Effects of laser polarizations on shock generation and shock ion acceleration in overdense plasmas

The effects of laser-pulse polarization on the generation of an electrostatic shock in an overdense plasma were investigated using particle-in-cell simulations. We found, from one-dimensional simulations, that total and average energies of reflected ions from a circular polarization- (CP) driven shock front are a few times higher than those from a linear polarization- (LP) driven one for a given pulse energy. Moreover, it was discovered that the pulse transmittance is the single dominant factor for determining the CP-shock formation, while the LP shock is affected by the plasma scale length as well as the transmittance. In two-dimensional simulations, it is observed that the transverse instability, such as Weibel-like instability, can be suppressed more efficiently by CP pulses.

Figure 1

Schematic figure of the system. Initial plasma density has a linear ramp rising over 10 $\mu \mathrm{m}$ in the front and an exponentially falling profile with scale length $L$ in the rear. When an ultrashort laser pulse propagates, the plasma density is compressed and some portion of the pulse energy penetrates through the compressed layer by relativistic transparency. The compressed density layer (shock) moves through the plasma even in the absence of a driving laser pulse, reflecting upstream ions with twice the velocity of the density layer, i.e., $\sim 2v_{\mathrm{sh}}$.

Figure 2

Number ($N$) and average ($\sum \gamma m{c}^2/N$) energy of reflected ions from the shock for (a) an LP pulse and (b) a CP pulse. The rear scale length is $\mathrm{L}=15\mu \mathrm{m}$ and the laser amplitude is $a_0=20$. (c) Ratio of the peak density of the compressed layer ($n_{\mathrm{peak}}$) to the peak initial density $n_0$ measured after 80 fs from the time when the entire laser pulse passes through the position of the peak initial density ($x=42 \mu \mathrm{m}$), corresponding to around 424 fs for LP and 322 fs for CP. The data were averaged over a 16-fs time interval. (d) Time evolution of the total energy ($\sum \gamma m{c}^2$) of reflected ions. (e) Time-averaged Mach number over a 16-fs interval around 833 fs, which is the time when the laser-plasma interaction ends. (f) Upstream temperature at 2–3 $\mu \mathrm{m}$ (order of Debye length) away from the compressed density layer, measured at the same time as the Mach number measurement. Error bars represent the standard deviation of the time average. The larger error cap corresponds to the LP data.

Figure 3

Phase and density illustration when an LP pulse with $a_0=20$ impinges on (a) $n_0=3n_c$, (b) $n_0=8n_c$, and (c) $n_0=10n_c$ plasmas and a CP pulse with same intensity impinges on (d) $n_0=1n_c$, (e) $n_0=2n_c$, and (f) $n_0=8n_c$ plasmas. $\mathrm{L}=15\mu \mathrm{m}$ for all cases.

Figure 4

Regime of shock formation and reflectance contour lines drawn on planes of $n_0$ and $a_0$ for different $L$'s. Shock or no-shock by [(a)–(c)] an LP pulse and [(d)–(f)] by a CP pulse is determined at the same time as in Fig. 3.

Figure 5

Distribution of magnetic field $B_z$ and ion density $n_i$ at $t=333$ fs when [(a) and (c)] an LP pulse impinges on $n_0=8n_c$ plasmas and [(b) and (d)] a CP pulse impinges on $n_0=8n_c$ plasmas. Magnetic field intensity and ion density were normalized.

Figure 6

Phase space of ions at $t=800$ fs for (a) an LP pulse and (b) a CP pulse.