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Novel Relativity Theories of Synthetic Aperture Radar
Published in Maged Marghany, Automatic Detection Algorithms of Oil Spill in Radar Images, 2019
where γ(v) is the Lorentz factors, which is the factor by which time, length and relativistic mass change for an object while that object is moving. The inverse term 11−v2c−2 in Equation 7.11 presents Lorentz factors. It is clear that the inverse of Lorentz factors is a function of velocity and leads to a circular arc (Fig. 7.3).
Coupled effect of spatio-temporal variation of Laguerre–Gaussian laser pulse on electron acceleration in magneto-plasma
Published in Waves in Random and Complex Media, 2022
With the advancement in the field of lasers, laser-plasma interaction has become an interesting area of research for scientists and researchers, consisting of a wide range of applications like higher harmonic generation, x-ray sources, particle accelerator, inertial confinement fusion, and many others. The interaction of highly intense laser pulses with a non-linear medium like plasma results in the occurrence of many non-linear processes like Raman forward scattering, Raman backward scattering, Brillouin scattering, etc. In addition to these non-linear processes, some self-acting processes like self-focusing and self-compression also take place. In the absence of a non-linear medium, diffraction broadening of the laser pulse takes place near the Rayleigh length distance and results in divergence of the laser pulse. Thus, diffraction is one of the major limitations, limiting the propagation of laser in a medium. While propagating in the plasma medium, a non-linear self-acting process assists the laser pulses to travel a few Rayleigh lengths of distance. When a high-intensity laser pulse having power greater than critical power interacts with a plasma medium, the relativistic effects came into action. The plasma electrons near the highly intense region achieve relativistic speeds. The effective mass of these electrons increases by the Lorentz factor due to their quiver motion. The effective mass of these plasma electrons further modifies the dielectric function and refractive index of the plasma medium, hence resulting in the spatial self-focusing of laser pulse [1–3].
Quantum theory for 1D X-ray free electron laser
Published in Journal of Modern Optics, 2018
In the absence of the ponderomotive potential, the value of the equilibrium canonical momentum is equal to with an equilibrium Lorentz factor corresponding to . This equilibrium momentum is directly related to the momentum of an ‘undulator’ electron, moving with the Bambini–Renieri velocity [19], which implies that the resonant energy for an electron is for in accordance with the classical X-ray FEL theory. Using this resonant energy and expanding Equation (13) near the equilibrium momentum results in a Hamiltonian for a non-relativistic particle in a potential:
The timestep constraint in solving the gravitational wave equations sourced by hydromagnetic turbulence
Published in Geophysical & Astrophysical Fluid Dynamics, 2020
Alberto Roper Pol, Axel Brandenburg, Tina Kahniashvili, Arthur Kosowsky, Sayan Mandal
The TT projection (see box 35.1 of Misner et al.1973) can be computed in Fourier space (indicated by a tilde) as where is the projection operator, is the wavevector, and is its unit vector with being the modulus. The stress-energy tensor consists of the sum of negative Reynolds and Maxwell stresses, expressed for flat space-time geometry as where p is the fluid pressure, is the radiation energy density, ρ being a normalised energy density (not to be confused with the previously introduced mass density), is the Lorentz factor, is the turbulent velocity, is the magnetic field, is the vacuum permeability and the ellipsis denotes viscous and resistive contributions that are ignored here. From now on, we adopt Lorentz–Heaviside units for the magnetic fields, such that . The MHD fields (p, ρ, and ) that appear in (5) are functions of comoving space and conformal time coordinates. They are expressed as comoving fields, leading to the comoving stress-energy tensor, as described in appendix 1.