Equivalence between Poly\'a-Szeg\H{o} and relative capacity inequalities under rearrangement

The transformations of functions acting on sublevel sets that satisfy a P\'olya-Szeg\H{o} inequality are characterized as those being induced by transformations of sets that do not increase the associated capacity.Comment: 9 page

Second-order L2L^2-regularity in nonlinear elliptic problems

A second-order regularity theory is developed for solutions to a class of quasilinear elliptic equations in divergence form, including the $p$-Laplace equation, with merely square-integrable right-hand side. Our results amount to the existence and square integrability of the weak derivatives of the nonlinear expression of the gradient under the divergence operator. This provides a nonlinear counterpart of the classical $L^2$-coercivity theory for linear problems, which is missing in the existing literature. Both local and global estimates are established. The latter apply to solutions to either Dirichlet or Neumann boundary value problems. Minimal regularity on the boundary of the domain is required. If the domain is convex, no regularity of its boundary is needed at all

Characterization of self-injected electron beams from LWFA experiments at SPARC_LAB

The plasma-based acceleration is an encouraging technique to overcome the limits of the accelerating gradient in the conventional RF acceleration. A plasma accelerator is able to provide accelerating fields up to hundreds of $GeV/m$, paving the way to accelerate particles to several MeV over a short distance (below the millimetre range). Here the characteristics of preliminary electron beams obtained with the self-injection mechanism produced with the FLAME high-power laser at the SPARC_LAB test facility are shown. In detail, with an energy laser on focus of $1.5\ J$ and a pulse temporal length (FWHM) of $40\ fs$, we obtained an electron plasma density due to laser ionization of about $6 \times 10^{18}\ cm^{-3}$, electron energy up to $350\ MeV$ and beam charge in the range $(50 - 100)\ pC$.Comment: 6 pages, 11 figures, conference EAAC201

Conceptual design of electron beam diagnostics for high brightness plasma accelerator

A design study of the diagnostics of a high brightness linac, based on X-band structures, and a plasma accelerator stage, has been delivered in the framework of the EuPRAXIA@SPARC_LAB project. In this paper, we present a conceptual design of the proposed diagnostics, using state of the art systems and new and under development devices. Single shot measurements are preferable for plasma accelerated beams, including emittance, while $\mu$m level and fs scale beam size and bunch length respectively are requested. The needed to separate the driver pulse (both laser or beam) from the witness accelerated bunch imposes additional constrains for the diagnostics. We plan to use betatron radiation for the emittance measurement just at the end of the plasma booster, while other single-shot methods must be proven before to be implemented. Longitudinal measurements, being in any case not trivial for the fs level bunch length, seem to have already a wider range of possibilities

Thermal issues for the optical transition radiation screen for the ELI-NP compton gamma source

A high brightness electron LINAC is being built in the Compton Gamma Source at the ELI Nuclear Physics facility in Romania. To achieve the design luminosity, a train of 32 bunches, 16 ns spaced, with a nominal charge of 250 pC will collide with a laser beam in two interaction points. Electron beam spot size is measured with Optical Transition Radiation (OTR) profile monitors. In order to measure the beam properties, the OTR screens must sustain the thermal and mechanical stress due to the energy deposited by bunches. This paper is an ANSYS study of the issues due to the high energy transferred to the OTR screens. Thermal multicycle analysis will be shown; each analysis will be followed by a structural analysis in order to investigate the performance of the materia