Relativistic Electron Layers Research Articles

Carrier-Envelope-Phase Controlled Attosecond Pulse Generation by Undulator Radiation

Practical aspects of the robust method we proposed for producing few-cycle attosecond pulses with arbitrary waveform in the extreme ultraviolet spectral range are studied numerically. It is based on the undulator radiation of relativistic ultrathin electron layers produced by laser-driven energy modulation. By using realistic specifications, we show that isolated waveform-controlled extreme ultraviolet attosecond pulses at 20 nm with 90 nJ energy and 80 as pulse duration, and at 60 nm with 200 nJ energy and 240 as duration can be generated, respectively.

Terawatt-scale optical half-cycle attosecond pulses

Extreme-ultravoilet (XUV) attosecond pulses with durations of a few tens of attosecond have been successfully applied for exploring ultrafast electron dynamics at the atomic scale. But their weak intensities limit the further application in demonstrating nonlinear responses of inner-shell electrons. Optical attosecond pulses will provide sufficient photon flux to initiate strong-field processes. Here we proposed a novel method to generate an ultra-intense isolated optical attosecond pulse through relativistic multi-cycle laser pulse interacting with a designed gas-foil target. The underdense gas target sharpens the multi-cycle laser pulse, producing a dense layer of relativistic electrons with a thickness of a few hundred nanometers. When the dense electron layer passes through an oblique foil, it emits single ultra-intense half-cycle attosecond pulse in the visible and ultraviolet spectral range. The emitted pulse has a peak intensity exceeding 1018 W/cm2 and full-width-half-maximum duration of 200 as. The peak power of this attosecond light source reaches 2 terawatt. The proposed method relaxes the single-cycle requirement on the driving pulse for isolated attosecond pulse generation and significantly boosts the peak power, thus it may open up the route to new experiments tracking the nonlinear response of inner-shell electrons as well as nonlinear attosecond phenomena investigation.

Interference in multilayer relativistic mirrors

In this paper, reflection coefficient of a relativistic ultra-thin electron multilayer is calculated using electromagnetic interference procedures. The relativistic electron layers are assumed to be formed by nonlinear plasma wake waves that constitute the electron density cusps. It is shown that the interference between successive relativistic mirrors is restricted by the condition, τp≫(2γ0)5/2/ωp0, where τp is the laser pulse duration. The results showed that tailoring the pulse amplitude, incident wave frequency value, incidence angle, and plasma density leads to increasing reflection coefficient a few orders of magnitudes. This constructive interference condition can be used for increasing conversion efficiency in the reflected energy from relativistic mirrors for the purpose of generating ultra-short coherence pulses in the extreme ultraviolet and x-ray regions. We also performed reflection from relativistic thin electron layers using relativistic 1D3V electromagnetic particle-in-cell (PIC) simulation. It was found that the results of PIC simulation are in agreement with analytical considerations.

Proposal for carrier-envelope-phase stable single-cycle attosecond pulse generation in the extreme-ultraviolet range.

A robust method for producing half-cycle-few-cycle attosecond pulses in the extreme ultraviolet spectral range is proposed. It is based on coherent undulator radiation of relativistic ultrathin electron layers (nanobunches), which are produced by nanobunching of ultrashort electron bunches by a 10-TW power laser in a modulator undulator. Our numerical calculations predict the generation of nanobunches shorter than 10nm. By using these electron nanobunches the production of carrier-envelope-phase stable attosecond pulses with up to a few tens of nJ energy and down to 10nm wavelength and 35as duration is predicted.

The ~10 hour modulation of the relativistic electron spectrum as a result of the periodic motion of the Jovian outer magnetosphere layer: Ulysses observations

We analyze relativistic (E>3MeV) electron observations during the dayside inbound trajectory of Ulysses (day 33 to day 38, 1992) in the Jovian magnetosphere and we demonstrate that the continuous presence of a relativistic electron layer at higher north latitudes (Ulysses reached ~40° lat. during closest approach the planet). In particular, we evaluated the cross-B field anisotropy of relativistic (E>3MeV) electrons intensity by the COSPIN/HET detector onboard Ulysses, and we found that between the times of plasma sheet crossings/approaches, when Ulysses was found far from the magnetodisc, at higher north latitudes, local increases in the relativistic electron intensity and intensity gradient in the northward direction were persistently observed. We also found that (1) the well known ~10h separated relativistic electron spectral index peaks (spectral softening) and (2) the detection of relativistic electron intensity gradient in the northward direction are related phenomena. We infer that phenomenon 1 and 2 are explained by the ~10h periodic upward-downward motion of the Jovian magnetosphere, and consequently of the outer magnetosphere relativistic electron layer. Τhe above results extends earlier results for low energy electrons and energetic protons (Anagnostopoulos et al., 1998, 2001b) to relativistic electron phenomena, and provide strong evidence, for the first time, that the well known ~10h rocking of the relativistic electron spectrum in the outer magnetosphere (the so called “clock phenomenon”) is a spatial and not a temporal effect, as was earlier hypothesized (Simpson et al.,1992).

Double Relativistic Electron Accelerating Mirror

In the present paper, the possibility of generation of thin dense relativistic electron layers is shown using the analytical and numerical modeling of laser pulse interaction with ultra-thin layers. It was shown that the maximum electron energy can be gained by optimal tuning between the target width, intensity and laser pulse duration. The optimal parameters were obtained from a self-consistent system of Maxwell equations and the equation of motion of electron layer. For thin relativistic electron layers, the gaining of maximum electron energies requires a second additional overdense plasma layer, thus cutting the laser radiation off the plasma screen at the instant of gaining the maximum energy (DREAM-schema).

Double-Relativistic-Electron-Layer Proton Acceleration with High-Contrast Circular-Polarization Laser Pulses

A new laser-proton acceleration scheme consisting of two relativistic electron layers, a suprathermal electron layer and a thermal electron cloud is proposed for a0 ≳ 80σ0, where a0 is the normalized laser field and σ0 is the normalized plasma surface density. This is essentially different from target normal sheath acceleration and radiation pressure acceleration. The persistent opaqueness of the first relativistic electron layer for the incident circular-polarization laser pulse and electron recirculation are key points in forming the new acceleration scheme. A proton beam with a uniform energy distribution in the energy range 1–2 GeV and a monoenergetic proton beam with hundreds of MeV have been predicted for a0 = 39.5.

Double relativistic electron-accelerating mirror

A numerical simulation of the interaction of a laser pulse with ultrathin targets has revealed a possibility of generating thin dense relativistic electron layers. The maximum kinetic energy of the electron mirror can be gained using an optimal combination of the target thickness and the laser pulse intensity and duration. It is proposed to use an additional (second) laser target, located at an optimal distance from the first target to cut off the laser pulse from the electron layer when the latter gains a maximum kinetic energy. This relativistic electron mirror can be used for efficient generation of ‘hard’ coherent radiation via counter reflection of an additional (probe) laser pulse from the mirror.

Numerical study on coherent keV x ray generation by the interaction of ultra-short intense lasers with thin solid foils

The scheme of x ray generation by the interaction of ultra-short intense laser puls with two thin solid foils is re-investigated by one-dimensional numerical simulation. Attention is paid particularly to the effects of the thickness and the density distribution of the source target on the frequency spectrum and the conversion efficiency of the produced x ray emission, where the source target provides a relativistic electron layer. When the thickness of the source target is comparable to or smaller than the wavelength of x ray /4x2 ( is the wavelength of the incident laser), quasi-monochromatic x ray spectrum can be generated. Otherwise the spectrum will be broadened significantly and the maximum frequency will decrease rapidly. In addition, the presence of inhomogeneous preplasma in front of the foil will induce a similar change of the spectrum.

CEP ef fects on monochromatic high frequency pulse generation from Thomson backscattering

Carrier-envelope phase effect of the monochromatic high frequency pulse generation from Thomson backscattering is investigated with an analytical model and verified by one dimensional particle in cell simulations. We show that the central frequency of the monochromatic light generated from Thomson backscattering is extremely sensitive to the carrier-envelope phase of the field driving the relativistic electron layers.

Uniform Laser-Driven Relativistic Electron Layer for Coherent Thomson Scattering

A novel scheme is proposed to generate uniform relativistic electron layers for coherent Thomson backscattering. A few-cycle laser pulse is used to produce the electron layer from an ultrathin solid foil. The key element of the new scheme is an additional foil that reflects the drive-laser pulse, but lets the electrons pass almost unperturbed. Making use of two-dimensional particle-in-cell simulations and well-known basic theory, it is shown that the electrons, after interacting with both the drive and reflected laser pulses, form a very uniform flyer freely cruising with a high relativistic γ factor exactly in the drive-laser direction (no transverse momentum). It backscatters the probe light with a full Doppler shift factor of 4γ(2). The reflectivity and its decay due to layer expansion are discussed.

Coherent Thomson backscattering from laser-driven relativistic ultra-thin electron layers

The generation of laser-driven dense relativistic electron layers from ultra-thin foils and their use for coherent Thomson backscattering is discussed, applying analytic theory and one-dimensional particle-in-cell simulation. The blow-out regime is explored in which all foil electrons are separated from ions by direct laser action. The electrons follow the light wave close to its leading front. Single electron solutions are applied to initial acceleration, phase switching, and second-stage boosting. Coherently reflected light shows Doppler-shifted spectra, chirped over several octaves. The Doppler shift is found ∝ γx 2=1/(1-βx 2), where βx is the electron velocity component in normal direction of the electron layer which is also the direction of the driving laser pulse. Due to transverse electron momentum py, the Doppler shift by 4γx 2=4γ2/(1+(py/mc)2)≈2γ is significantly smaller than full shift of 4γ2. Methods to turn py→0 and to recover the full Doppler shift are proposed and verified by 1D-PIC simulation. These methods open new ways to design intense single attosecond pulses.

Simulation of coherent synchrotron radiation emission from rotating relativistic electron layers

The electromagnetic radiation of rotating relativistic electron layers is studied numerically using particle-in-cell simulation. This system is general enough to be applied to problems involving the coherent synchrotron radiation (CSR) instability in bunch compressors and possibly in radio pulsars where the CSR instability may be used to explain the high brightness temperature and the observed spectra. The results of the simulation confirm all relevant scaling properties predicted by theoretical models and suggest that their range of validity is bigger than conservative estimates indicate. This is important for radio pulsars where the allowed parameter range is unknown.

Bunching instability of rotating relativistic electron layers and coherent synchrotron radiation

We study the stability of a collision-less, relativistic, finite-strength, cylindrical layer of charged particles in free space by solving the linearized Vlasov-Maxwell equations and compute the power of the emitted electromagnetic waves. The layer is rotating in an external magnetic field parallel to the layer. This system is of interest to understanding the high brightness temperature of pulsars which cannot be explained by an incoherent radiation mechanism. Coherent synchrotron radiation has also been observed recently in bunch compressors used in particle accelerators. We consider equilibrium layers with a "thermal" energy spread and therefore a nonzero radial thickness. The particles interact with their retarded electromagnetic self-fields. The effect of the betatron oscillations is retained. A short azimuthal wavelength instability is found which causes a modulation of the charge and current densities. The growth rate is found to be an increasing function of the azimuthal wave number, a decreasing function of the Lorentz factor, and proportional to the square root of the total number of electrons. We argue that the growth of the unstable perturbation saturates when the trapping frequency of electrons in the wave becomes comparable to the growth rate. Owing to this saturation we can predict the radiation spectrum for a given set of parameters. Our predicted brightness temperatures are proportional to the square of the number of particles and scale by the inverse five-third power of the azimuthal wave number which is in rough accord with the observed spectra of radio pulsars.

Generation of electromagnetic waves by relativistic electrons in a cavity with crossed radial electrostatic and axial magnetic fields under plasma resonance conditions

A theoretical analysis is made of the conditions for generation of electromagnetic waves by a thin cylindrical layer of relativistic electrons rotating in crossed axial magnetic and radial electrostatic fields in a cylindrical cavity. A dispersion equation is obtained to describe the interaction between waves and electrons under plasma resonance conditions. The dependence of the growth rates on the relativistic factor and the magnetic field are studied.

Excitation of the Electromagnetic Radiation by Thin Layer of Relativistic Electrons under Cyclotron Resonance Conditions

Excitation of the Electromagnetic Radiation by Thin Layer of Relativistic Electrons under Cyclotron Resonance Conditions

Diocotron instability for relativistic non-neutral electron flow in planar magnetron geometry

Diocotron stability properties of relativistic non-neutral electron flow in a planar magnetron are investigated within the framework of the cold-fluid-Maxwell equations. The eigenvalue equation for the extraordinary-mode waves in a relativistic velocity-sheared electron layer is obtained, and is solved in the massless, guiding-center approximation. Approximating the electromagnetic field in the anode resonator by the lowest-order mode, the dispersion relation for the diocotron instability is obtained. Although the tenuous beam approximation is assumed, the eigenvalue equation and corresponding dispersion relation are both fully electromagnetic, and valid for relativistic electron flow. The dispersion relation is numerically investigated for a broad range of system parameters. From numerical calculations of the dispersion relation, it is shown that the typical growth rate of the diocotron instability indicates a strong instability. The early evolution of the diocotron instability as an important precursor to the evolution of the full magnetron oscillation is discussed.

Particle-in-cell simulations of azimuthal instabilities in relativistic electron layers

Negative-mass and cyclotron-maser instabilities in electron rings or layers lead to breaking of the azimuthal symmetry. The short-wavelength modes are generally thought to be harmless since they saturate by increasing the thickness and energy spread of the original layer. The long-wavelength (or low-order) modes, on the other hand, can be devastating to the integrity of the layer. Linear theory has predicted that the growth rates for negative-mass instability modes are proportional to the azimuthal mode number, so that the low-order modes would not be important until quite late in time. In contrast, the simulations presented here show that low-order modes can arise quite early in time, out of nonlinear states of the high-order modes. At low currents, azimuthal instabilities can be effectively suppressed (as predicted by linear theory) by starting out with a thicker layer, with the particle energy varying with radius. The dispersion in circulation frequency so introduced effectively damps all growing waves. Unfortunately, at high currents (field reversal factors ζ≳2%), making the layer thicker does not help. All growth rates are faster at the higher densities, and the high mode numbers grow to substantial amplitudes before damping is effective. Beating of nearby high-order modes gives rise to global modes that destroy the layer within a few rotations.

Dispersion relation for a large-orbit gyrotron

The interaction between a beam of large-orbit axis encircling electrons and a waveguide is studied by linearizing the fluid equations. A dispersion relation is derived for an annular layer of relativistic electrons of small thickness guided by a uniform magnetic field along the waveguide axis. It is shown in the general case that the dispersion relation couples the TE and TM modes of the waveguide at the two resonances omega -kz upsilon 0z=(l+or-1) omega c and omega -kz upsilon 0z=l omega c. The resonance at omega -kz upsilon 0z=(l+or-1) omega c which is associated with the finite velocity shear (( delta nu 0z/ delta rho ) not=0) and finite kz is shown to give the dominant contribution to the dispersion relation.

Kinetic equilibrium properties of relativistic non-neutral electron flow in a cylindrical diode with applied magnetic field.

The equilibrium properties of a relativistic non-neutral electron layer confined in a magnetically insulated cylindrical diode are investigated within the framework of the steady-state (\ensuremath{\partial}/\ensuremath{\partial}t=0) Vlasov-Maxwell equations. The analysis is carried out for an infinitely long cylindrical electron layer with axis of symmetry parallel to an applied magnetic field ${B}_{0}$e\ensuremath{\rightarrow}${^}_{z}$, which provides radial confinement of the electrons. The theoretical analysis is specialized to the class of self-consistent Vlasov equilibria ${f}_{b}^{0}$(x\ensuremath{\rightarrow},p\ensuremath{\rightarrow}) in which all electrons have the same canonical angular momentum (${P}_{\ensuremath{\theta}}$=${P}_{0}$=const) and the same energy (H=${\mathrm{mc}}^{2}$), i.e., ${f}_{b}^{0}$=(n${^}_{b}$${R}_{c}$/2\ensuremath{\pi}m)\ensuremath{\delta}(H-${\mathrm{mc}}^{2}$ )\ensuremath{\delta}(${P}_{\ensuremath{\theta}}$-${P}_{0}$). One of the most important features of the analysis is that the closed analytic expressions for the self-consistent electrostatic potential ${\ensuremath{\varphi}}_{0}$(r) and the \ensuremath{\theta} component of vector potential ${A}_{0}$(r) are obtained. Moreover, all essential equilibrium quantities, such as electron density profile ${n}_{b}^{0}$(r), total magnetic field ${B}_{0z}$(r), perpendicular temperature profile ${T}_{\ensuremath{\perp}b}^{0}$(r), etc., can be calculated self-consistently from these potentials. As a special case, the equilibrium properties of a planar diode are investigated in the limit of large aspect ratio, further simplifying the functional form of the electrostatic and vector potentials. Detailed equilibrium properties are investigated numerically for a cylindrical diode over a broad range of system parameters, including diode voltage ${V}_{0}$, cathode electric field, electron density n${^}_{b}$ at the cathode, diode polarity, and applied magnetic field ${B}_{0}$.