Chirped-Standing-Wave Acceleration of Ions with Intense Lasers

We propose a novel mechanism for ion acceleration based on the guided motion of electrons from a thin layer. The electron motion is locked to the moving nodes of a standing wave formed by a chirped laser pulse reflected from a mirror behind the layer. This provides a stable longitudinal field of charge separation, thus giving rise to chirped-standing-wave acceleration of the residual ions of the layer. We demonstrate, both analytically and numerically, that stable proton beams, with energy spectra peaked around 100 MeV, are feasible for pulse energies at the level of 10 J. Moreover, a scaling law for higher laser intensities and layer densities is presented, indicating stable GeV-level energy gains of dense ion bunches, for soon-to-be-available laser intensities.

Figure 1

(a) CSWA target: a high-density mirror and a thin layer fixed in a certain position in front by a micron-thin mesh, leaving voids for the standing wave to form. (b) A chirped laser pulse impinges on the target. (c) A standing wave forms, locks, and displaces the thin layer’s electrons, which drag the layer’s ions. (d) Ions and electrons propagate away from the mirror.

Figure 2

A 2D PIC simulation for a laser energy ${ϵ}_0=30\mathrm{J}$, bandwidth $\mathrm{\Delta }{\omega }_0=0.5{\omega }_0$, and chirp $\mathcal{C}=-3.5$. (a)–(c) Transverse field $E_y$ (blue), electrons (green), and protons (red) as functions of 2D coordinates. (d)–(f) A 1D cut additionally showing the longitudinal field component $E_x$ (magenta) and particle distributions in phase space $x\text{−}{p}_x$. Three time instants are shown: before the layer starts transmitting the incident radiation [(a),(d)], during CSWA with a standing wave formed in the laser’s reflection [(b),(e)], or by a mode of radiation locked between the layer and the mirror [(c),(f)]. (j) Spectra of protons from the thin plasma layer (effectively 3D) at times $t_2$, $t_3$, and a later time $t_4$ propagating within a forward cone of 10° opening angle (red lines) or in an arbitrary direction at $t_4$ (black dashed line).

Figure 3

Maximum proton energy ${ϵ}_p$ (energy above which 1% of all protons lie) as a function of the pulse chirp $\mathcal{C}$ and the laser energy ${ϵ}_0$. All parameters are as in Fig. 2 except $\mathrm{\Delta }{\omega }_0=0.3{\omega }_0$. Black line: Optimum chirp from Eq. (9). White dashed lines and adjacent numbers: Maximum proton energy from Eq. (8) in MeV.