Achieving Stable Radiation Pressure Acceleration of Heavy Ions via Successive Electron Replenishment from Ionization of a High-$Z$ Material Coating

A method to achieve stable radiation pressure acceleration (RPA) of heavy ions from laser-irradiated ultrathin foils is proposed, where a high-$Z$ material coating in front is used. The coated high-$Z$ material, acting as a moving electron repository, continuously replenishes the accelerating heavy ion foil with comoving electrons in the light-sail acceleration stage due to its successive ionization under laser fields with Gaussian temporal profile. As a result, the detrimental effects such as foil deformation and electron loss induced by the Rayleigh-Taylor-like and other instabilities in RPA are significantly offset and suppressed so that stable acceleration of heavy ions are maintained. Particle-in-cell simulations show that a monoenergetic ${\mathrm{Al}}^{13+}$ beam with peak energy 3.8 GeV and particle number $10^{10}$ (charge $>20\mathrm{nC}$) can be obtained at intensity $10^{22}\mathrm{W}/{\mathrm{cm}}^2$.

Figure 1

The growths of the RT instability (blue) [Eq. (2)] and Coulomb explosion (red) [Eq. (3)] with time $t$ for protons (dashed curve) and ${\mathrm{Al}}^{13+}$ ions (solid curve), respectively, where a flat-top laser of $a=316$ is assumed to irradiate $1.0\mu \mathrm{m}$ proton and ${\mathrm{Al}}^{13+}$ foils with the same electron density $n_e=50n_c$. It shows that, to achieve the same energy/nucleon at $\gamma =2$, the acceleration time for ${\mathrm{Al}}^{13+}$ is twice as long and the instability growth is about three times larger than for protons.

Figure 2

Schematic of stable heavy ion RPA via successive electron replenishment from ionization of a high-$Z$ coating. (a) Laser fields ionize Au and Al, expelling Au electrons into Al. (b) The successive ionized electrons from the Au coating catch up and comove with the accelerating Al foil, keeping a negative gradient electric field for stable RPA.

Figure 3

Electron density $\ln (n_e/n_c)$ (a)–(c), Au ion density $\ln (n_{\mathrm{Au}}/n_c)$ (d)–(f), Al ion density $\ln (n_{\mathrm{Al}}/n_c)$ (g)–(i) at $t=4$, 13 and $19T_0$ in the acceleration of an Al foil by laser at $I_0=10^{22}\mathrm{W}/{\mathrm{cm}}^2$, where a 2 nm Au coating is used. The Al ion density for the cases without ionization effect (j)–(l) and without the Au coating (m)–(o) are also plotted. Insets show zoomed density maps in the dotted-dashed boxes, which indicates the seriousness of the RT instability.

Figure 4

The longitudinal profiles of electron density $n_e/n_c$ and electric field $E_x$ (green line) at $t=13T_0$ with (a) and without (b) ionization in simulation of Fig. 3. In (a), the cyan, red, magenta, and blue lines represent the initial electrons from Al ions, the ionized electrons from Al, the initial electrons from Au, and the ionized electrons from Au, respectively, while the black line shows the sum of all electrons. In (b), the cyan and magenta lines correspond to the electrons from Al and Au, respectively, and the black line shows their sum. (c) and (d) Laser intensity distributions with and without ionization. (e) The energy spectra of ${\mathrm{Al}}^{13+}$ within $|y|<2\mu \mathrm{m}$ by our scheme (red), without ionization (blue), and without Au coating (green) at $t=20T_0$. The magenta line corresponds to Au ions, but with $dN/d{E}_k$ multiplied by 5 times. (f) The total energy of the ${\mathrm{Al}}^{13+}$ beam increasing with time for the 2D (blue star) and 3D (red triangle) simulations. Inset of (e) shows the ${\mathrm{Al}}^{13+}$ spectra for the cases of, respectively, with (red line) and without (green line) Au coating by using a Gaussian and elliptically polarized laser pulse with ellipticity $|E_y|/|E_z|=0.8$, where other parameters are the same as here.

Figure 5

3D PIC simulation results: the ${\mathrm{Al}}^{13+}$ density isosurface for $n=3n_c$ with (a) and without (b) the ionization effect at $t=20T_0$. (c) The corresponding energy spectra of ${\mathrm{Al}}^{13+}$ within $r<2\mu \mathrm{m}$ with (red curve) and without (blue curve) the ionization effect.