Interaction of Superintense Laser Pulses with Relativistic Ions

At high intensities, three-step recollision processes driven by low frequency laser pulses, such as high-order harmonic generation and high-order above-threshold ionization, are normally severely suppressed by the magnetic-field component of the laser field. It is shown that this suppression is not severe, even for ponderomotive energies well above 10 keV, for multicharged ions moving at a sufficiently high relativistic velocity against a counterpropagating infrared laser pulse. Numerical results are presented for high-order harmonic emission by a single ${\mathrm{N}\mathrm{e}}^{9+}$ ion moving with a Lorentz factor $\gamma =15$ against a Nd:glass laser beam. The calculations are done within a Coulomb-corrected nondipole strong field approximation. The approximation is tested by comparing with accurate results.

Figure 1

The magnitude squared of the Fourier transform of the dipole moment as a function of the harmonic order, for a ${\mathrm{H}\mathrm{e}}^{+}$ ion exposed to a 2-cycle laser pulse of 800 nm wavelength and ${10}^{16}\mathrm{W}{\mathrm{c}\mathrm{m}}^{-2}$ peak intensity. Nondipole effects are negligible here. The vector potential is $\mathbf{A}(t)=\widehat{ϵ}(F_L/{\omega }_L){sin}^2({\omega }_{L}t/4)\sin ({\omega }_{L}t+\phi )$, where $\widehat{ϵ}$ is the polarization vector and the carrier phase $\phi =0$. The adiabatic approximation is not made. Solid lines: the predictions of the SFA, with (upper curves) and without (lower curves) the Coulomb corrections in the ionization and recombination amplitudes. For clarity, the results with Coulomb corrections are shifted upwards by a factor 1000. Circles: the spectrum resulting from a fully numerical solution of the time-dependent Schrödinger equation, and a copy of this spectrum shifted upwards by a factor 1000.

Figure 2

The rate of emission of harmonic photons in the direction of propagation of the driving laser pulse, ${\Omega }^3|d_{ϵ}(\Omega ){|}^2/(2\pi c^3)$, as a function of the photon energy for (a) a ${\mathrm{N}\mathrm{e}}^{9+}$ ion moving at $\gamma =15$ in the laboratory frame, and (b) an ${\mathrm{A}\mathrm{r}}^{7+}$ ion at rest, as obtained within the Coulomb-corrected SFA. The rate and the photon energy are given in the ion's rest frame. For each ion, the upper curve shows the results obtained within the dipole approximation and the lower curve the results obtained without making this approximation. The laser field is monochromatic and linearly polarized. In the laboratory frame, the intensity is ${10}^{17}\mathrm{W}{\mathrm{c}\mathrm{m}}^{-2}$ and the wavelength is 1053.7 nm.

Figure 3

The ratio $w({\pi }_k)/w(0)$, indicative of the importance of the magnetic-drift induced suppression of recollision, for ions exposed to an intense 1053.7 nm laser pulse. Dashed line: ions at rest. Solid lines: ions moving at a Lorentz factor of 5, 15, or 30.