Mode conversion and laser energy absorption by plasma under an inhomogeneous external magnetic field

The interaction of a high-frequency laser with plasma in the presence of an inhomogeneous external magnetic field has been studied here with the help of particle-in-cell simulations. It has been shown that the laser enters the plasma as an extraordinary wave (X-wave), where the electric field of the wave oscillates perpendicular to both the external magnetic field and propagation direction and as it travels through the plasma, its dispersion property changes due to the inhomogeneity of the externally applied magnetic field. Our study shows that the X-wave's electromagnetic energy is converted to an electrostatic mode as it encounters the upper-hybrid (UH) resonance layer. In the later stage of the evolution, this electrostatic wave breaks and converts its energy to electron kinetic energy. Our study reveals two additional processes involved in decay of the electrostatic mode at the UH resonance layer. We have shown that the energy of the electrostatic mode at the upper-hybrid resonance layer also converts to a low-frequency lower-hybrid mode and high-frequency electromagnetic harmonic radiations. The dependence of energy conversion processes on the gradient of the external magnetic field has also been studied and analyzed.

Figure 1

(a) The simulation setup and a summary of the physical processes observed in our study have been illustrated by this schematic. We have performed 1D PIC simulation with a laser pulse being incident from the left side of the simulation box on the vacuum-plasma interface at $x=100$. The polarization of the incident laser was considered to be in the X-mode configuration, i.e., ${\vec{E}}_l\perp {\vec{B}}_0$. Here $t_0, t_1, t_2$, and $t_3$ represent different times (in ascending order) of the simulation run. (b) The external magnetic field and corresponding upper hybrid frequency ${\omega }_{\mathrm{uh}}=\sqrt{{\omega }_{\mathrm{pe}}^2+{\omega }_{\mathrm{ce}}^2}$ have been shown as a function of $x$. Here ${\omega }_{\mathrm{pe}}$ and ${\omega }_{\mathrm{ce}}$ represent electron plasma frequency and electron cyclotron frequency, respectively. The green dotted vertical line in panel (b) represents the location at which upper-hybrid resonance (${\omega }_l={\omega }_{\mathrm{uh}}$) occurs.

Figure 2

The $\widehat{y}$ and $\widehat{x}$ components of electric field ${\tilde{E}}_y$ and ${\tilde{E}}_x$ with respect to $x$ have been shown at different times of the simulation runs in panels (a) and (b), respectively. Here the $x$ locations of the fields at different times of the simulation run ($t=500$ to 2500) have been shown by the different colors. The structure highlighted by the green dotted box represent higher harmonics.

Figure 3

The variation of (a) electromagnetic field (EMF) energy, (b) energy associated with the longitudinal component of the electric field $E_x^2/2$, and (c) kinetic energy of electron with space and time have been illustrated in panels (a), (b), and (c), respectively.

Figure 4

The absolute amplitudes of Fourier spectra obtained from time-series data of ${\tilde{E}}_y$ and ${\tilde{E}}_x$ at different $x$ locations have been shown in panels (a) and (b), respectively. It is to be noted that these Fourier spectra have been evaluated at different time durations up to $t=3500$. The absolute amplitudes of Fourier spectra obtained from the space distributions of ${\tilde{E}}_y$ and ${\tilde{E}}_x$ at different times of the simulation run have been elucidated by various colored lines in panels (c) and (d), respectively.

Figure 5

The zoomed view of $\widehat{y}$ and $\widehat{x}$ components of electric field $E_y$ and $E_x$ have been shown as function of $x$ for different instants of time in the later phase of the simulation run.

Figure 6

In (a)–(d), the variation of electron density with $x$ have been shown at different instants of time. Panels (e)–(h) illustrate the same for ion density.

Figure 7

The absolute amplitudes of Fourier spectra obtained from the space distribution of longitudinal electric field $E_x$ at (a) $t=2500$, (b) $t=3500$, and (c) $t=4500$ have been shown.

Figure 8

(a) Electron counts as a function of kinetic energy at three different instants of time of the simulation run have been shown. (b) The time variation of spatially averaged field energy densities have been shown. Here red, yellow, blue, and green colored lines represent kinetic energies of electrons and ions, energy density associated with the longitudinal electric field, and energy density associated with the transverse components of electromagnetic fields, respectively.

Figure 9

The space variation of $\widehat{y}$ component of electric field has been shown at different times in the later stage of the simulation run in panel (a). The absolute amplitudes of Fourier spectra obtained from the time-series data of $E_y$ at the locations $x=1000$ and $x=1800$ for time durations $t=(2500\text{−}3000$) (red), and $t=(4000\text{−}5000$) (blue) have been shown in panels (b1) and (b2), respectively.

Figure 10

(a) The four different external magnetic field profiles considered in our simulations have been shown. (b) The variation of electron kinetic energy with time has been demonstrated for these four different external magnetic field ($B_0$) profiles. (c) The decaying parts of the electron kinetic energy for each case have been shown along with the linearly fitted lines.

Figure 11

The variation of ion kinetic energy with time has been shown in panel (a) for four different externally applied magnetic field ($B_0$) profiles. In the panel (b), we have shown the time evolution of spatially averaged energy densities associated with the transverse components of electromagnetic fields, i.e., $E_y^2/2+B_z^2/2$ for these profiles of $B_0$. In panel (c) and panel (b) inset, transverse EMF energy has been shown in zoomed scale.