Coulomb-Driven Energy Boost of Heavy Ions for Laser-Plasma Acceleration

An unprecedented increase of kinetic energy of laser accelerated heavy ions is demonstrated. Ultrathin gold foils have been irradiated by an ultrashort laser pulse at a peak intensity of $8\times 10^{19}\mathrm{W}/{\mathrm{cm}}^2$. Highly charged gold ions with kinetic energies up to $>200\mathrm{MeV}$ and a bandwidth limited energy distribution have been reached by using 1.3 J laser energy on target. 1D and 2D particle in cell simulations show how a spatial dependence on the ion’s ionization leads to an enhancement of the accelerating electrical field. Our theoretical model considers a spatial distribution of the ionization inside the thin target, leading to a field enhancement for the heavy ions by Coulomb explosion. It is capable of explaining the energy boost of highly charged ions, enabling a higher efficiency for the laser-driven heavy ion acceleration.

Figure 1

Raw spectra from Thomson spectrometer (single shot measurement), particle density in false color coding. Each trace represents a different charge-to-mass ratio $Z/m$. Gray shade indicates end of detector. Light ion traces (${\mathrm{H}}^{+}$, ${\mathrm{C}}^{6+}–{\mathrm{C}}^{3+}$, ${\mathrm{O}}^{8+}–{\mathrm{O}}^{5+}$) are identified. Overlay shows theoretical parabolas at different charge states of gold ions (black dots). Straight lines mark theoretical constant energy at each degree of ionization for gold, $m=197\mathrm{u}$.

Figure 2

Maximum (black) and minimum (green) kinetic energy of gold ions in dependence of their charge state $Z$. For $Z<25$, the detector’s range is cutting the low energetic part of the spectra. Red line shows a $(Z-6{)}^{2.7}$ and black line a $Z^2$ to $E_{\mathrm{kin}}^{\max }$, both fit functions with the same scaling coefficient.

Figure 3

(a) The associated evaluated energy distribution for selected, single traces of gold ions of Figs. 1 and 2 is shown, exhibiting a pronounced maximum. $dE$ is given by the binning of the spectrometer’s resolution. (b) STEM measurement of freestanding target foil reveals a cracklike structure. Dark cracks mark here the carbon substrate layer.

Figure 4

(a) The dependence of gold ionization on the electric field $E_L$ in units of $a_0$ calculated with the Ammasov-Delone-Krainov model. The dashed line (red) fits $Z(a_0)=23\times a_0^{0.4}$. (b) $E_L$ calculated from the analytical model (red line) and PIC simulation (green dotted line) considering ion layers of the following degrees of ionization: the distribution of ion charge is 0–1 nm $Z=42$, 1–2 nm $Z=33$, 2–18 nm $Z=15$, 18–19 nm $Z=33$, 19–20 nm $Z=42$. Black line, $E_L$ calculated with an averaged ionization degree of $Z=15$.

Figure 5

The dependence of maximal ion energy on its ionization degree: the experimental data of Fig. 2 are deep blue squares, 2D PIC-simulation data are red squares, the Schreiber model is the black line, and our model is the red line. The distribution of ion ionization is according to the 1D PIC simulation in Fig. 4.