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

Plasma boosted electron beams for driving Free Electron Lasers

In this paper, we report results of simulations, in the framework of both EuPRAXIA \cite{Walk2017} and EuPRAXIA@SPARC\_LAB \cite{Ferr2017} projects, aimed at delivering a high brightness electron bunch for driving a Free Electron Laser (FEL) by employing a plasma post acceleration scheme. The boosting plasma wave is driven by a tens of \SI{}{\tera\watt} class laser and doubles the energy of an externally injected beam up to \GeV{1}. The injected bunch is simulated starting from a photoinjector, matched to plasma, boosted and finally matched to an undulator, where its ability to produce FEL radiation is verified to yield O(\num{e11}) photons per shot at \nm{2.7}.Comment: 5 pages, 2 figure

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

Emittance measurements at the TTF photoinjector

The TTF Free Electron Laser requires high current electron bunches with small emittances. The beam is produced by an injector based on a laser driven rf gun. The design aims for a bunch charge of 1 nC, a bunch length in the mm range, and a normalized transverse emittance approaching1mm mrad. Emittance measurements in the photoinjector after preacceleration to 17MeV are presented and compared to simulations

Optical issues for the diagnostic stations 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 the laser beam in the interaction point. Electron beam spot size is measured with optical transition radiation (OTR) profile monitors. In order to measure the beam properties, the optical radiation detecting system must have the necessary accuracy and resolution. This paper deals with the studies of different optic configurations to achieve the magnification, resolution and accuracy in order to measure very small beam (below 30 μm) or to study the angular distribution of the OTR and therefore the energy of the beam. Several configurations of the optical detection line will be studied both with simulation tools (e.g. Zemax) and experimentally. The paper will deal also with the sensibility of optic system (in terms of depth of field, magnification and resolution) to systematic error

Quadrupole scan emittance measurements for the ELI-NP compton gamma source

The high brightness electron LINAC of the Compton Gamma Source at the ELI Nuclear Physics facility in Roma- nia is accelerating a train of 32 bunches with a nominal total charge of 250 pC and nominal spacing of 16 ns . To achieve the design gamma flux, all the bunches along the train must have the designed Twiss parameters. Beam sizes are mea- sured with optical transition radiation monitors, allowing a quadrupole scan for Twiss parameters measurements. Since focusing the whole bunch train on the screen may lead to permanent screen damage, we investigate non-conventional scans such as scans around a maximum of the beam size or scans with a controlled minimum spot size. This paper discusses the implementation issues of such a technique in the actual machine layou