Plasma Photocathodes

Plasma wakefield accelerators offer accelerating and focusing electric fields three to four orders of magnitude larger than state-of-the-art radiofrequency cavity-based accelerators. Plasma photocathodes can release ultracold electron populations within such plasma waves and thus open a path toward tunable production of well-defined, compact electron beams with normalized emittance and brightness many orders of magnitude better than state-of-the-art. Such beams will have far-reaching impact for applications such as light sources, but also open up new vistas on high energy and high field physics. This paper reviews the innovation of plasma photocathodes, and reports on the experimental progress, challenges, and future prospects of the approach. Details of the proof-of-concept demonstration of a plasma photocathode in 90° geometry at SLAC FACET within the E-210: Trojan Horse program are described. Using this experience, alongside theoretical and simulation-supported advances, an outlook is given on future realizations of plasma photocathodes such as the upcoming E-310: Trojan Horse-II program at FACET-II with prospects toward excellent witness beam parameter quality, tunability, and stability. Future installations of plasma photocathodes also at compact, hybrid plasma wakefield accelerators, will then boost capacities and open up novel capabilities for experiments at the forefront of interaction of high brightness electron and photon beams.     

The Kinematic Flow Structure for the Gvirtzman–Gorelick In Situ VOC Remediation System

Potential theory and Stokes' stream function techniques are used to investigate the flow structure around the recirculation system developed by Gvirtzman and Gorelick (1992, 1993), which consists of an extraction well and a gallery (trench) for the recharge of treated water to the aquifer. Analytical formulas are derived for the drawdown, velocity, and stream function for a model in which the extraction well is modeled as a uniformly distributed line sink and the gallery is modeled as a uniformly distributed ring source. Travel times are reported for water particles traveling along the streamlines containing 50 and 90% of the flow for various degrees of well penetration and various radii of the ring source. The travel times along the streamline resulting in the shortest travel time (not necessarily the shortest path) are also reported for various degrees of well penetration and various radii of the ring source. The method completely eliminates the use of numerical finite-difference or finite-element methods and can be used for optimization of technological parameters of this remediation system.     

Formation of the paramagletic Ni(I) π-allyl complex in the Ni(allyl)2 - (2,6-diisopropylphenyl)diazabutadiene system

It has been shown that the reaction of Ni(allyl)₂ with (2,6-diisopropylphenyl)diazabutadiene gives the imino-amide Ni complex (1). The imino-amide moiety of this complex undergoes some complicated rearrangements resulting in spontaneous formation of a paramagnetic π-allyl Ni(I) complex. Nickel complexes formed in the system have been studied with ESR, FTIR, 2D NMR, and mass spectrometry. The structure of complex 1 was studied with X-ray diffraction.     

Synthesis, structure and magnetic properties of Nd3+ and Pr3+ 2D polymers with tetrafluoro-p-phthalate

Two lanthanide tetrafluoro-p-phthalate (L(2-)) complexes, Ln(L)(1.5)·DMF·H(2)O (Ln = Pr(3+) (1), Nd(3+) (2)), were synthesized using pyridine as a base. The compounds were found to be isostructural, and the structure of 1 has been determined by single crystal X-ray diffraction (monoclinic, space group C2, a = 22.194(2) ?, b = 11.4347(12) ?, c = 11.7160(12) ?, β = 94.703(2)°, V = 2963.3(5) ?(3), Z = 4). The crystal structure of 1 consists of dinuclear Pr(3+) units, which are connected by tetrafluoro-p-phthalate, forming separate 2D polymeric layers. The Ln(3+) ions in the dinuclear Ln(2) units are linked by two μ-O atoms and by two bridging O-C-O groups. The structure is porous with DMF and water molecules located between layers. Non-coordinated DMF molecules occupy about 27% of the unit cell volume. A systematic analysis of reported structures of Ln(III) polymers with p-phthalate and its derivatives shows that the ca. known 60 structures can be divided into six possible structural types depending on the presence of certain structural motifs. The magnetic properties of compounds 1 and 2 were studied. The dependence of χ(M)T on T (where χ(M) is magnetic susceptibility per dinuclear lanthanide unit) for 1 and 2 was simulated using two different models, based on: (i) the Hamiltonian ? = Δ?(z)(2)+ μ(B)g(J)H?, which utilises an axial splitting parameter Δ and temperature-independent paramagnetism (tip) and (ii) crystal field splitting. It was found that both models gave satisfactory fits, indicating that the Ln-Ln exchange interactions are small and the symmetry of the coordination environment is the main factor influencing the magnetic properties of these compounds.     

Some interesting properties of maximin strategies

Since the seminal paper of Nash (1950) game theoretic literature has focused mostly on equilibrium and not on maximin (minimax) strategies. We study the properties of these strategies in non-zero-sum strategic games that possess (completely) mixed Nash equilibria. We find that under certain conditions maximin strategies have several interesting properties, some of which extend beyond 2-person strategic games. In particular, for n-person games we specify necessary and sufficient conditions for maximin strategies to yield the same expected payoffs as Nash equilibrium strategies. We also show how maximin strategies may facilitate payoff comparison across Nash equilibria as well as refine some Nash equilibrium strategies.     

Existence of solutions for some non‐Fredholm integro‐differential equations with the bi‐Laplacian

We prove the existence of solutions for some semilinear elliptic equations in the appropriate H⁴ spaces using the fixed‐point technique where the elliptic equation contains fourth‐order differential operators with and without Fredholm property, generalizing the previous results.     

A Solid-State NMR Investigation of MQ Silicone Copolymers

The structure of MQ copolymers of the general chemical formula [(CH₃)₃SiO_0.5]_m [SiO₂]_n was characterized by means of solid-state magic angle spinning (MAS) nuclear magnetic resonance (NMR) spectroscopy. The MQ copolymers are highly branched polycyclic compounds (densely cross-linked nanosized networks). MQ copolymers were prepared by hydrolytic polycondensation in active medium. ²⁹Si NMR spectra were obtained by single pulse excitation (or direct polarization, DP) and cross-polarization (CP) ²⁹Si{¹H} techniques in concert with MAS. It was shown that material consist of monofunctional M (≡SiO Si (CH₃)₃) and two types of tetrafunctional Q units: Q⁴ ((≡SiO)₄ Si) and Q³ ((≡SiO)₃ SiOH). Spin–lattice relaxation times T ₁ measurements of ²⁹Si nuclei and analysis of ²⁹Si{¹H} variable contact time signal intensities allowed us to obtain quantitative data on the relative content of different sites in copolymers. These investigations indicate that MQ copolymers represent dense structure with core and shell.     

On the correlation between the triton binding energy and the neutron-deuteron doublet scattering length

A detailed explanation of the well-known Phillips line is presented. This line, which represents the correlation between calculated values of the triton binding energy and then-d doublet scattering length, is shown to be due to the fact that the binding energies of both the triton and the deuteron, as well as the energy eigenvalue of the two-nucleon singlet virtual state, are all small on the energy scale of nuclear forces. The equivalent statement is that the Phillips line is due to the loose spatial structure of these few-nucleon systems. These conclusions are obtained on the basis of (i) qualitative analysis of the problem. (ii) calculation of the above correlation in both zero and linear approximations in the range of nuclear forces, and (iii) comparison of the results of the calculation with the Phillips line.