Optimized $K\alpha$ x-ray flashes from femtosecond-laser-irradiated foils

We investigate the generation of ultrashort $K\alpha$ pulses from plasmas produced by intense femtosecond $p$-polarized laser pulses on Copper and Titanium targets. Particular attention is given to the interplay between the angle of incidence of the laser beam on the target and a controlled prepulse. It is observed experimentally that the $K\alpha$ yield can be optimized for correspondingly different prepulse and plasma scale-length conditions. For steep electron-density gradients, maximum yields can be achieved at larger angles. For somewhat expanded plasmas expected in the case of laser pulses with a relatively poor contrast, the $K\alpha$ yield can be enhanced by using a near-normal-incidence geometry. For a certain scale-length range (between 0.1 and 1 times a laser wavelength) the optimized yield is scale-length independent. Physically this situation arises because of the strong dependence of collisionless absorption mechanisms—in particular resonance absorption—on the angle of incidence and the plasma scale length, giving scope to optimize absorption and hence the $K\alpha$ yield. This qualitative description is supported by calculations based on the classical resonance absorption mechanism and by particle-in-cell simulations. Finally, the latter simulations also show that even for initially steep gradients, a rapid profile expansion occurs at oblique angles in which ions are pulled back toward the laser by hot electrons circulating at the front of the target. The corresponding enhancement in $K\alpha$ yield under these conditions seen in the present experiment represents strong evidence for this suprathermal shelf formation effect.

Figure 1

(Color online) Schematic of the experimental setup.

Figure 2

Spectrum of the laser produced $K\alpha$ emission of Cu.

Figure 3

(Color online) $K\alpha$ emission as a function of the relative position of laser focus respect to the target surface on massive Cu and Ti targets. The lines between the data points are only to guide the eye.

Figure 4

Measured dependence of x-ray yield on laser energy for a $20\mu \text{m}$ Cu foil. The angle of incidence is $45°$.

Figure 5

Normalized $K\alpha$ emissions per pulse as a function of main pulse delay at fixed angle of incidence of $45°$ on different target thickness. (a) Cu-Target, ${\text{N}}_0=5.2\times {10}^8\text{photons}/\text{sr}$ and $8.2\times {10}^7\text{photons}/\text{sr}$ for $\text{d}=20\mu \text{m}$ and 300 nm, respectively. (b) Ti-Target, ${\text{N}}_0=1.4\times {10}^9\text{photons}/\text{sr}$ and $1.2\times {10}^8\text{photons}/\text{sr}$ for $d=20\mu \text{m}$ and 300 nm, respectively. (c) Hard x-ray background signal as a function of main pulse delay on $20\mu \text{m}$ targets.

Figure 6

(Color online) $K\alpha$ emission per pulse as a function of main pulse delay at different angle of incidence, (a) Cu and (b) Ti. The measured $K\alpha$ yield at negative or zero delay is the same as obtained without prepulse.

Figure 7

(Color online) Absorption measurement with main pulse only, measured at the constant laser intensity. Scale on left-hand side: absorption, scale on right-hand side: Cu and $\text{Ti}K\alpha$ yield at $\Delta t=0$ (data taken from Fig. 6).

Figure 8

(Color online) $K\alpha$ emission per pulse as a function of the angle of incidence at fixed prepulse delay. a) Cu at $\Delta t=0$, 4, 7, and 15 ps. (b) Ti at similar delay times.

Figure 9

(Color online) Cu and $\text{Ti}K\alpha$ yield per pulse at the maximum peak and at negative time delay (or without prepulse). The lines are to guide the eye only.

Figure 10

(Color online) (a) Shows the optimal delay time for the prepulse to have the maximum $K\alpha$ emission, extracted from Fig. 6. (b) Normalization the experimental data and theoretical calculation of the optimal plasma scale length for resonance absorption (dashed curve, $Y$ axis on the right-hand side). The theoretical curve is estimated from ${\left(2\pi L/\lambda \right)}^{2/3}{\text{sin}}^2\theta =0.6$ (Ref. [33]).

Figure 11

(Color online) Calculated laser energy absorbed by hot electrons as a function of the initial plasma density scale length and incidence angle for (a) Cu and (b) for Ti targets.

Figure 12

(Color online) Simulated $K\alpha$ yield per pulse as a function of the initial plasma density scale length and incidence angle for (a) Ti and (b) Cu targets.

Figure 13

Comparison of simulated maximum $\text{Ti}K\alpha$ yield per pulse and yield for a density scale-length $L/\lambda =0.01$ (no prepulse).