Variational Formulation of Macro-Particle Models for Electromagnetic Plasma Simulations

A variational method is used to derive a self-consistent macro-particle model for relativistic electromagnetic kinetic plasma simulations. Extending earlier work [E. G. Evstatiev and B. A. Shadwick, J. Comput. Phys., vol. 245, pp. 376-398, 2013], the discretization of the electromagnetic Low Lagrangian is performed via a reduction of the phase-space distribution function onto a collection of finite-sized macro-particles of arbitrary shape and discretization of field quantities onto a spatial grid. This approach may be used with both lab frame coordinates or moving window coordinates; the latter can greatly improve computational efficiency for studying some types of laser-plasma interactions. The primary advantage of the variational approach is the preservation of Lagrangian symmetries, which in our case leads to energy conservation and thus avoids difficulties with grid heating. Additionally, this approach decouples particle size from grid spacing and relaxes restrictions on particle shape, leading to low numerical noise. The variational approach also guarantees consistent approximations in the equations of motion and is amenable to higher order methods in both space and time. We restrict our attention to the 1-1/2 dimensional case (one coordinate and two momenta). Simulations are performed with the new models and demonstrate energy conservation and low noise.Comment: IEEE Transaction on Plasma Science (TPS) Special Issue: Plenary and Invited Papers of the Pulsed Power and Plasma Science Conference (PPPS 2013

Exactly Conservative Integrators

Traditional numerical discretizations of conservative systems generically yield an artificial secular drift of any nonlinear invariants. In this work we present an explicit nontraditional algorithm that exactly conserves these invariants. We illustrate the general method by applying it to the three-wave truncation of the Euler equations, the Lotka--Volterra predator--prey model, and the Kepler problem. This method is discussed in the context of symplectic (phase space conserving) integration methods as well as nonsymplectic conservative methods. We comment on the application of our method to general conservative systems.Comment: 30 pages, postscript (1.3MB). Submitted to SIAM J. Sci. Comput

An algorithm for feedback linearization

AbstractPrevious methods for exact linearization by feedback have relied on solving Frobenius systems of partial differential equations of dimensions equal to the Kronecker indices. We will describe an algorithm whereby one may find the linearizing feedback for any controlable linearizable system having distinct Kronecker indices with p-controls by purely algebraic calculations and integration of at most p one-dimensional Frobenius systems. The paper concludes with a concrete example considered by Hunt-Su-Meyer in their paper [3]

Summer Carbonate Chemistry in the Dalton Polynya, East Antarctica

The carbonate chemistry in the Dalton Polynya in East Antarctica (115°–123°E) was investigated in summer 2014/2015 using high‐frequency underway measurements of CO2 fugacity (fCO2) and discrete water column measurements of total dissolved inorganic carbon (TCO2) and total alkalinity. Air‐sea CO2 fluxes indicate this region was a weak net source of CO2 to the atmosphere (0.7 ± 0.9 mmol C m−2 day−1) during the period of observation, with the largest degree of surface water supersaturation (ΔfCO2 = +45 μatm) in ice‐covered waters near the Totten Ice Shelf (TIS) as compared to the ice‐free surface waters in the Dalton Polynya. The seasonal depletion of mixed‐layer TCO2 (6 to 51 μmol/kg) in ice‐free regions was primarily driven by sea ice melt and biological CO2 uptake. Estimates of net community production (NCP) reveal net autotrophy in the ice‐free Dalton Polynya (NCP = 5–20 mmol C m−2 day−1) and weakly heterotrophic waters near the ice‐covered TIS (NCP = −4–0 mmol C m−2 day−1). Satellite‐derived estimates of chlorophyll a (Chl a) and sea ice coverage suggest that the early summer season in 2014/2015 was anomalous relative to the long‐term (1997–2017) record, with lower surface Chl a concentrations and a greater degree of sea ice cover during the period of observation; the implications for seasonal primary production and air‐sea CO2 exchange are discussed. This study highlights the importance of both physical and biological processes in controlling air‐sea CO2 fluxes and the significant interannual variability of the CO2 system in Antarctic coastal regions

Late-summer biogeochemistry in the Mertz Polynya: East Antarctica

A marked reconfiguration of the Mertz Polynya following the 2010 calving of the Mertz Glacier Tongue has been associated with a decrease in the size and activity of the polynya. We report observations of the oceanic carbonate (CO2) system in late-summer 2013, the third post-calving summer season. Estimates of seasonal net community production (NCP) based on inorganic carbon deficits and the oxygen-argon ratio indicate that the waters on the shelf to the east of Commonwealth Bay (adjacent to the Mertz Glacier) remain productive compared to pre-calving conditions. The input of residual or excess alkalinity from melting sea ice is found to contribute to the seasonal enhancement of carbonate saturation state and pH in shelf waters. Mean rates of NCP in 2012-2013 are more than twice as large as those observed in the pre-calving summers of 2001 and 2008 and suggest that the new (post-calving) configuration of the polynya favors enhanced net community production and a stronger surface ocean sink for atmospheric CO2 due at least in part to the redistribution of sea ice and associated changes in summer surface stratification

Optically controlled laser–plasma electron accelerator for compact gamma-ray sources

Generating quasi-monochromatic, femtosecond γ-ray pulses via Thomson scattering (TS) demands exceptional electron beam (e-beam) quality, such as percent-scale energy spread and five-dimensional brightness over 1016 Am–2.We show that near-GeV e-beams with these metrics can be accelerated in a cavity of electron density, driven with an incoherent stack of Joule-scale laser pulses through ammsize, dense plasma (n0 ~ 1019 cm−3). Changing the time delay, frequency difference, and energy ratio of the stack components controls the e-beam phase space on the femtosecond scale, while the modest energy of the optical driver helps afford kHz-scale repetition rate at manageable average power. Blue-shifting one stack component by a considerable fraction of the carrier frequency makes the stack immune to self-compression. This, in turn, minimizes uncontrolled variation in the cavity shape, suppressing continuous injection of ambient plasma electrons, preserving a single, ultra-bright electron bunch. In addition, weak focusing of the trailing component of the stack induces periodic injection, generating, in a single shot, a train of bunches with controllable energy spacing and femtosecond synchronization. These designer e-beams, inaccessible to conventional acceleration methods, generate, via TS, gigawatt γ-ray pulses (or multi-color pulse trains) with the mean energy in the range of interest for nuclear photonics (4–16MeV), containing over 106 photons within a microsteradian-scale observation cone