Time-dependent electron-ion collision frequency at arbitrary laser intensity-temperature ratio

Abstract

In superintense laser beams collisional absorption exhibits a large amplitude modulation over a laser cycle. In this paper formulas for the time-dependent electron-ion collision frequency nu(ei)(t) are presented. On the basis of a ballistic interaction model we deduce an expression for nu(ei)(t) which holds for an arbitrary isotropic distribution function and arbitrary anharmonic oscillatory electron motion [Eq. (4)]. For a Maxwellian we present compact formulas for the various ratios v(os)(t)/v(th). It is shown that the strong time dependence over one laser cycle leads to the generation of intense odd harmonics. The cycle-averaged collision frequency nu(ei);(t) is compared with expressions derived from the more complex dielectric model. It is shown that the correct choice of cutoffs as a consequence of dynamical screening is essential.

Enhanced inverse bremsstrahlung heating rates in a strong laser field

“…We will identify them as the impact approximation [3,6], or the ballistic model [10]. From the conservation of energy for such collisions, one finds that the change in the average electron kinetic energy, which is related to the electron drift velocity, is proportional to the change in the electron momentum.…”

“…Several classical models of the effective collision frequency have been derived from explicit treatment of the dynamics of electron-ion scattering assuming instantaneous and elastic interactions [3,6,10]. We will identify them as the impact approximation [3,6], or the ballistic model [10].…”

“…depends on the full electron velocity v = v 0 + v E cos φ [10,25] and ρ max = v/ω and ρ min = max{2Ze 2 /mv 2 ,h/mv} are the classical cut-offs at large and small impact parameters. According to Eq.…”

“…Advances in laser technology, particularly those related to the generation of ultra-short laser pulses and progress in inertial confinement fusion studies have challenged our understanding of scattering processes over a wide range of conditions and plasma parameters. Nonetheless, heating rate calculations [1,2,3,4,5,6,7,8,9,10] in strong laser fields have involved simplifications that are equivalent to a Born approximation for electron trajectories in the Coulomb fields. This approximation, although well-accepted in the physics community, should be revisited in view of recently discovered nonlinear processes such as harmonic generation and above threshold ionization [11,12,13] that have been explained as being due to strong modifications of electron orbits in the laser field during electronion scattering events.…”

“…For the purpose of making comparisons, seminal works by Dawson and Oberman [1] and Silin [2] and numerous subsequent publications on high field effects [3,4,5,6,7,8,9,10] are classified into several broad categories: classical-mechanical analysis of binary electron-ion collisions in the dielectric approximation [1,7,8,9]; kinetic theory which uses the Landau-type collision integral in the oscillating electron field [2]; ballistic model (or the model of instantaneous electron-ion collision) [3,6,10]; "first principle" quantum-mechanical calculations [3,4]; and, more recently, the quantum kinetic theory in the dielectric approximation [5]. All theories consider the two body scattering problem as a starting point and their predictions lead to remarkably similar expressions which may differ only by a logarithmic factor.…”