Hole Boring in a DT Pellet and Fast-Ion Ignition with Ultraintense Laser Pulses

Recently achieved high intensities of short laser pulses open new prospects in their application to hole boring in inhomogeneous overdense plasmas and for ignition in precompressed DT fusion targets. A simple analytical model and numerical simulations demonstrate that pulses with intensities exceeding ${10}^{22}\mathrm{W}/{\mathrm{cm}}^2$ may penetrate deeply into the plasma as a result of efficient ponderomotive acceleration of ions in the forward direction. The penetration depth as big as hundreds of microns depends on the laser fluence, which has to exceed a few tens of $\mathrm{GJ}/{\mathrm{cm}}^2$. The fast ions, accelerated at the bottom of the channel with an efficiency of more than 20%, show a high directionality and may heat the precompressed target core to fusion conditions.

Figure 1

Schematic structure of the piston and the electrostatic shock maintained by the radiation pressure. The frame is moving with the piston velocity. Curves: laser intensity, blue; electron density, green; electrostatic field, black; ion density, red.

Figure 2

(a) Piston velocity as a function of plasma density for a circularly polarized laser pulse. Each curve corresponds to the value of dimensionless vector potential $a=(I/m_e{n}_c{c}^3{)}^{1/2}$, shown in the legend. (b) Density dependence of time $T_p$ required for the laser pulse to traverse a plasma layer with an exponential density profile with $L=20\mu \mathrm{m}$, $n_{i\min }=n_c$, and $n_{i\max }=100n_c$. The color of curves corresponds to the same field amplitudes as in (a). (c) Ion energy as a function of plasma density for several values of $a$. (d) Stopping range of ions with energies shown in (c) for the same density values. The dashed line represents the maximum areal density of the fusion pellet to be heated by ions.

Figure 3

Interaction of a circularly polarized laser pulse of intensity $4\times {10}^{22}\mathrm{W}/{\mathrm{cm}}^2$ with plasma having an exponential profile. Momentum distribution $p_x(x)$ for (a) electrons and (b) ions at instant $t=30\lambda /c$. (c) Ion energy and (d) momentum distributions at the final instant $T_b=250\lambda /c$. The thin continuous line represents the analytical distribution function, Eq. (5). Simulation parameters are given in the text.

Figure 4

Channel formation in plasma and ion acceleration in the laser piston regime. Ion density distribution at instants (a) $90\lambda /c$ and (b) $190\lambda /c$. (c) Angular energy distribution and (d) the energy distribution of accelerated ions in the domain $|y|\le 10\lambda$. Simulation parameters are the same as in Fig. 3.