Two-dimensional theory of Cherenkov radiation from short laser pulses in a magnetized plasma

The Cherenkov wakes excited by intense laser drivers in a perpendicularly magnetized plasma are a potential source of high-power terahertz radiation. We present a two-dimensional (2D) theory of the emission of magnetized wakes excited by a short laser pulse. The 2D model reveals the important role of the transverse size of the laser pulse missed in previous simple one-dimensional estimations of the radiation. We derived expressions for the radiated fields and for the angular/frequency distribution of the radiated energy. Beats in the radiation pattern behind the moving pulse are predicted and explained. For the interpretation of existing experimental results, the time dependence of the energy flux parallel and perpendicular to the laser path is examined.

Figure 1

Integration contour in the complex $s$ plane.

Figure 2

(Color online). Distribution of the magnetic field $B_y$ behind the laser driver [normalized to $\mid {\tilde{\Phi }}_0\left({\omega }_p\right)\mid \ell {\omega }_p^2{\omega }_c∕\left(\sqrt{\pi }{c}^2\right)$] for (a) ${\omega }_p\ell ∕c=0.3$ and (b) ${\omega }_p\ell ∕c=2.0$. For both cases, ${\omega }_c∕{\omega }_p=0.3$.

Figure 3

Graphical solution of Eq. (15). There are two roots ${\omega }_{1,2}$ for $\alpha <{\alpha }_0$; these roots merge together at ${\omega }_0$ for $\alpha ={\alpha }_0$. The dependence $c{g}^{\prime }\left(\omega \right)$ is plotted for ${\omega }_c∕{\omega }_p=0.3$.

Figure 4

(a) Spectral density of the radiated energy $w_{\omega }\left(\omega \right)$ [normalized to ${\mid {\tilde{\Phi }}_0\left({\omega }_p\right)\mid }^2{\ell }^2{\omega }_p^4∕\left(16\pi c^3\right)$] for ${\omega }_c∕{\omega }_p=0.3$ and ${\omega }_p\ell ∕c=1.0,0.5$ (values shown near corresponding curves). (b) Corresponding angular distribution $w_{\theta }\left(\theta \right)$ [normalized to ${\mid {\tilde{\Phi }}_0\left({\omega }_p\right)\mid }^2{\ell }^2{\omega }_p^5∕\left(16\pi c^3\right)$].

Figure 5

The energy $W_{\xi }$ [normalized to ${\mid {\tilde{\Phi }}_0\left({\omega }_p\right)\mid }^2{\ell }^2{\omega }_p^5∕\left(16\pi c^3\right)$] passed to the moment $\xi$ through the unit area placed at $x=15c∕{\omega }_p$ as a function of $\xi$ for: (a) ${\omega }_c∕{\omega }_p=0.3$ and ${\omega }_p\ell ∕c=2.0,1.0,0.5,0.3$ (values shown near corresponding curves); (b) ${\omega }_p\ell ∕c=0.5$ and ${\omega }_c∕{\omega }_p=0.1,0.15,0.2,0.3$ (values shown near corresponding curves).

Figure 6

The radial energy flux $S_x$ [normalized to ${\mid {\tilde{\Phi }}_0\left({\omega }_p\right)\mid }^2{\ell }^2{\omega }_p^6∕\left(16\pi c^3\right)$] at $x=15c∕{\omega }_p$ as a function of $\xi$ for ${\omega }_c∕{\omega }_p=0.5$ and ${\omega }_p\ell ∕c=0.5$.