Long lasting plasma density structures utilizing tailored density profiles

Abstract

Using fully kinetic Particle In Cell simulations, we investigate the stability and performance of autoresonant plasma beat wave excitation in plasmas with tailored density profiles. We show that a prescribed spatial variation of the background density sustains continuous phase locking between the driving laser beat and the excited plasma mode, thereby enabling precise control of the plasma wave packet shape and group velocity and providing an alternative to frequency chirping of the drive lasers. The density gradient scale is found to govern the nonlinear autoresonant growth, and the attainable saturation amplitude can exceed the classical Rosenbluth Liu prediction and, for appropriate laser intensities, approach the nonrelativistic wave breaking limit. We show that a four laser configuration in a steep parabolic density profile can generate a specially confined two phase quasiperiodic plasma lattice. The generation of such structures may lead to novel applications in plasma photonics.

Figures (10)

• Figure 1: Top panels: The spatial profile of the plasma wave at different times, for the linearly increasing plasma density profile. Solid black curves correspond to the amplitude prediction Eq. (\ref{['el']}), and the dotted black line indicates the RL limit at the reference point. Bottom panels: The spatio-temporal evolution of the phase difference between the three interacting waves: $\Phi(x)=\phi_1(x)-\phi_2(x)-\phi_L(x)$, with $\phi_{1}$, $\phi_{2}$ and $\phi_{L}$ representing the complex phase of the laser beams and the plasma wave, respectively. Here, the solid black curves mark the location of the highest plasma wave amplitude. The density gradient length is increased between the panels from left to right: $L=180\pi$, $L=360\pi$, and $L=720\pi$. The simulations use the normalized laser amplitude $a_1=a_2=0.1$ and the reference plasma density $n_{\rm re}(x_{\rm re})=0.0004n_{\rm cr}$.
• Figure 2: Top panels: The maximum value of $E_L/E_0$ over the simulation domain as a function of time for a wide range of gradient lengths (see legend in (a)); The horizontal black dotted represents the RL limit at the reference point $x_{\rm re}$. Bottom panels: Dephasing length $L_{\rm dep}$ as a function of density gradient length. The laser amplitude for (a) and (c) is $a_{1,2}$=0.1 and for (b) and (d) $a_{1,2}$=0.2. The inserts in panel (c) show the spatio-temporal evolution of the phase difference $\Phi(x)$ at a fixed gradient length $L_{\rm gra}=1440\pi$, for intensities $a_{1,2}=0.1$ and $a_{1,2}=0.2$; these cases are indicated by the open black circles in panel (c) and (d). The reference density is $n_{\rm re}(x_{\rm re})=0.0004n_{\rm cr}$. The green lines in panel (c) and (d) are predictions using Eq. (\ref{['linear dephase1']}).
• Figure 3: The relation between $n_e|_{\rm sa}/n_{\rm re}$ and the electric field $E_{\rm L,sa}/E_0$ at the end of autoresonance, shown by the blue curve. The two points indicate representative cases with laser field amplitudes $a = 0.1$ (left) and $a = 0.2$ (right).
• Figure 4: Autoresonant plasma wave excitation in a linearly increasing plasma density profile. The saturated plasma wave amplitude (a) and the dephasing length in (b) are shown as functions of the density gradient length and laser amplitude, for the reference plasma density $n_{\rm re}(x_{\rm re})=0.0004n_{\rm cr}$.
• Figure 5: Saturated plasma wave amplitude $E_{\rm L,sa}/E_0$ (left axis) as a function of laser amplitude $a$ for the linear density profiles with $L_{\rm gra} = 360\pi$ (solid red squares) and $L_{\rm gra} = 720\pi$ (solid blue diamonds); The solid black curve shows the RL limit, while the dashed black curve shows the data-driven estimate from Eq. \ref{['linear intensity']}. Corresponding dephasing lengths $L_{\rm dep}$ (right axis) are plotted using open symbols for both cases. The dashed red and blue curves indicate the analytical predictions from Eq. \ref{['linear dephase1']}.