Large-amplitude electromagnetic radiofrequency fields are created by the charge-separation induced in interactions of high-intensity, short-pulse lasers with solid targets and have intensity that decreases with the distance from the target. Alternatively, it was experimentally proved very recently that charged particles emitted by petawatt laser–target interactions can be deposited on a capacitor-collector structure, far away from the target, and lead to the rapid (nanosecond-scale) generation of large quasi-static electric fields ($\mathrm{MV}/\mathrm{m}$), over wide regions. We demonstrate here the generation of both these fields in experiments at the PHELIX laser facility, with approximately $20\;\mathrm{J}$ energy and approximately ${10}^{19}\;\mathrm{W}/\mathrm{c}{\mathrm{m}}^2$ intensity, for picoseconds laser pulses, interacting with pre-ionized polymer foams of near critical density. Quasi-static fields, up to tens of kV/m, were here observed at distances larger than $1\;\mathrm{m}$ from the target, with results much higher than the radiofrequency component. This is of primary importance for inertial-confinement fusion and laser–plasma acceleration and also for promising applications in different scenarios.

An analytical model for hole boring proton acceleration by a circularly-polarized CO₂ laser pulse in a gas jet is developed. The plasma density profile near the density peak is taken to be rectangular, with inner region thickness l around a laser wavelength and density 10% above the critical, while the outside density is 10% below the critical. On the rear side, plasma density falls off rapidly to a small value. The laser suffers strong reflection from the central region and, at normalized amplitude a₀≥1, creates a double layer. The space charge field of the double layer, moving with velocity v_fz^, reflects up-stream protons to 2v_f velocity, incurring momentum loss at a rate comparable to radiation pressure. Reflection occurs for v_f≤ω_p (z_flm/m_p)^-1/2 , where m and m_p are the electron and proton masses, z_f is the distance traveled by the compressed electron layer and ω_p is the plasma frequency. For Gaussian temporal profile of the laser and parabolic density profile of the upstream plasma, the proton energy distribution is narrowly peaked.