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Register a new userReview and Recent Advances in PIC Modeling of Relativistic Beams and Plasmas
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Brendan B. Godfrey
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Particle-in-Cell (PIC) simulation codes have wide applicability to first-principles modeling of multidimensional nonlinear plasma phenomena, including wake-field accelerators. This review addresses both finite difference and pseudo-spectral PIC algorithms, including numerical instability suppression and generalizations of the spectral field solver.
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Modern particle accelerators and their applications increasingly rely on precisely coordinated interactions of intense charged particle and laser beams. Femtosecond-scale synchronization alongside micrometre-scale spatial precision are essential e.g. for pump-probe experiments, seeding and diagnostics of advanced light sources and for plasma-based accelerators. State-of-the-art temporal or spatial diagnostics typically operate with low-intensity beams to avoid material damage at high intensity. As such, we present a plasma-based approach, which allows measurement of both temporal and spatial overlap of high-intensity beams directly at their interaction point. It exploits amplification of plasma afterglow arising from the passage of an electron beam through a laser-generated plasma filament. The corresponding photon yield carries the spatiotemporal signature of the femtosecond-scale dynamics, yet can be observed as a visible light signal on microsecond-millimetre scales.
A method of slicing of high-energy electron beams following their interaction with the transverse component of the wakefield left in a plasma behind a high intensity ultra short laser pulse is proposed. The transverse component of the wakefield focuses a portion of the electron bunch, which experiences betatron oscillations. The length of the focused part of the electron bunch can be made substantially less than the wakefield wavelength.
Rapidly growing numerical instabilities routinely occur in multidimensional particle-in-cell computer simulations of plasma-based particle accelerators, astrophysical phenomena, and relativistic charged particle beams. Reducing instability growth to acceptable levels has necessitated higher resolution grids, high-order field solvers, current filtering, etc. except for certain ratios of the time step to the axial cell size, for which numerical growth rates and saturation levels are reduced substantially. This paper derives and solves the cold beam dispersion relation for numerical instabilities in multidimensional, relativistic, electromagnetic particle-in-cell programs employing either the standard or the Cole-Karkkainnen finite difference field solver on a staggered mesh and the common Esirkepov current-gathering algorithm. Good overall agreement is achieved with previously reported results of the WARP code. In particular, the existence of select time steps for which instabilities are minimized is explained. Additionally, an alternative field interpolation algorithm is proposed for which instabilities are almost completely eliminated for a particular time step in ultra-relativistic simulations.
In a previous paper we showed that dynamical density shocks occur in the non-relativistic expansion of dense single component plasmas relevant to ultrafast electron microscopy; and we showed that fluid models capture these effects accurately. We show that the non-relativistic decoupling of the relative and center of mass motions ceases to apply and this coupling leads to novel behavior in the relativistic dynamics under planar, cylindrical, and spherical symmetries. In cases where the relative motion of the bunch is relativistic, we show that a dynamical shock emerges even in the case of a uniform bunch with cold initial conditions; and that density shocks are in general enhanced when the relative motion becomes relativistic. Furthermore, we examine the effect of an extraction field on the relativistic dynamics of a planar symmetric bunch.
Introduced more than a half century ago, Granger causality has become a popular tool for analyzing time series data in many application domains, from economics and finance to genomics and neuroscience. Despite this popularity, the validity of this notion for inferring causal relationships among time series has remained the topic of continuous debate. Moreover, while the original definition was general, limitations in computational tools have primarily limited the applications of Granger causality to simple bivariate vector auto-regressive processes or pairwise relationships among a set of variables. Starting with a review of early developments and debates, this paper discusses recent advances that address various shortcomings of the earlier approaches, from models for high-dimensional time series to more recent developments that account for nonlinear and non-Gaussian observations and allow for sub-sampled and mixed frequency time series.
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