Initial Electron Momentum Research Articles

Laser-assisted radiative recombination in a cold hydrogen plasma

Abstract We study the process of laser-assisted radiative recombination of an electron with a proton in a cold hydrogen plasma employing the semiclassical Kramers’ approach which involves calculation of classical trajectories in combined laser and Coulomb fields and the use of the correspondence principle. Due to the Coulomb focusing effect, recombination is the most effective when the initial electron momentum is parallel to the laser polarization. Orders of magnitude enhancement of the cross section, as compared to the laser-free case, is observed in this case. With increasing angle between the electron momentum and polarization, the recombination cross section drops. However, even after averaging over Maxwellian velocity distribution we obtain a substantial enhancement of the recombination rate constant, as compared to the zero-field case. For the field intensities in the range 30–350 MW cm−2, the enhancement occurs in the region of the radiation wavelength from 5 to 20 µm and for the plasma temperature from 20 to 300 K.

Notes on inverse Compton scattering

The paper considers some kinematic conditions for the inverse Compton scattering of photons by relativistic electrons and the polarizations of colliding particles, which affect the value of the differential cross section of the process. A significant influence of the electron and photon helicity on the value of the cross section was found. In the ultrarelativistic case, a surprising effect of an almost twofold increase in the cross section of scattering in the direction of the initial electron momentum was also discovered, when the initial photon momentum is perpendicular to that of the initial electron.

Resonant Ultrarelativistic Electron–Positron Pair Production by High-Energy Electrons in the Field of an X-ray Pulsar

The process of resonant high-energy electron–positron pair production by an ultrarelativistic electron colliding with the field of an X-ray pulsar is theoretically investigated. Resonant kinematics of the process is studied in detail. Under the resonance condition, the intermediate virtual photon in the X-ray pulsar field becomes a real particle. As a result, the initial process of the second order in the fine structure constant effectively reduces into two successive processes of the first order: X-ray-stimulated Compton effect and X-ray-stimulated Breit–Wheeler process. For a high-energy initial electron all the final ultrarelativistic particles propagate in a narrow cone along the direction of the initial electron momentum. The presence of threshold energy for the initial electron which is of order of 100 MeV for 1-KeV-frequency field is shown. At the same time, the energy spectrum of the final particles (two electrons and a positron) highly depends on their exit angles and on the initial electron energy. This result significantly distinguishes the resonant process from the non-resonant one. It is shown that the resonant differential probability significantly exceeds the non-resonant one.

Resonant Laser-Assisted Process of Ultrarelativistic Electrons Bremsstrahlung in the Field of a Nucleus

The scrutiny of the resonant laser-assisted bremsstrahlung (LAB) of ultrarelativistic electrons within the laser plasma ambience in the field of a nucleus is presented. The kinematics of the explored process can develop within two probable channels. Thus, for the first channel an electron radiates a spontaneous photon and subsequently scatters on a nucleus. In contrast, for the second channel an electron scatters on a nucleus and consequently a spontaneous photon emits. It is important to underline, that within the laser field plasma the ultrarelativistic electron in the intermediate state emerges to the mass shell and transforms into the real particle. Furthermore, the second order effect functionally transmits into two sequential first order procedures (implementing the laser-stimulated Compton process and the laser-assisted Mott scattering) with respect to the fine structure constant. We evaluated the fluctuation of the spontaneous photon resonant frequency for the various initial parameters criteria. As a result, in the investigation a specific diapason of the resonant frequency modification for the second reaction scheme was highlighted when the ultrarelativistic electron at first scatters on a nucleus and then radiates a spontaneous photon. The designated interval consists of three frequency levels in alternative to the first channel interaction pattern. Moreover, the study delineates the occurrence of the particles propagation within a narrow angle cone in the vector direction parallel to the initial electron momentum. To summarize, the article estimates that the magnitude of the differential cross-section in the resonant conditions substantially exceeds the cross-section of the process without the laser plasma ambience. In addition, pulsed laser radiation laboratories (SLAC, FAIR, XFEL, ELI, XCELS) maintain the ability to verify the project calculations.

Direct Experimental Access to the Nonadiabatic Initial Momentum Offset upon Tunnel Ionization

We report on the nonadiabatic offset of the initial electron momentum distribution in the plane of polarization upon single ionization of argon by strong field tunneling and show how to experimentally control the degree of nonadiabaticity. Two-color counter- and corotating fields (390 and 780nm) are compared to show that the nonadiabatic offset strongly depends on the temporal evolution of the laser electric field. We introduce a simple method for the direct access to the nonadiabatic offset using two-color counter- and corotating fields. Further, for a single-color circularly polarized field at 780nm, we show that the radius of the experimentally observed donutlike distribution increases for increasing momentum in the light propagation direction. Our observed initial momentum offsets are well reproduced by the strong-field approximation. A mechanistic picture is introduced that links the measured nonadiabatic offset to the magnetic quantum number of virtually populated intermediate states.

Polarization-sensitive pulse reconstruction by momentum-resolved photoelectron streaking.

The precise knowledge of the electric field in close proximity to metallic and dielectric surfaces is a prerequisite for pump-probe experiments aiming at the control of dynamic surface processes. We describe a model to reconstruct this electric field in immediate surface proximity from data taken in photoelectron THz-streaking experiments with an angle-resolved electron analyzer. Using Monte-Carlo simulations we are able to simulate streaking experiments on arbitrary surfaces with a variety of initial electron momentum distributions and to reconstruct the effective electric field at the surface. Our results validate the approach and suggest energy regimes for optimal pulse reconstruction.

Mott scattering in a field of two pulsed laser waves

Laser-modified Mott scattering in a field of two unidirectional pulsed waves is considered. The primary object of research is the cross section distribution of the final electron energy at a fixed geometry of the scattering process. The parametric interference effect is manifested within the plane formed by both the direction of the laser-wave propagation and the initial electron momentum (the interference region). The induced processes of the correlated emission and absorption of external-field photons are preferred in the interference region for the circular polarization of both laser waves. A comparative analysis of the electron energy spectra is provided in the interference region and the region where the parametric interference effect is hardly manifested, at the same parameters of a laser field and the initial electron energy. The cross section of laser-modified electron-nucleus scattering at the specified final electron energy in the interference region may be one order of magnitude greater than the cross section at the other geometry of scattering.

Parametric interference Compton effect in two pulsed laser waves

We study the emission of a photon by an electron moving in a pulsed plane wave field of high intensity. The wave field is modelled as the superposition of two co-propagating, elliptically polarised, plane waves of different frequencies. Upon calculating the differential probability of the process we identify a kinematic region associated with a parametric interference effect. Geometrically, this region is characterised by the final photon being emitted into the plane defined by the initial electron momentum and the wave propagation direction. Quantitatively, the parametric interference effect leads to an increase in partial emission probabilities of the processes with correlated absorption of photons of both waves by an order of magnitude.

Influence of the spatial and temporal distribution of an incident laser beam profile on the energy distribution of ionized photoelectrons

We discuss the effects of two different spatial and temporal laser beam profiles on the energy distribution of ionized photoelectrons. Two types of profiles of laser radiation, Gaussian and Lorentzian, are considered. The influence of the nonzero initial momentum of ejected photoelectrons is observed. We find that selection of the laser beam profile influences the maximal energy distribution. It is also shown that the nonzero initial electron momentum has a more significant influence for the Lorentzian beam profile.

Parametric interference effect in electron-nucleus scattering in the field of two pulsed laser waves

Electron scattering on a nucleus in a field of two unidirectional pulsed laser waves is considered. The parametric interference effect is studied, which manifests in electron scattering within the plane formed by both the direction of laser-wave propagation and the initial electron momentum (the interference region). In this kinematics the electron emits and absorbs photons of both waves in a correlated manner. The distribution of the differential cross section of the final-electron energy for the process of electron-nucleus scattering in the field of two pulsed waves is considered. This distribution in the interference region differs qualitatively and quantitatively from the corresponding distribution in any other geometry. The appearance of the parametric interference effect may be experimentally verified by measuring the energy spectrum of final electrons in the framework of modern research projects, which use sources of pulsed laser radiation (XFEL, ELI, PHELIX).

Parametric interference electron–muon scattering in the field of two pulse laser waves

The nonresonant process of electron scattering at the muon in the two pulse field circularly polarized moderately strong electromagnetic waves in the interference region has been studied theoretically. Such a region occurs if an electron (and a muon) is scattered in the plane formed by the initial electron (and muon) momentum and the wave vector. In such geometry, the stimulated emission and absorption of photons by first and second waves get correlated. A significant increase of the partial scattering cross section of the process is found for non-relativistic electrons even in the case of moderate laser pulse intensities. The received results can be tested at the FAIR project.

The interference effect in electron scattering on a nucleus in the field of two pulsed laser waves of circular polarization

Electron scattering on a nucleus in the field of two unidirectional pulsed laser waves of circular polarization is considered. The interference effect was detected if an electron scatters in the plane determined by the direction of laser wave propagation and the initial electron momentum. In this kinematics the electron emits and absorbs photons of both waves in a correlated manner. Broadening of partial differential cross sections is studied near the interference outgoing angle of the electron. It is shown that the partial probability of stimulated processes in the interference region may be five orders of magnitude greater than the corresponding probability of processes in any other geometry. The results may be experimentally verified, for example, in the framework of the FAIR (Facility for Antiproton and Ion Research, Darmstadt, Germany) project.

Inverse bremsstrahlung heating rate for dense plasmas in laser fields

We report a theoretical analysis of inverse bremsstrahlung heating rate in the eikonal approximation. The present analysis is performed for a dense plasma using the screened electron-ion interaction potential for the ion charge state Zi = 1 and for both the weak and strong plasma screening cases. We have also compared the eikonal results with the first Born approximation (FBA) [M. Moll et al., New J. Phys. 14, 065010 (2012)] calculation. We find that the magnitudes of inverse bremsstrahlung heating rate within the eikonal approximation (EA) are larger than the FBA values in the weak screening case (κ = 0.03 a.u.) in a wide range of field strength for three different initial electron momenta (2, 3, and 4 a.u.). But for strong screening case (κ = 0.3 a.u.), the heating rates predicted by the two approximations do not differ much after reaching their maximum values. Furthermore, the individual contribution of photoemission and photoabsorption processes to heating rate is analysed for both the weak and strong screening cases. We find that the single photoemission and photoabsorption rates are the same throughout the field strength while the multiphoton absorption process dominates over the multiphoton emission process beyond the field strength ≈ 4×108 V/cm. The present study of the dependence of heating rate on the screening parameter ranging from 0.01 to 20 shows that whereas the heating rate predicted by the EA is greater than the FBA up to the screening parameter κ = 0.3 a.u., the two approximation methods yield results which are nearly identical beyond the above value.

Effect of anisotropic band curvature on carrier multiplication in graphene

We study relaxation of an excited electron in the conduction band of intrinsic graphene at zero temperature due to production of interband electron-hole pairs. The electronic band curvature, being anisotropic because of trigonal warping, is shown to suppress relaxation for a range of directions of the initial electron momentum. For other directions, relaxation is allowed only if the curvature exceeds a finite critical value; otherwise, a non-decaying quasiparticle state is found to exist.

Particular features of a Vavilov-Cherenkov-like phenomenon with emission of surface plasmons

We consider a phenomenon of the Vavilov-Cherenkov type that can be observed in a space with a metal-dielectric boundary that well reflects light. An electron that initially uniformly moves at a constant velocity near this boundary creates surface plasmon-polaritons the phase velocity of which is lower than the electron velocity. The momentum of a photon in the created plasmon-polariton is calculated. This momentum may be almost as high as the doubled initial electron momentum. The velocity of the electron that created the photon in the plasmon-polariton may also become almost zero. We show that, at a nonzero temperature, this process has a nonzero probability.

Thomson and Compton scattering with an intense laser pulse

Our paper concerns the scattering of intense laser radiation on free electrons and it is focused on the relation between nonlinear Compton and nonlinear Thomson scattering. The analysis is performed for a laser field modeled by an ideal pulse with a finite duration, a fixed direction of propagation and indefinitely extended in the plane perpendicular to it. We derive the classical limit of the quantum spectral and angular distribution of the emitted radiation, for an arbitrary polarization of the laser pulse. We also rederive our result directly, in the framework of classical electrodynamics, obtaining, at the same time, the distribution for the emitted radiation with a well defined polarization. The results reduce to those established by Krafft et al. [Phys. Rev. E 72, 056502 (2005)] in the particular case of linear polarization of the pulse, orthogonal to the initial electron momentum. Conditions in which the differences between classical and quantum results are visible are discussed and illustrated by graphs.

Multiphoton stimulated bremsstrahlung for broad (in the momentum representation) electron wave packets in an ultrashort laser pulse field

We consider features of absorption and emission of external laser field quanta by a broad (in the momentum representation) electron wave packet during its scattering from a potential center. Various scattering modes for the electron wave packet in a high-intensity laser field are analyzed using perturbation theory of potential energy. It is found that the absorption of laser field energy by an electron is substantially more effective as compared to the case of a plane wave. The important role of a number of interference effects associated with the large width of the initial electron momentum distribution is demonstrated.

Erratum: Nonlinear Compton scattering with a laser pulse [Phys. Rev. A80, 053403 (2009)

A factor with the expression p0 2/(n · p2) is missing from the right-hand side of Eqs. (32), (34), and (38) and the numerical computations based on them. However, this factor differs by less than 10−5 from 1 for all the plots corresponding to an electron initially at rest, which stay, therefore, practically correct. The only figure to be amended is Fig. 4 since, for the very high initial electron momentum it corresponds, the factor is close to 0.5. The deviation from 0.5 being no bigger than 10−6, a simple division by 2 is enough to get the true values of σ (2) from the published ones in Fig. 4. Nevertheless, we present here the corrected Fig. 4. Furthermore, the phrase after Eq. (47) must be replaced by “In both cases it is obvious that the envelope has negligible values except for a finite duration, proportional to the parameter τ in the expression of the envelope, and, as a consequence, the factor τp (the effective pulse duration) used in Eq. (31) should be chosen proportional to τ ; we have taken τp = 2λτ .” The error was the omission of the factor 2 in the expression of τp. Our numerical calculation did include this factor.

Relativistic reversal of the ponderomotive force in a standing laser wave

Effect of relativistic reversal of the ponderomotive force (PF), reported earlier for a collinear configuration of electron and laser standing wave [A. E. Kaplan and A. L. Pokrovsky, Phys. Rev. Lett., 95, 053601 (2005)], is studied here theoretically for various types of polarizations of the laser beam. We demonstrated that the collinear configuration, in which the laser wave is linearly polarized with electric field $\stackrel{P\vec}{E}$ parallel to the initial electron momentum ${\stackrel{P\vec}{p}}_{0}$, is the optimal configuration for the relativistic reversal. In that case, the transverse PF reverses its direction when the incident momentum is ${p}_{0}=mc$. The reversal effect vanishes in the cases of circular and linear with $\stackrel{P\vec}{E}\ensuremath{\perp}{\stackrel{P\vec}{p}}_{0}$ polarizations. We have discovered, however, that the counter-rotating circularly polarized standing waves develop attraction and repulsion areas along the axis of laser, in the laser field whose intensity is homogeneous in that axis, i.e., has no field gradient.

A review of electron–phonon coupling seen in the high‐Tc superconductors by angle‐resolved photoemission studies (ARPES)

AbstractThis issue of pss (b) – basic solid state physics contains a collection of Review Articles on the rather controversially discussed topic of Electron–Phonon Interaction in High‐Temperature Superconductors, guest‐edited by Miodrag Kulić, Johann Wolfgang Goethe‐Universität Frankfurt/Main, Germany, with a Preface written by V. L. Ginzburg and E. G. Maksimov [1].The cover picture, taken from the review [2] by T. Cuk et al., shows plots of the electron–phonon coupling vertex, g2(k, k′), where k, k′ are the initial and final electron momentum for electrons scattered by the bond‐buckling phonon B1g (the out‐of‐phase vibration of the in‐plane oxygen) in a tight‐binding model of the copper–oxygen plane. The momentum dependence of this vertex, along with the d‐wave superconducting gap and the van Hove singularity at the anti‐node, accounts for the momentum dependence of the collective mode coupling seen in angle‐resolved photoemission data on Bi2212.The present issue also sees the start of our rapid research letters, the fastest peer‐reviewed publication medium in solid state physics. For more information see www.pss‐rapid.com and the Editorial by the Editor‐in‐Chief Martin Stutzmann on page 7 [3].