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This work shows for the first time experimentally the close relation between return currents from relativistic laser-driven target polarization and the quality of the relativistic laser plasma interaction for laser driven secondary sources. Such currents rise in all interaction schemes where targets of any kind are charged by escaping laser-accelerated relativistic electrons. Therefore, return currents can be used as a metrological online tool in the optimization of many laser-driven secondary sources and for diagnosing their stability. We demonstrate the destruction free measurement of return currents at the example of a tape target system irradiated by the 1 PW VEGA3 laser at CLPU at its maximum capabilities for laser-driven ion acceleration. Such endeavour paves the ground for feedback systems that operate at the high-repetition-rate of PW-class laser systems.

We report the first high-repetition rate generation and simultaneous characterization of nanosecond-scale return currents of kA-magnitude issued by the polarization of a target irradiated with a PW-class high-repetition-rate Ti:Sa laser system at relativistic intensities. We present experimental results obtained with the VEGA-3 laser at intensities from 5e18 - 1.3e20 W/cm2. A non-invasive inductive return-current monitor is adopted to measure the derivative of return-currents on the order of kA/ns and analysis methodology is developed to derive return-currents. We compare the current for copper, aluminium and Kapton targets at different laser energies. The data shows the stable production of current peaks and clear prospects for the tailoring of the pulse shape, promising for future applications in high energy density science, e.g. electromagnetic interference stress tests, high-voltage pulse response measurements, and charged particle beam lensing. We compare the target discharge of the order of hundreds of nC with theoretical predictions and a good agreement is found., Comment: submitted

The k-symplectic formulation of field theories is especially simple, since only tangent and cotangent bundles are needed in its description. Its defining elements show a close relationship with those in the symplectic formulation of mechanics. It will be shown that this relationship also stands in the presymplectic case. In a natural way, one can mimick the presymplectic constraint algorithm to obtain a constraint algorithm that can be applied to $k$-presymplectic field theory, and more particularly to the Lagrangian and Hamiltonian formulations of field theories defined by a singular Lagrangian, as well as to the unified Lagrangian-Hamiltonian formalism (Skinner--Rusk formalism) for k-presymplectic field theory. Two examples of application of the algorithm are also analyzed., Comment: 22 pp

A geometric framework for describing and solving time-dependent implicit differential equations F(t,x,x')=0 is studied, paying special attention to the linearly singular case, where F is affine in the velocities: A(t,x)x' = b(t,x). This framework is based on the jet bundle of a time-dependent configuration space, and is an extension of the geometric framework of the autonomous case. When A is a singular matrix, the solutions can be obtained by means of constraint algorithms, either directly or through an equivalent autonomous system that can be constructed using the vector hull functor of affine spaces. As applications, we consider the jet bundle description of time-dependent lagrangian systems and the Skinner-Rusk formulation of time-dependent mechanics., Comment: 20 pages

Lagrangian systems with nonholonomic constraints may be considered as singular differential equations defined by some constraints and some multipliers. The geometry, solutions, symmetries and constants of motion of such equations are studied within the framework of linearly singular differential equations. Some examples are given; in particular the well-known singular lagrangian of the relativistic particle, which with the nonholonomic constraint v^2=c^2 yields a regular system., Comment: 19 pages