Tracing dynamics of laser-induced fields on ultrathin foils using complementary imaging with streak deflectometry

We present a detailed study of the electric and magnetic fields, which are created on plasma vacuum interfaces as a result of highly intense laser-matter interactions. For the field generation ultrathin polymer foils (30–50 nm) were irradiated with high intensity femtosecond (${10}^{19}–{10}^{20}\mathrm{W}/{\mathrm{cm}}^2$) and picosecond ($\sim {10}^{17}\mathrm{W}/{\mathrm{cm}}^2$) laser pulses with ultrahigh contrast (${10}^{10}–{10}^{11}$). To determine the temporal evolution and the spatial distribution of these fields the proton streak deflectometry method has been developed further and applied in two different imaging configurations. It enabled us to gather complementary information about the investigated field structure, in particular about the influence of different field components (parallel and normal to the target surface) and the impact of a moving ion front. The applied ultrahigh laser contrast significantly increased the reproducibility of the experiment and improved the accuracy of the imaging method. In order to explain the experimental observations, which were obtained by applying ultrashort laser pulses, two different analytical models have been studied in detail. Their ability to reproduce the streak deflectometry measurements was tested on the basis of three-dimensional particle simulations. A modification and combination of the two models allowed for an extensive and accurate reproduction of the experimental results in both imaging configurations. The controlled change of the laser pulse duration from 50 femtoseconds to 2.7 picoseconds led to a transition of the dominating force acting on the probing proton beam at the rear side of the polymer foil. In the picosecond case the $(\stackrel{\rightharpoonup }{v}x\stackrel{\rightharpoonup }{B})$-term of the Lorentz force dominated over the counteracting $\stackrel{\rightharpoonup }{E}$-field and was responsible for the direction of the net force. The applied proton deflectometry method allowed for an unambiguous determination of the magnetic field polarity at the rear side of the ultrathin foil.

Figure 1

Temporal pulse (a) shape and intensity distribution (b) (color coded, and marked area for determination of encircled energy content) used in experiments (example of laser probe beam).

Figure 2

Setup and imaging configurations: (a) longitudinal configuration, (b) transversal configuration.

Figure 3

Proton streak deflectometry measurements in transversal imaging configuration. The absolute x-position ($d_x$) of the polymer foil was changed in consecutive shots: (a) $d_x=-1854\mu \mathrm{m}$, (b) $d_x=-654\mu \mathrm{m}$, (c) $d_x=-254\mu \mathrm{m}$, (d) $d_x=545\mu \mathrm{m}$.

Figure 4

Measured proton spectra corresponding to the deflectograms of Fig. 3 [spectrum (a)] and Fig. 3 [spectrum (b)].

Figure 5

Successive shots while probing in longitudinal geometry and varying the ${\mathrm{x}}_F$ parameter. The probe timing ($t_{\mathrm{pump}}$) corresponds to the proton t-pump energies ${\epsilon }_{\mathrm{pump}}=2.4\mathrm{MeV}$ (a) and ${\epsilon }_{\mathrm{pump}}=2.6\mathrm{MeV}$ [(b) and (c)], respectively.

Figure 6

Measured deflectogram (a) in longitudinal probing geometry and model simulation (b) with an unrealistic high electron temperature of 13 MeV and other adapted parameters (model C variation without temporal development of the Debye length).

Figure 7

Spatial distribution of the normal electric field component $E_N(r=0,z,t)$ in the z-direction at different times (red: 0 ps, orange: 0.5 ps, green: 1 ps, light blue: 1.5 ps, dark blue: 2 ps. For the field calculations the parameters of Tables 1, 2 and 2 have been used: (a) model A, (b) model B, (c) model C.

Figure 8

Experimental [(a)–(c)] and simulated [(d)–(l)] streak deflections in longitudinal [(a), (d), (g), (j)] and transversal [(b), (c), (e), (f), (h), (i), (k), (l)] imaging configuration.

Figure 9

Comparison between long-pulse-induced (a) and short-pulse-induced (b) streak deflections.

Figure 10

Deflection of a single proton at the rear side of the polymer foil due to the influence of the $(\stackrel{\rightharpoonup }{v}x\stackrel{\rightharpoonup }{B})$-term of the Lorentz force.

Figure 11

Proton deflectogram: (a) experiment, (b) model calculation obtained for a ps-pulse irradiation of a 30 nm plastic foil in a longitudinal probing geometry, (c) calculated magnetic field accounting for the deflection.