Unified Model for the Free-Electron Avalanche in Laser-Irradiated Dielectrics

We develop a model describing the free-electron generation in transparent solids under high-intensity laser irradiation. The multiple rate equation model unifies key points of detailed kinetic approaches and simple rate equations to a widely applicable description, valid on a broad range of time scales. It follows the nonstationary energy distribution of electrons on ultrashort time scales as well as the transition to the asymptotic avalanche regime for longer irradiations. The role of photoionization and impact ionization is clarified in dependence on laser pulse duration and intensity.

Figure 1

Illustration of the processes providing changes in the density and the energy, respectively, of free electrons in the conduction band of a dielectric.

Figure 2

Temporal evolution of the fraction of high-energy electrons $\tilde{\alpha }{n}_k/n_{\mathrm{ges}}$ for different laser field amplitudes calculated by the MRE (2) (solid lines). The asymptotical values coincide with the avalanche coefficient ${\alpha }_{\mathrm{asymp}}$ from Eq. (7). For times up to the range of $t_{\mathrm{MRE}}$ the fraction of high-energy electrons strongly changes in time. The dashed line shows the normalized fraction of high-energy electrons calculated with the full kinetic approach from Ref. 6 for $E_L=50\mathrm{MV}\mathrm{/}\mathrm{cm}$.

Figure 3

Contribution of impact ionization to the total free electron density generated by a 300 fs FWHM Gaussian laser pulse with a maximum electric field of $E_{L,0}=70\mathrm{MV}\mathrm{/}\mathrm{cm}$. Curve 1 was calculated with the MRE (2), curve 2 is the result of the full kinetic approach from Ref. 6, curve 3 was calculated with the standard rate Eq. (1) using $\alpha (E_L)={\alpha }_{\mathrm{asymp}}$ according to Eq. (7), and curve 4 is the result of Eq. (1) with a common estimation for the avalanche parameter, ${\alpha }_{\mathrm{est}}=W_{\mathrm{1}\mathrm{pt}}\hslash {\omega }_L/{\epsilon }_{\mathrm{crit}}$.