Focusing of laser-generated ion beams by a plasma cylinder: similarity theory and the thick lens formula

It is shown that plasma-based optics can be used to guide and focus highly divergent laser-generated ion beams. A hollow cylinder is considered, which initially contains a hot electron population. Plasma streaming toward the cylinder axis maintains a focusing electrostatic field due to the positive radial pressure gradient. The cylinder works as thick lens, whose parameters are obtained from similarity theory for freely expanding plasma in cylindrical geometry. Because the lens parameters are energy dependent, the lens focuses a selected energy range of ions and works as a monochromator. Because the focusing is due to the quasineutral part of the expanding plasma, the lens parameters depend on the hot electron temperature $T_e$ only, and not their density

Asymptotic behaviour of Functional Identities

2010 Mathematics Subject Classification: Primary 16R60, Secondary 16R10, 15A03, 15A69.We calculate the asymptotics of functional codimensions fcn(A) and generalized functional codimensions gfc n (A) of an arbitrary not necessarily associative algebra A over a field F of any characteristic. Namely, fcn(A) ∼ gfcn(A) ∼ dim(A^2) · (dim A^n) as n → ∞ for any finite-dimensional algebra A. In particular, codimensions of functional and generalized functional identities satisfy the analogs of Amitsur’s and Regev’s conjectures. Also we precisely evaluate fcn(UT2(F)) = gfcn(UT2(F)) = 3^(n+1) − 2^(n+1).* Supported by post doctoral fellowship from Atlantic Association for Research in Mathematical Sciences (AARMS), Atlantic Algebra Centre (AAC), Memorial University of Newfoundland (MUN), and Natural Sciences and Engineering Research Council of Canada (NSERC)

Graded group actions and generalized HH-actions compatible with gradings

We introduce the notion of a graded group action on a graded algebra or, which is the same, a group action by graded pseudoautomorphisms. An algebra with such an action is a natural generalization of an algebra with a super- or a pseudoinvolution. We study groups of graded pseudoautomorphisms, show that the Jacobson radical of a group graded finite dimensional associative algebra $A$ over a field of characteristic $0$ is stable under graded pseudoautomorphisms, prove the invariant version of the Wedderburn-Artin Theorem and the analog of Amitsur's conjecture for the codimension growth of graded polynomial $G$-identities in such algebras $A$ with a graded action of a group $G$.Comment: 19 page

Similarity for ultra-relativistic laser plasmas and the optimal acceleration regime

A similarity theory is developed for ultra-relativistic laser-plasmas. It is shown that the most fundamental S-similarity is valid for both under- and overdense plasmas. Optimal scalings for laser wake field electron acceleration are obtained heuristically. The strong message of the present work is that the bubble acceleration regime [see Pukhov, Meyer-ter-Vehn, Appl. Phys. B, vol. 74, 355 (2002)] satisfies these optimal scalings

EFFECT OF CA2+ AND AL3+ IONS ON INTERACTION BETWEEN BACTERIA AND MINERAL SORBENTS

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Scalings for ultra-relativistic laser plasmas and monoenergetic electrons

The similarity theory is derived for ultra-relativistic laser-plasma interactions. First, it is shown that the most fundamental S-similarity is valid for both under- and overdense plasmas. Then, the particular case of tenious plasma is considered in great detail. It is shown that the electron dynamics in this case has two characteristic scales. The fast scale corresponds to relaxation to some attractor solution. The slow dynamics describes an adiabatic evolution of this attractor. This leads to a remarkable wave breaking exclusion rule in the 3D geometry. A similarity theory for the slow dynamics allows obtaining simple ``engineering'' scalings for the maximum electron energies, the number of accelerated electrons, the electron beam density, and for the acceleration distance. These scalings are aimed at design of a high-energy laser-plasma accelerator generating electron beams with superior properties

Magnetic Coupling Between Non-Magnetic Ions: Eu3+ in EuN and EuP

We consider the electronic structure of, and magnetic exchange (spin) interactions between, nominally nonmagnetic Eu^3+ ions (4f^6, S=3, L=3, J=0) within the context of the rocksalt structure compounds EuN and EuP. Both compounds are ionic [Eu^3+; N^3- and P^3-] semimetals similar to isovalent GdN. Treating the spin polarization within the 4f shell, and then averaging consistent with the J=0 configuration, we estimate semimetallic band overlaps (Eu 5d with pnictide 2p or 3p) of ~0.1 eV (EuN) and ~1.0 eV (EuP) that increase (become more metallic) with pressure. The calculated bulk modulus is 130 (86) GPa for EuN (EuP). Exchange (spin-spin) coupling calculated from correlated band theory is small and ferromagnetic in sign for EuN, increasing in magnitude with pressure. Conversely, the exchange coupling is antiferromagnetic in sign for EuP and is larger in magnitude, but decreases with compression. Study of a two-site model with S_1*S_2 coupling within the J=0,1 spaces of each ion illustrates the dependence of the magnetic correlation functions on the model parameters, and indicates that the spin coupling is sufficient to alter the Van Vleck susceptibility. We outline a scenario of a spin-correlation transition in a lattice of S=3, L=3, J=0 nonmagnetic ions