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We present an accurate approach of the basic ultra-relativistic effects which occur at the interactions between laser beams and electrons and correspond to laser beam intensities greater than 1020 W/cm2. These effects are the generation of extremely bright pulses and the existence of a very large frequency spectrum of the radiation generated by this interaction, containing relative intense harmonics of orders higher than 800. Our results are in good agreement with the experimental results published in the literature.
The relativistic mirror (RM) is an interesting subject which introduced in the nonlinear regime of the laser–plasma interaction. Reflection of counter-propagating probe pulse from relativistic flying mirror has some excellent features, such as frequency up-shifting and compressing by a factor of 4γ2. In the high-intensity laser–plasma interaction, sometimes a sequence of RMs creates. For example, electron density cusps generate in the nonlinear laser wakefield generation or flying electron sheaths create in the blown-out regime of the laser foil interaction. Under these circumstances, the second counter-propagated seed (probe) pulse can be reflected back and forth between two or more successive RMs. This structure may be used as a relativistic cavity (RECA). Amplification and threshold conditions for the gain medium and pumping rate in the RECA are obtained, and it is shown that amplification can be started from background simultaneous emission (without seed pulse). A new feature of RECA is it's bidirectional (two frequencies) characteristic. Thereupon, the gain process can be implemented on the two different transitions in this bidirectional gain structure. In the RECA, driver pulse may be assembled as a pumping operation, and background plasma medium with high degree ionized substances is a good candidate for gain medium in the UV or X-ray regions. In this paper, we propose a new all-optical cavity for the generation of the ultrashort laser pulse in the UV or X-ray regions.
In the paper, relativistic self-focusing in the interaction of laser beam and plasma with periodical density ripple has been studied by the applied WKB approximation and higher-order paraxial theory. The result shows that under the influence of relativistic nonlinear effect, the dielectric function shows the fierce oscillational variation with similar periodicity, which then leads to the intense relativistic beam self-focusing along the propagation distance, such self-focusing also presents similar periodic variation. Besides, in the plasma with periodical density ripple, the initial density and the density ripple amplitude have obvious influence on self-focusing. When the two factors increase, then there will be more strength self-focusing. Choosing the appropriate initial density and the periodic density parameter is benefit to the formation of the more stable self-focusing.
Földes and Pokol in their letter “Inertial fusion without compression does not work either with or without nanoplasmonics” criticized our works. Here, we refute their argumentation. Our proposed improvement is the combination of two basic research discoveries: (i) the possibility of detonations on space-time hypersurfaces with time-like normal (i.e., simultaneous detonation in a whole volume) and (ii) to increase the ignition volume to the whole target, by regulating the laser light absorption using nanoantennas. These principles can be realized in an in-line, one-dimensional configuration, in the simplest way with two opposing laser beams as in particle colliders.
The study of spherically symmetric motion is important for the theory of explosion waves. In this paper, we consider a ‘spherical piston’ problem for the relativistic Euler equations, which describes the wave motion produced by a sphere expanding into an infinite surrounding medium. We use the reflected characteristics method to construct a global piecewise smooth solution with a single shock of this spherical piston problem, provided that the speed of the sphere is a small perturbation of a constant speed.
In this paper, self-focusing of finite Airy–Gaussian (AiG) laser beams in collisionless plasma has been investigated. The source of nonlinearity considered herein is relativistic. Based on the Wentzel–Kramers–Brillouin (WKB) and paraxial-ray approximations, the nonlinear coupled differential equations for beam-width parameters in transverse dimensions of AiG beams have been established. The effect of beam's modulation parameter and linear absorption coefficient on the self-focusing/defocusing of the beams is specifically considered. It is found that self-focusing/defocusing of finite AiG beams depends on the range of modulation parameter. The extent of self-focusing is found to decrease with increase in absorption.
This article presents a preliminary study of the longitudinal self-compression of ultra-intense Gaussian laser pulse in a magnetized plasma, when relativistic nonlinearity is active. This study has been carried out in 1D geometry under a nonlinear Schrodinger equation and higher-order paraxial (nonparaxial) approximation. The nonlinear differential equations for self-compression and self-focusing have been derived and solved by the analytical and numerical methods. The dielectric function and the eikonal have been expanded up to the fourth power of r (radial distance). The effect of initial parameters, namely incident laser intensity, magnetic field, and initial pulse duration on the compression of a relativistic Gaussian laser pulse have been explored. The results are compared with paraxial-ray approximation. It is found that the compression of pulse and pulse intensity of the compressed pulse is significantly enhanced in the nonparaxial region. It is observed that the compression of the high-intensity laser pulse depends on the intensity of laser beam (a0), magnetic field (ωc), and initial pulse width (τ0). The preliminary results show that the pulse is more compressed by increasing the values of a0, ωc, and τ0.
In this paper, the generation of relativistic electron mirrors (REM) and the reflection of an ultra-short laser off the mirrors are discussed, applying two-dimension particle-in-cell simulations. REMs with ultra-high acceleration and expanding velocity can be produced from a solid nanofoil illuminated normally by an ultra-intense femtosecond laser pulse with a sharp rising edge. Chirped attosecond pulse can be produced through the reflection of a counter-propagating probe laser off the accelerating REM. In the electron moving frame, the plasma frequency of the REM keeps decreasing due to its rapid expansion. The laser frequency, on the contrary, keeps increasing due to the acceleration of REM and the relativistic Doppler shift from the lab frame to the electron moving frame. Within an ultra-short time interval, the two frequencies will be equal in the electron moving frame, which leads to the resonance between laser and REM. The reflected radiation near this interval and corresponding spectra will be amplified due to the resonance. Through adjusting the arriving time of the probe laser, a certain part of the reflected field could be selectively amplified or depressed, leading to the selective adjustment of the corresponding spectra.
In 1905, Einstein published his paper on the special theory of relativity. Although Lorentz and Poincaré had introduced a number of the essential feature of the special theory, Einstein's' paper went much deeper and showed that we live in four-dimensional space-time. A consequence of this approach was the derivation of the mass-energy relation E = mc2. The route to the special theory of relativity was not straightforward, but Einstein's approach was quickly adopted and the mass energy relation confirmed by the Cockcroft and Walton experiment of 1932. In this chapter, the theory of special relativity is developed through the use of four-vectors, providing a robust framework for carrying out calculations in special relativity.
Exact solution of two-dimensional Dirac equation for Coulomb potential (Dirac–Kepler problem) is presented. Linear and nonlinear screening of the Coulomb potential is discused. The main focus is on the phenomenon of relativistic collapse of supercritical charges, which was discussed for many years in high-energy physics (this is the process that determines the end of the periodic table) and was at last discovered in graphene. We introduce Hartree–Fock theory for massless Dirac electrons and show that their Coulomb interaction essentially renormalizes Fermi velocity in such a way that Dirac cone is, strictly speaking, no more cone.
With many physical applications already on the table, in this chapter, we return to some of the simplified ones and re-complexify them. These problems require more sophisticated, and incomplete, solutions. Instead of finding the position of the bob for the simple pendulum, we find the period of motion for the ``real" pendulum. Instead of the classical harmonic oscillator, with its familiar solution, we study the period of the relativistic harmonic oscillator, and find that in the high energy limit, a mass attached to a spring behaves very differently from its non-relativistic counterpart.
Ultraintense laser-driven relativistic electrons provide a way of heating matter to high energy density states related to many applications. However, the transport of relativistic electrons in solid targets has not been understood well yet, especially in dielectric targets. We present the first detailed two-dimensional particle-in-cell simulations of relativistic electron transport in a silicon target by including the field ionization and collisional ionization processes. An ionization wave is found propagating in the insulator, with a velocity dependent on laser intensity and slower than the relativistic electron velocity. Widely spread electric fields in front of the sheath fields are observed due to the collective effect of free electrons and ions. The electric fields are much weaker than the threshold electric field of field ionization. Two-stream instability behind the ionization front arises for the cases with laser intensity greater than
that produce high relativistic electron current densities.
The process of high energy electron acceleration along the surface of grating targets (GTs) that were irradiated by a relativistic, high-contrast laser pulse at an intensity
was studied. Our experimental results demonstrate that for a GT with a periodicity twice the laser wavelength, the surface electron flux is more intense for a laser incidence angle that is larger compared to the resonance angle predicted by the linear model. An electron beam with a peak charge of
, for electrons with energies
, was measured. Numerical simulations carried out with parameters similar to the experimental conditions also show an enhanced electron flux at higher incidence angles depending on the preplasma scale length. A theoretical model that includes ponderomotive effects with more realistic initial preplasma conditions suggests that the laser-driven intensity and preformed plasma scale length are important for the acceleration process. The predictions closely match the experimental and computational results.
In this paper, we present the stationary axisymmetric configuration of a resistive magnetised thick accretion disc in the vicinity of external gravity and intrinsic dipolar magnetic field of a slowly rotating black hole. The plasma is described by the equations of fully general relativistic magnetohydrodynamics (MHD) along with the Ohm’s law and in the absence of the effects of radiation fields. We try to solve these two-dimensional MHD equations analytically as much as possible. However, we sometimes inevitably refer to numerical methods as well. To fully understand the relativistic geometrically thick accretion disc structure, we consider all three components of the fluid velocity to be non-zero. This implies that the magnetofluid can flow in all three directions surrounding the central black hole. As we get radially closer to the hole, the fluid flows faster in all those directions. However, as we move towards the equator along the meridional direction, the radial inflow becomes stronger from both the speed and the mass accretion rate points of view. Nonetheless, the vertical (meridional) speed and the rotation of the plasma disc become slower in that direction. Due to the presence of pressure gradient forces, a sub-Keplerian angular momentum distribution throughout the thick disc is expected as well. To get a concise analytical form of the rate of accretion, we assume that the radial dependency of radial and meridional fluid velocities is the same. This simplifying assumption leads to radial independency of mass accretion rate. The motion of the accreting plasma produces an azimuthal current whose strength is specified based on the strength of the external dipolar magnetic field. This current generates a poloidal magnetic field in the disc which is continuous across the disc boundary surface due to the presence of the finite resistivity for the plasma. The gas in the disc is vertically supported not only by the gas pressure but also by the magnetic pressure.
Self-focusing of Gaussian laser beam has been investigated in quantum plasma under the effect of applied axial magnetic field. The nonlinear differential equation has been derived for studying the variations in the beam-width parameter. The effect of initial plasma electron temperature and the axial magnetic field on self-focusing and normalized intensity are studied. Our investigation reveals that normalized intensity increases to tenfolds where quantum effects are dominant. The normalized intensity further increases to twelvefolds on increasing the magnetic field.
The study of radially symmetric motion is important for the theory of explosion waves. We construct rigorously self-similar entropy solutions to Riemann initial-boundary value problems for the radially symmetric relativistic Euler equations. We use the assumption of self-similarity to reduce the relativistic Euler equations to a system of nonlinear ordinary differential equations, from which we obtain detailed structures of solutions besides their existence. For the ultra-relativistic Euler equations, we also obtain the uniqueness of the self-similar entropy solution to the Riemann initial-boundary value problems.
An analytical and numerical study has been carried out for the generation of terahertz (THz) radiation by beating of two intense cosh-Gaussian laser beams (decentered Gaussian beams) in the rippled density magnetized plasma under the relativistic–ponderomotive regime. In this process, both laser beams exert a relativistic–ponderomotive force on plasma electrons at the beat frequency and impart them an oscillatory velocity in the presence of a static magnetic field. Due to coupling between this nonlinear oscillatory velocity with density ripple, nonlinear current is generated that excites the THz radiation at the different frequency. Higher-order paraxial-ray approximation (non-paraxial theory) has been used in this study. The effects of the decentered parameter, magnetic field, and density ripple on the THz radiation generation in ripple density magnetized plasma have been investigated. Further, the effect of beating of laser beams on the THz field amplitude and the efficiency of THz radiation have been studied. The amplitude and efficiency of the emitted radiation are found to be highly sensitive to the decentered parameter, magnetic field, and density ripple. It has been found that the amplitude and efficiency of the generated THz radiation increase significantly with increasing the values of decentered parameter, magnetic field, and density ripple.
In the literature, there have been several methods and definitions for working out whether two theories are “equivalent” (essentially the same) or not. In this article, we do something subtler. We provide a means to measure distances (and explore connections) between formal theories. We introduce two natural notions for such distances. The first one is that of axiomatic distance, but we argue that it might be of limited interest. The more interesting and widely applicable notion is that of conceptual distance which measures the minimum number of concepts that distinguish two theories. For instance, we use conceptual distance to show that relativistic and classical kinematics are distinguished by one concept only.
The formation of a collisional shock wave by the light pressure of a short-laser pulse at intensities in the range of 1018–1023 W/cm2 is considered. In this regime the thermodynamic parameters of the equilibrium states, before and after the shock transition, are related to the relativistic Rankine–Hugoniot equations. The electron and ion temperatures associated with these shock waves are calculated. It is shown that if the time scale of energy dissipation is shorter than the laser pulse duration a collisional shock is formed. The electrons and the ions in the shock-heated layer may have equal or different temperatures, depending on the laser pulse duration, the material density and the laser intensity. This shock wave may serve as a heating mechanism in a fast ignition scheme.