Electron and nuclear dynamics of molecular clusters in ultraintense laser fields. III. Coulomb explosion of deuterium clusters
Authors: Last Isidore , Jortner Joshua 
Published: July 2004

In this paper we present a theoretical and computational study of the energetics and temporal dynamics of Coulomb explosion of molecular clusters of deuterium (D2)n/2 (n=480−7.6×104, cluster radius R0=13.1–70 Å) in ultraintense laser fields (laser peak intensity I=1015–1020W cm−2). The energetics of Coulomb explosion was inferred from the dependence of the maximal energy EM and the average energy Eav of the product D+ ions on the laser intensity, the laser pulse shape, the cluster radius, and the laser frequency. Electron dynamics of outer cluster ionization and nuclear dynamics of Coulomb explosion were investigated by molecular dynamics simulations. Several distinct laser pulse shape envelopes, involving a rectangular field, a Gaussian field, and a truncated Gaussian field, were employed to determine the validity range of the cluster vertical ionization (CVI) approximation. The CVI predicts that Eav, EM∝R02 and that the energy distribution is P(E)∝E1/2. For a rectangular laser pulse the CVI conditions are satisfied when complete outer ionization is obtained, with the outer ionization time toi being shorter than both the pulse width and the cluster radius doubling time τ2. By increasing toi, due to the increase of R0 or the decrease of I, we have shown that the deviation of Eav from the corresponding CVI value (EavCVI) is (EavCVI−Eav)/EavCVI≃(toi/2.91τ2)2. The Gaussian pulses trigger outer ionization induced by adiabatic following of the laser field and of the cluster size, providing a pseudo-CVI behavior at sufficiently large laser fields. The energetics manifest the existence of a finite range of CVI size dependence, with the validity range for the applicability of the CVI being R0⩽(R0)I, with (R0)I representing an intensity dependent boundary radius. Relating electron dynamics of outer ionization to nuclear dynamics for Coulomb explosion induced by a Gaussian pulse, the boundary radius (R0)I and the corresponding ion average energy (Eav)I were inferred from simulations and described in terms of an electrostatic model. Two independent estimates of (R0)I, which involve the cluster size where the CVI relation breaks down and the cluster size for the attainment of complete outer ionization, are in good agreement with each other, as well as with the electrostatic model for cluster barrier suppression. The relation (Eav)I∝(R0)I2 provides the validity range of the pseudo-CVI domain for the cluster sizes and laser intensities, where the energetics of D+ ions produced by Coulomb explosion of (D)n clusters is optimized. The currently available experimental data [Madison et al., Phys. Plasmas 11, 1 (2004)] for the energetics of Coulomb explosion of (D)n clusters (Eav=5–7 keV at I=2×1018 W cm−2), together with our simulation data, lead to the estimates of R0=51–60 Å, which exceed the experimental estimate of R0=45 Å. The predicted anisotropy of the D+ ion energies in the Coulomb explosion at I=1018 W cm−2 is in accord with experiment. We also explored the laser frequency dependence of the energetics of Coulomb explosion in the range ν=0.1–2.1 fs−1 (λ=3000–140 nm), which can be rationalized in terms of the electrostatic model.