All orders structure and efficient computation of linearly reducible elliptic Feynman integrals

We define linearly reducible elliptic Feynman integrals, and we show that they can be algorithmically solved up to arbitrary order of the dimensional regulator in terms of a 1-dimensional integral over a polylogarithmic integrand, which we call the inner polylogarithmic part (IPP). The solution is obtained by direct integration of the Feynman parametric representation. When the IPP depends on one elliptic curve (and no other algebraic functions), this class of Feynman integrals can be algorithmically solved in terms of elliptic multiple polylogarithms (eMPLs) by using integration by parts identities. We then elaborate on the differential equations method. Specifically, we show that the IPP can be mapped to a generalized integral topology satisfying a set of differential equations in $\epsilon$-form. In the examples we consider the canonical differential equations can be directly solved in terms of eMPLs up to arbitrary order of the dimensional regulator. The remaining 1-dimensional integral may be performed to express such integrals completely in terms of eMPLs. We apply these methods to solve two- and three-points integrals in terms of eMPLs. We analytically continue these integrals to the physical region by using their 1-dimensional integral representation.Comment: The differential equations method is applied to linearly reducible elliptic Feynman integrals, the solutions are in terms of elliptic polylogarithms, JHEP version, 50 page

The Zeldovich approximation: key to understanding Cosmic Web complexity

We describe how the dynamics of cosmic structure formation defines the intricate geometric structure of the spine of the cosmic web. The Zeldovich approximation is used to model the backbone of the cosmic web in terms of its singularity structure. The description by Arnold et al. (1982) in terms of catastrophe theory forms the basis of our analysis. This two-dimensional analysis involves a profound assessment of the Lagrangian and Eulerian projections of the gravitationally evolving four-dimensional phase-space manifold. It involves the identification of the complete family of singularity classes, and the corresponding caustics that we see emerging as structure in Eulerian space evolves. In particular, as it is instrumental in outlining the spatial network of the cosmic web, we investigate the nature of spatial connections between these singularities. The major finding of our study is that all singularities are located on a set of lines in Lagrangian space. All dynamical processes related to the caustics are concentrated near these lines. We demonstrate and discuss extensively how all 2D singularities are to be found on these lines. When mapping this spatial pattern of lines to Eulerian space, we find a growing connectedness between initially disjoint lines, resulting in a percolating network. In other words, the lines form the blueprint for the global geometric evolution of the cosmic web.Comment: 37 pages, 21 figures, accepted for publication in MNRA

Caustic Skeleton & Cosmic Web

We present a general formalism for identifying the caustic structure of an evolving mass distribution in an arbitrary dimensional space. For the class of Hamiltonian fluids the identification corresponds to the classification of singularities in Lagrangian catastrophe theory. Based on this we develop a theoretical framework for the formation of the cosmic web, and specifically those aspects that characterize its unique nature: its complex topological connectivity and multiscale spinal structure of sheetlike membranes, elongated filaments and compact cluster nodes. The present work represents an extension of the work by Arnol'd et al., who classified the caustics for the 1- and 2-dimensional Zel'dovich approximation. His seminal work established the role of emerging singularities in the formation of nonlinear structures in the universe. At the transition from the linear to nonlinear structure evolution, the first complex features emerge at locations where different fluid elements cross to establish multistream regions. The classification and characterization of these mass element foldings can be encapsulated in caustic conditions on the eigenvalue and eigenvector fields of the deformation tensor field. We introduce an alternative and transparent proof for Lagrangian catastrophe theory, and derive the caustic conditions for general Lagrangian fluids, with arbitrary dynamics, including dissipative terms and vorticity. The new proof allows us to describe the full 3-dimensional complexity of the gravitationally evolving cosmic matter field. One of our key findings is the significance of the eigenvector field of the deformation field for outlining the spatial structure of the caustic skeleton. We consider the caustic conditions for the 3-dimensional Zel'dovich approximation, extending earlier work on those for 1- and 2-dimensional fluids towards the full spatial richness of the cosmic web

The Zeldovich & Adhesion approximations, and applications to the local universe

The Zeldovich approximation (ZA) predicts the formation of a web of singularities. While these singularities may only exist in the most formal interpretation of the ZA, they provide a powerful tool for the analysis of initial conditions. We present a novel method to find the skeleton of the resulting cosmic web based on singularities in the primordial deformation tensor and its higher order derivatives. We show that the A_3-lines predict the formation of filaments in a two-dimensional model. We continue with applications of the adhesion model to visualise structures in the local (z < 0.03) universe.Comment: 9 pages, 8 figures, Proceedings of IAU Symposium 308 "The Zeldovich Universe: Genesis and Growth of the Cosmic Web", 23-28 June 2014, Tallinn, Estoni

Hybrid modeling of relativistic underdense plasma photocathode injectors

The dynamics of laser ionization-based electron injection in the recently introduced plasma photocathode concept is analyzed analytically and with particle-in-cell simulations. The influence of the initial few-cycle laser pulse that liberates electrons through background gas ionization in a plasma wakefield accelerator on the final electron phase space is described through the use of Ammosov-Deloine-Krainov theory as well as nonadiabatic Yudin-Ivanov (YI) ionization theory and subsequent downstream dynamics in the combined laser and plasma wave fields. The photoelectrons are tracked by solving their relativistic equations of motion. They experience the analytically described transient laser field and the simulation-derived plasma wakefields. It is shown that the minimum normalized emittance of fs-scale electron bunches released in mulit-GV/m-scale plasma wakefields is of the order of 10-2 mm mrad. Such unprecedented values, combined with the dramatically increased controllability of electron bunch production, pave the way for highly compact yet ultrahigh quality plasma-based electron accelerators and light source applications

Ultracold electron bunch generation via plasma photocathode emission and acceleration in a beam-driven plasma blowout

Beam-driven plasma wakefield acceleration using low-ionization-threshold gas such as Li is combined with laser-controlled electron injection via ionization of high-ionization-threshold gas such as He. The He electrons are released with low transverse momentum in the focus of the copropagating, nonrelativistic-intensity laser pulse directly inside the accelerating or focusing phase of the Li blowout. This concept paves the way for the generation of sub-μm-size, ultralow-emittance, highly tunable electron bunches, thus enabling a flexible new class of an advanced free electron laser capable high-field accelerator. © 2012 American Physical Society

Design considerations for the use of laser-plasma accelerators for advanced space radiation studies

We present design considerations for the use of laser-plasma accelerators for mimicking space radiation and testing space-grade electronics. This novel application takes advantage of the inherent ability of laser-plasma accelerators to produce particle beams with exponential energy distribution, which is a characteristic shared with the hazardous relativistic electron flux present in the radiation belts of planets such as Earth, Saturn and Jupiter. Fundamental issues regarding laser-plasma interaction parameters, beam propagation, flux development, and experimental setup are discussed