stream FEL are studied numerically.

Axial magnetic field effect in numerical analysis of high power Cherenkov free electron laser

Cherenkov free electron laser(CFEL) is simulated numerically by using the single particle method to optimize the electron beam. The electron beam is assumed to be moving near the surface of a flat dielectric slab along a growing radiation. The set of coupled nonlinear differential equations of motion is solved to study the electron dynamics. For three sets of parameters, in high power CFEL, it is found that an axial magnetic field is always necessary to keep the electron beam in the interaction region and its optimal strength is reported for each case. At the injection point, the electron beam’s distance above the dielectric surface is kept at a minimum value so that the electrons neither hit the dielectric nor move away from it to the weaker radiation fields and out of the interaction region. The optimal electron beam radius and current are thereby calculated. This analysis is in agreement with two previous numerical studies for a cylindrical waveguide but is at odds with analytical treatments of a flat dielectric that does not use an axial magnetic field. This is backed by an interesting physical reasoning.

Gain calculation of a free-electron laser operating with a non-uniform ion-channel guide

Amplification of an electromagnetic wave by a free electron laser （FEL） with a helical wiggler and an ion channel with a periodically varying ion density is examined. The relativistic equation of motion for a single electron in the combined wiggler and the periodic ionbchannel fields is solved and the classes of possible trajectories in this configuration are discussed. The gain equation for the FEL in the low-gain-per-pass lirnit is obtained by adding the effect of the periodic ion channel. Numerical calculation is employed to analyse the gain induced by the effects of the non-uniform ion density. The variation of gain with ion-channel density is demonstrated. It is shown that there is a gain enhancement for group I orbits in the presence of a non-uniform ion-channel but not in a uniform one. It is also shown that periodic ion-channel guiding is used to reach the maximum peak gain in a low ion-channel frequency （low ion density）.

De Haas-van Alphen Effect of Free Electron Gas Revisited

The free electron gas in a uniform magnetic field at low temperature is restudied. The grand partition function previously obtained by Landau＇s quantitative calculation contains three parts, which are all approximate. An improved calculation is presented, in which two of the three parts are obtained in exact forms. A simple remedy for Landau and Lifshitz＇s qualitative calculation in the textbook is also given, which turns the qualitative result into the same one as obtained by the improved quantitative calculation. The chemical potential is solved approximately and the thermodynamic quantities are caiculated explicitly in both a weak field and a strong field. The thermodynamic quantities in a strong field obtained here contain both non-oscillating and oscillating corrections to the corresponding results derived from Landau＇s grand partition function. In particular, Landau＇s grand partition function is not sufficiently accurate to yield our nonzero results for the specific heat and the entropy. An error in the Laplace-transform method for the problem is corrected. The results previously obtained by this method are also improved.

The effects of self-fields on the electron trajectory and gain in a two-stream electromagnetically pumped free-electron laser with axial guiding field

A theory of a two-stream flee-electron laser in a combined electromagnetic wiggler （EMW） is developed, in which we use an axial-guide magnetic field and take into account the effects of the self-fields. The electron trajectories and the small signal gain are derived. The stability of the trajectories, the characteristics of the linear-gain, and the normalised maximum gain are studied numerically. The results show that there are nine stable groups of orbits in the presence of self-fields instead of seven groups reported in the absence of the self-field. It is also shown that the normalised gains of four groups of the orbits are decreasing and those for the rest of them are increasing with growing J20. Furthermore, it is found that the two-stream laser with seff-field enhances the maximum gain in comparison with the single stream case.

Effects of self-fields on electron trajectory and gain in two-stream electromagnetically pumped free-electron laser with ion channel guiding

A theory for the two-stream free-electron laser with an electromagnetic wiggler （EMW） and an ion channel guiding is developed. In the analysis, the effects of self-fields have been taken into account. The electron trajectories and the small signal gain are derived. The stability of the trajectories, the characteristics of the linear gain and the normalized maximum gain are studied numerically. The dependence of the normalized frequency ω corresponding to the maximum gain on the ion-channel frequency is presented. The results show that there are seven groups of orbits in the presence of the self-fields, which are similar to those reported in the absence of the self-fields. It is also shown that the normalized gains of 2 groups decrease while the rest increase with the increasing normalized ion-channel frequency. Furthermore, it is found that the two-stream instability and the self-field lead to a decrease in the maximum gain except for group 4.

The effects of self-fields on the electron trajectory in a two-stream free electron laser with a helical wiggler and an axial guiding magnetic field

A theory for the two-stream free-electron laser（TSFEL） with a helical wiggler and an axial guide magnetic field is developed.In the analysis,the effects of self-fields are taken into account.An analysis of the two-stream steady-state electron trajectories is given by solving the equation of motion.Numerical calculations show that there are seven groups of orbits in the presence of self-fields instead of two groups reported in the absence of self-fields.The stability of the trajectories is studied numerically.

Electron inelastic mean free paths in solids:A theoretical approach

In the present paper, the inelastic mean free path （IMFP） of incident electrons is calculated as a function of energy for silicon （Si）, oxides of silicon （SiO2）, SiO, and A1203 in bulk form by employing atomic/molecular inelastic cross sections derived by using a semi-empirical quantum mechanical method developed earlier. A general agreement of the present results is found with most of the available data. It is of great importance that we have been able to estimate the minimum IMFP, which corresponds to the peak of inelastic interactions of incident electrons in each solid investigated. New results are presented for SiO, for which no comparison is available. The present work is important in view of the lack of experimental data on the IMFP in solids.

Effects of self-fields on gain in two-stream free electron laser with helical wiggler and an axial guiding magnetic field

The theory for the two-stream free electron laser （FEL） consisting of a relativistic electron beam transporting along the axis of a helical wiggler in the presence of an axial guiding magnetic field is proposed and investigated. In the analysis, the effects of self-fields are taken into account. The electron trajectories and the small signal gain are derived. The characteristics of the linear-gain and the normalized maximum gain are studied numerically. The results show that there are seven stable groups of orbits in the presence of self-fields instead of two groups reported in the absence of the self-fields. It is also shown that the normalized gains of three groups decrease while the rest increase with the increasing of normalized cyclotron frequency g20. Furthermore, it is found that the two-stream instability and the self-field lead to a decrease in the maximum gain except for group 3. The results show that the normalized maximum gain is enhanced in comparison with that of the single stream.

A Novel Classical Model of the Free Electron

Previous models of the free electron using classical physics equations have predicted attributes that are inconsistent with the experimentally observed attributes. For example, the magnetic moment has been calculated for the observed spinning electric charge. For the calculated moment to equal the observed moment, the electron would either have to spin at two hundred times the speed of light or have a charge radius two hundred times greater than the classical radius. A similar inconsistency results when the mass derived from the spin angular momentum is compared with the observed mass. A classical model is herein proposed which eliminates the magnetic moment inconsistency and also predicts the radius of the electron. The novel feature of the model is the replacement of a single charge with two opposite charges, one on the outer surface of the electron and the other at the center.

Nonequilibrium Solvent Free Energy Curve from Molecular Theory in Electron Transfer Reaction

The microscopic moleeular theory for electron transfer in a model solvent ishahr developed. The nonlinear response of the solvent molecules is be computedquanitatively in a new way. Adopting computer simulation daa and choosingappropriate reaction coordinae, a reasonable free energy dinram is constructed and thercorganhaion energy for the product state is calculated.

A Physical Insight into the Origin of the Corrections to the Magnetic Moment of Free and Bound Electron

The main goal of the present work is a unitary approach of the physical origin of the corrections to the magnetic moment of free and bound electron. Based on this approach, estimations of lowest order corrections were easily obtained. In the non-relativistic limit, the Dirac electron appears as a distribution of charge and current extended over a region of linear dimension of the order of Compton wavelength, which generates its magnetic moment. The e.m. mass (self-energy) of electron outside this region does not participate to this internal dynamics, and consequently does not contribute to the mass term in the formula of the magnetic moment. This is the physical origin of the small increase of the magnetic moment of free electron compared to the value given by Dirac equation. We give arguments that this physical interpretation is self-consistent with the QED approach. The bound electron being localized, it has kinetic energy which means a mass increase from a relativistic point of view, which determines a magnetic moment decrease (relativistic Breit correction). On the other hand, the e.m. mass of electron decreases at the formation of the bound state due to coulomb interaction with the nucleus. We estimated this e.m. mass decrease of bound electron only in its internal dynamics region, and from it the corresponding increase of the magnetic moment (QED correction). The corrections to the mass value are at the origin of the lowest order corrections to the magnetic moment of free and bound electron.

Free Electron Characteristic Peculiarities Caused by Lattice Vibrations in Metals

It is shown that the traditional explanation of the free electron properties, such as mean free electron path, drift mobility, and the relaxation time, by lattice vibrations, is not valid for real free randomly moving (RM) electrons in materials with degenerate electron gas. It is shown that the effective density of the free RM electrons in elemental metals is completely determined by density-of-states at the Fermi surface and by absolute temperature. The study has shown that the lattice vibrations excite not only the free RM electrons but also produce the same number of weakly screened ions (so-named electronic defects), which cause the scattering of the free RM electrons and related electron kinetic characteristics.

Theoretical calculations of hardness and metallicity for multibond hexagonal 5d transition metal diborides with ReB_2 structure

The hardness, electronic, and elastic properties of 5d transition metal dibofides with ReB2 structure are studied theoretically by using the first principles calculations. The calculated results are in good agreement with the previous experimental and theoretical results. Empirical formulas for estimating the hardness and partial number of effective free electrons for each bond in multibond compounds with metallicity are presented. Based on the formulas, IrB2 has the largest hardness of 21.8 GPa, followed by OsB2 （21.0 GPa） and ReB2 （19.7 GPa）, indicating that they are good candidates as hard materials.