We prove an asymptotic formula for the second moment of central values of Dirichlet L-functions restricted to a coset. More specifically, consider a coset of the subgroup of characters modulo d inside the full group of characters modulo q. Suppose that $\nu _p(d) \geq \nu _p(q)/2$ for all primes p dividing q. In this range, we obtain an asymptotic formula with a power-saving error term; curiously, there is a secondary main term of rough size $q^{1/2}$ here which is not predicted by the integral moments conjecture of Conrey, Farmer, Keating, Rubinstein, and Snaith. The lower-order main term does not appear in the second moment of the Riemann zeta function, so this feature is not anticipated from the analogous archimedean moment problem.

We also obtain an asymptotic result for smaller d, with $\nu _p(q)/3 \leq \nu _p(d) \leq \nu _p(q)/2$, with a power-saving error term for d larger than $q^{2/5}$. In this more difficult range, the secondary main term somewhat changes its form and may have size roughly d, which is only slightly smaller than the diagonal main term.

We present a novel scheme for rapid quantitative analysis of debris generated during experiments with solid targets following relativistic laser–plasma interaction at high-power laser facilities. Results are supported by standard analysis techniques. Experimental data indicate that predictions by available modelling for non-mass-limited targets are reasonable, with debris of the order of hundreds of μg per shot. We detect for the first time two clearly distinct types of debris emitted from the same interaction. A fraction of the debris is ejected directionally, following the target normal (rear and interaction side). The directional debris ejection towards the interaction side is larger than on the side of the target rear. The second type of debris is characterized by a more spherically uniform ejection, albeit with a small asymmetry that favours ejection towards the target rear side.

Understanding the physics of electromagnetic pulse (EMP) emission and nozzle damage is critical for the long-term operation of laser experiments with gas targets, particularly at facilities looking to produce stable sources of radiation at high repetition rates. We present a theoretical model of plasma formation and electrostatic charging when high-power lasers are focused inside gases. The model can be used to estimate the amplitude of gigahertz EMPs produced by the laser and the extent of damage to the gas jet nozzle. Looking at a range of laser and target properties relevant to existing high-power laser systems, we find that EMP fields of tens to hundreds of kV/m can be generated several metres from the gas jet. Model predictions are compared with measurements of EMPs, plasma formation and nozzle damage from two experiments on the VEGA-3 laser and one experiment on the Vulcan Petawatt laser.

The California Department of Public Health (CDPH) reviewed 109 cases of healthcare personnel (HCP) with laboratory-confirmed mpox to understand transmission risk in healthcare settings. Overall, 90% of HCP with mpox had nonoccupational exposure risk factors. One occupationally acquired case was associated with sharps injury while unroofing a patient’s lesion for diagnostic testing.

The ability to quickly refresh gas-jet targets without cycling the vacuum chamber makes them a promising candidate for laser-accelerated ion experiments at high repetition rate. Here we present results from the first high repetition rate ion acceleration experiment on the VEGA-3 PW-class laser at CLPU. A near-critical density gas-jet target was produced by forcing a 1000 bar H$_2$ and He gas mix through bespoke supersonic shock nozzles. Proton energies up to 2 MeV were measured in the laser forward direction and 2.2 MeV transversally. He$^{2+}$ ions up to 5.8 MeV were also measured in the transverse direction. To help maintain a consistent gas density profile over many shots, nozzles were designed to produce a high-density shock at distances larger than 1 mm from the nozzle exit. We outline a procedure for optimizing the laser–gas interaction by translating the nozzle along the laser axis and using different nozzle materials. Several tens of laser interactions were performed with the same nozzle which demonstrates the potential usefulness of gas-jet targets as high repetition rate particle source.