Anisotropic electron-distribution function in inverse-bremsstrahlung-heated plasmas

The electron-distribution function in homogeneous plasmas heated by a high-frequency laser field is calculated in velocity space from the Vlasov-Landau equation. The kinetic model is valid for moderate laser intensity defined by the relevant parameter $\alpha =v_0^2/v_t^2<0.5$ where $v_0$ and $v_t$ are the peak velocity of oscillation in the high-frequency electric field and the thermal velocity, respectively. The results obtained constitute an improvement of the results reported in the literature devoted to weak electric field intensities. The electron-distribution function is calculated solving the kinetic equation with the use of the Legendre polynomial expansion within the laser field dipole approximation. It results in an infinite set of equations for the isotropic component $f_0\left(v\right)$ and the anisotropic components $f_{n\ge 1}\left(v\right)$ that we have solved numerically with appropriate truncation. For the second anisotropy $f_2\left(v\right)$, we found that its maximum increases from the weak electric field intensity $\left(\alpha <0.01\right)$ to a moderate one $\left(\alpha =0.5\right)$ by a factor $f_{2max}\left(\alpha =0.5\right)/f_{2max}\left(\alpha =0.01\right)\approx 48$. Applications to the radiation pressure, electromagnetic instabilities, and photoabsorption are also considered.

Figure 1

Second anisotropy $f_2\left(y\right)$ as a function of the normalized square velocity $y=v^2/2v_t^2$ for $\alpha ={10}^{-6},{10}^{-4},{10}^{-2},0.1$, and $0.5$. The dashed curve corresponds to the analytic expression (26).

Figure 2

Second anisotropy $f_2\left(y\right)$ for $\alpha ={10}^{-4},{10}^{-2},0.3$, and $0.5$ as a function of $y=v^2/2v_t^2$. The simulation is performed with the numerical fit (22) for the solid lines and a Maxwellian for the dashed lines.

Figure 3

Second anisotropy (solid line) and higher anisotropies $f_4\left(y\right)$ (dashed line) and $f_6\left(y\right)$ (dotted line) as a function of $y=v^2/2v_t^2$ for $\alpha =0.5$.

Figure 4

Moments $M_2^{3/2}$ calculated with the numerical fit (22) (solid line) and a Maxwellian (dotted line) as a function of $\alpha$. The dashed line corresponds to the moment $M_4^{5/2}$.

Figure 5

Normalized conductivity $\sigma /\left[\frac{n_e{e}^2{\hslash }^2}{m_e{T}^2}\frac{n_e}{Z{v}_t^3}{\left(\frac{Z{e}^2}{4\pi {\varepsilon }_0{m}_e}\right)}^2\right]$ as a function of $\mathrm{\Omega }=\frac{\hslash \omega }{T}$ for $\alpha \ll 1$ (dashed line) corresponding to the thermal equilibrium and $\alpha =0.5$ (solid line).

Figure 6

Coefficient $C_1\left(v\right)=-\frac{\partial f_0}{\partial v}-\frac{2}{5v^3}\frac{\partial }{\partial v}\left(v^3{f}_2\right)$ (dashed line) and $C_2\left(v\right)=-\frac{\partial f_0}{\partial v}$ (solid line) as a function of $y=v^2/2v_t^2$ for various values of $\alpha$.