A spectral, quasi-cylindrical and dispersion-free Particle-In-Cell algorithm

We propose a spectral Particle-In-Cell (PIC) algorithm that is based on the combination of a Hankel transform and a Fourier transform. For physical problems that have close-to-cylindrical symmetry, this algorithm can be much faster than full 3D PIC algorithms. In addition, unlike standard finite-difference PIC codes, the proposed algorithm is free of numerical dispersion. This algorithm is benchmarked in several situations that are of interest for laser-plasma interactions. These benchmarks show that it avoids a number of numerical artifacts, that would otherwise affect the physics in a standard PIC algorithm - including the zero-order numerical Cherenkov effect.Comment: 23 pages, 8 figure

All-optical Compton scattering at shallow interaction angles

All-optical Compton sources combine laser-wakefield accelerators and intense scattering pulses to generate ultrashort bursts of backscattered radiation. The scattering pulse plays the role of a small-period undulator (∼1μm) in which relativistic electrons oscillate and emit X-ray radiation. To date, most of the working laser-plasma accelerators operate preferably at energies of a few hundreds of megaelectronvolts and the Compton sources developed so far produce radiation in the range from hundreds of kiloelectronvolts to a few megaelectronvolts. However, for such applications as medical imaging and tomography the relevant energy range is 10–100 keV. In this article, we discuss different scattering geometries for the generation of X-rays in this range. Through numerical simulations, we study the influence of electron beam parameters on the backscattered photons. We find that the spectral bandwidth remains constant for beams of the same emittance regardless of the scattering geometry. A shallow interaction angle of 30∘ or less seems particularly promising for imaging applications given parameters of existing laser-plasma accelerators. Finally, we discuss the influence of the radiation properties for potential applications in medical imaging and non-destructive testing

Laser-plasma interactions with a Fourier-Bessel Particle-in-Cell method

A new spectral particle-in-cell (PIC) method for plasma modeling is presented and discussed. In the proposed scheme, the Fourier-Bessel transform is used to translate the Maxwell equations to the quasi-cylindrical spectral domain. In this domain, the equations are solved analytically in time, and the spatial derivatives are approximated with high accuracy. In contrast to the finite-difference time domain (FDTD) methods that are commonly used in PIC, the developed method does not produce numerical dispersion, and does not involve grid staggering for the electric and magnetic fields. These features are especially valuable in modeling the wakefield acceleration of particles in plasmas. The proposed algorithm is implemented in the code PLARES-PIC, and the test simulations of laser plasma interactions are compared to the ones done with the quasi-cylindrical FDTD PIC code CALDER-CIRC.Comment: submitted to Phys. Plasma

Four-loop verification of algorithm for Feynman diagrams summation in N=1 supersymmetric electrodynamics

A method of Feynman diagrams summation, based on using Schwinger-Dyson equations and Ward identities, is verified by calculating some four-loop diagrams in N=1 supersymmetric electrodynamics, regularized by higher derivatives. In particular, for the considered diagrams correctness of an additional identity for Green functions, which is not reduced to the gauge Ward identity, is proved.Comment: 14 pages, 9 figure