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The generation of intense, femtosecond-scale X-ray pulses is crucial for probing matter under extreme temporal and field conditions. Current chirped-pulse amplification (CPA) techniques in free-electron lasers (FELs), however, face…
In recent work, we have proposed a theory for the derivation of an exact nonlinear dispersion relation for elastic wave propagation which here we consider for a thin rod (linearly nondispersive) and a thick rod (linearly dispersive). The…
Despite the rapidly evolving field of computational electromagnetics, few open-source tools have managed to tackle the problem of automatic mesh generation for properly discretizing the problem of interest into a finite set of elements…
We prove L^p estimates for a class of two-dimensional multilinear forms that naturally generalize (dyadic variants of) both classical paraproducts and the twisted paraproduct introduced in [5] and studied in [1] and [6]. The method we use…
Recent studies have shown direct ion heating (vashistha2020new,Juneja_2023) by lasers EM (Electromagnetic) wave interacting with a plasma threaded by an external uniform magnetic field. The EM wave frequency was near the lower hybrid (LH)…
We recently demonstrated a widely tunable THz molecular laser and reported mathematical formulas and a table for comparing how various molecules would perform as such lasers (Chevalier et al., Science, 15 November 2019, p. 856-860). Here we…
In this work, new closed-form formulas for the matrix exponential are provided. Our method is direct and elementary, it gives tractable and manageable formulas not current in the extensive literature on this essential subject. Moreover,…
We studied angular distributions of x rays emitted in resonant recombination of highly charged iron and krypton ions, resolving dielectronic, trielectronic, and quadruelectronic channels. A tunable electron beam drove these processes,…
Several problems in magnetically confined fusion, such as the computation of exterior vacuum fields or the decomposition of the total magnetic field into separate contributions from the plasma and the external sources, are best formulated…
It has by now become a standard approach to use the theory of sparse (or toric) elimination, based on the Newton polytope of a polynomial, in order to reveal and exploit the structure of algebraic systems. This talk surveys compact…
A general explicit form for generating functions for approximating fractional derivatives is derived. To achieve this, an equivalent characterisation for consistency and order of approximations established on a general generating function…
This dissertation explores the interaction between high-intensity lasers and plasmas to accelerate electrons and produce radiation via experimental and computational efforts. The laser pulses used in this dissertation have ultrashort…
Using three-dimensional particle-in-cell simulations we show that a strongly nonlinear plasma wave excited by an ultrahigh intensity laser pulse works as a compact high-brightness source of X-ray radiation. It has been recently suggested by…
An infinite log-gas formalism, due to Dyson, and independently Fogler and Shklovskii, is applied to the computation of conditioned gap probabilities at the hard and soft edges of random matrix $\beta$-ensembles. The conditioning is that…
An expression for the effective Coulomb logarithm in one-component-plasma is proposed, which allows to extend the applicability of the classical formula for the self-diffusion coefficient to the strongly coupled regime. The proposed…
Here we experimentally map the dynamics of electron plasma waves in laser solid interaction. We do time resolved measurements of second harmonic and hard X-ray generation from interaction of intense ($10^{16} W cm^{-2}$, 100 fs, 800nm)…
The density matrix in the Lindblad form is used to describe the behavior of the Free-Electron Laser (FEL) operating in a quantum regime. The detrimental effects of the spontaneous emission on coherent FEL operation are taken into account.…
Let $\lambda:[0,+\infty)\mapsto\mathbb{R}$ be the driving function of a chordal Loewner process. In this paper we find new conditions on $\lambda$ which imply that the process is generated by a simple curve. This result improves former one…
We have studied the linear dispersion relation for Langmuir waves in plasmas of very high density, based on the Dirac-Heisenberg-Wigner formalism. The vacuum contribution to the physical observables leads to ultra-violet divergences, that…
Exact expressions for all the steady-state fields (E, H, D, B) in uniaxial linear media composed of an arbitrary number of layers having arbitrary thicknesses subjected to normal incidence are derived. Generic boundary condition relations…