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The Lambert W function gives the solutions of a simple exponential polynomial. The generalized Lambert W function was defined by Mez\"{o} and Baricz, and has found applications in delay differential equations and physics. In this article we…
The paper presents a study of wakefield generation and electron injection via propagation of radially polarized laser pulses in homogeneous pre-ionized plasma. The analytical study is based on Lorentz force and continuity equations.…
Based on a Problem and its solution published on the pages of SIAM Review, we give an interesting integral representation for the Lambert $W$ function in this short note. In particular, our result yields a new integral representation for…
We consider the reflection of relativistically strong radiation from plasma and identify the physical origin of the electrons' tendency to form a thin sheet, which maintains its localisation throughout its motion. Thereby we justify the…
We modify the recent analytic formula given by Allen and Casper for the rate at which piecewise linear cosmic string loops lose energy to gravitational radiation to yield the analogous analytic formula for the rate at which loops radiate…
I show that the general implicit-function problem (or parametrized fixed-point problem) in one complex variable has an explicit series solution given by a trivial generalization of the Lagrange inversion formula. I give versions of this…
We extend a factorization theorem by Gwo\'zdziewicz and Hejmej from the ring of formal power series to any complete regular local ring $ R $. More precisely, let $ f \in R $ and assume that its Newton polyhedron has a loose edge such that…
The $\psi(x)$-function, which solves the equation $x = \sinh(aw)e^w$ for $0<a<1$, has a natural connection to the renowned Lambert $W$ function and also physical relevance through its connection to the Lenz-Ising model of ferromagnetism. We…
The Lambert W function has utility for solving various exponential and logarithmic equations arranged in the form of $g(x)e^{g(x)}$. Using the Lambert W function and tetration, a variety of categorized inversion formulas are presented.…
A scheme to generate magnetized relativistic plasmas in laboratory is proposed. It is based on interaction of ultra-high-intensity sub-picosecond laser pulses with few-micron thick foils or films. By means of Particle-In-Cell simulations it…
We present a generalization of Vlasov-Maxwell kinetic theory that accounts for intense electromagnetic fields. A strongly-radiating, possibly optically-thick plasma is decomposed into fragments, each comprising a charged particle together…
Based on the known implicit solution for nonlinear plasma waves, an explicit solution was obtained in the form of decomposition into harmonics. The solution obtained exhibits a mechanism for steepening of nonlinear plasma wave as a result…
We propose a new electromagnetic-emission mechanism in magnetized, force-free plasma, which is driven by the evolution of the underlying dynamic spacetime. In particular, the emission power and angular distribution of the emitted…
Starting from the equations of collisionless linear gyrokinetics for magnetised plasmas with an imposed inhomogeneous magnetic field, we present the first known analytical, closed-form solution for the resulting velocity-space integrals in…
The commented paper claims to provide a new expression for an energy stored around a general radiator. The major purpose of this comment is to show that the claim is unjustified. Alongside with this issue, it is pointed out that some of the…
Implicit particle-in-cell codes offer advantages over their explicit counterparts in that they suffer weaker stability constraints on the need to resolve the higher frequency modes of the system. This feature may prove particularly valuable…
The Lambert W function, implicitly defined by W(x) exp{W(x)}=x, is a "new" special function that has recently been the subject of an extended upsurge in interest and applications. In this note, I point out that the Lambert W function can…
Propagation features of circularly polarized (CP) electromagnetic waves in magnetized plasmas are determined by the plasma density and the magnetic field strength. This property can be applied to design a unique plasma photonic device for…
An analytical formulation of a radially polarized laser pulse propagating in a homogeneous, magnetized plasma is presented using Lorentz force, continuity and Maxwells equations. Perturbation technique and quasi-static approximation (QSA)…
This study presents an investigation of second harmonic generation (SHG) resulting from interaction of radially polarized laser beam propagating in homogeneous, unmagnetized plasma. Lorentz force and continuity equations have been used to…