Effects of laser prepulses on laser-induced proton generation

Low-intensity laser prepulses (<1013 W cm−2, nanosecond duration) are a major issue in experiments on laser-induced generation of protons, often limiting the performances of proton sources produced by high-intensity lasers (≈1019 W cm−2, picosecond or femtosecond duration). Depending on the intensity regime, several effects may be associated with the prepulse, some of which are discussed in this paper: (i) destruction of thin foil targets by the shock generated by the laser prepulse; (ii) creation of preplasma on the target front side affecting laser absorption; (iii) deformation of the target rear side; and (iv) whole displacement of thin foil targets affecting the focusing condition. In particular, we show that under oblique high-intensity irradiation and for low prepulse intensities, the proton beam is directed away from the target normal. Deviation is towards the laser forward direction, with an angle that increases with the level and duration of the ASE pedestal. Also, for a given laser pulse, the beam deviation increases with proton energy. The observations are discussed in terms of target normal sheath acceleration, in combination with a laser-controllable shock wave locally deforming the target surface.

We will show how, depending on target thickness and prepulse intensity, three different regimes can be obtained. The first two are well known in the literature: 1. For 'thick' targets and at low pedestal intensities, the shock is very weak and travels slowly in the material. Thereby it has no time to break out on the target rear side before the arrival of the main laser pulse (picosecond duration), accelerating the energetic proton beam. 2. For 'thin' targets and high pedestal intensities, a strong shock is launched in the material and travels quickly. Thereby it has the time to break out on the target rear side and induces a vaporization of the material (plasma formation) with the creation of a long gradient scale length, which prevents significant proton acceleration. 3. Finally, there is an intermediate regime, in which the shock breaks out on the target rear side but it is so weak that it just produces a deformation of the target surface but not its vaporization. This may produce deformation of the target rear side and therefore interesting effects consisting in the deflection of the laser beam, which indeed could even be controlled.
Also note that a thin foil target can also be displaced as a whole by the effect of ablation pressure, thereby strongly affecting focusing conditions (especially because in this kind of experiment, tight focusing is used to achieve large intensities on the target). Finally, among the effects induced by the laser prepulse, a very important one is related to the creation of a preplasma on the target front side. Such a preplasma may strongly affect laser absorption and the generation of fast electrons, but also produce conditions for self-focusing or filamentation of the laser beam in the plasma corona. High-pressure phase diagram of Al [6] (1 Mbar = 100 GPa) showing the melting curve, the vaporization curve, and the shock adiabatic, together with experimental data.

Laser-produced shocks and proton generation
The effects related to the shock induced by the laser prepulse depend on the following: 1) Shock pressure (which increases with laser intensity): at high pressure the shock will produce vaporization of the target rear side and plasma formation. 2) Target thickness and pedestal duration: to avoid breakout, we need the target thickness d to satisfy the relation where D is the shock velocity and τ the duration of the laser prepulse (before the arrival of the main laser pulse). The shock velocity is related to shock pressure by the relation [3] where P S is the shock pressure, γ the adiabatic constant of the material and ρ o its initial density. Although (2) is strictly valid only for a perfect gas, in reality in the high pressure range (Megabar) all materials approach the perfect gas state so that relation (2) is qualitatively true for most materials and, quantitatively, is quite close to the real numbers. Finally, the shock pressure is given by [4] P S (Mbar) = 8.6 I 10 14 where the intensity I is measured in W cm −2 , the laser wavelength λ in µm and A and Z are the atomic weight and number of the irradiated material. Note that 5 × 10 12 W cm −2 produces a pressure of the order of 1.  At 10 12 W cm −2 , laser ablation generates a relatively cold and plastic deformation of the target. Increasing the intensity by one order of magnitude heats the shocked material and creates a density ramp at the rear surface. Such a ramp has been shown to decrease the maximum proton energy.
of about 10 and 13 km s −1 (i.e. µm ns −1 ). Therefore, if for instance we consider a prepulse duration of 1 ns, we see that the shock does not have the time to break out for Al targets thicker than 13 µm. Indeed the two velocities are not so different due to the weak dependence of velocity on pressure and to the weak dependence of pressure on intensity. However, in order to assess the real effects of shock breakout, we must locate such pressures in the high-pressure phase diagram of Al [6], shown in figure 2. Here, we can notice the melting temperature of Al at standard pressure (T ≈ 933 K), the melting point along the Hugoniot of the material (T ≈ 5000 K) and, the boiling temperature at standard pressure (T ≈ 2500 K). The Hugoniot curve is the ensemble of states in a material that can be reached by shock compression. This is named as shock adiabat in figure 2.
We must also consider the fact that, as described in [3], at the time at which the shock breaks out on the target rear side, the shock pressure will not be maintained since the shocked material will face vacuum (or a gas at very low pressure). This will cause the motion of the material in the forward direction (i.e. the direction of the shock front), while at the same time a relaxation wave is created. If the shock is not too strong it can be shown that the velocity of the free surface of the material is about 2U (where U is the fluid velocity in the material behind the shock front moving with velocity D), while the relaxation wave, virtually decompressing the material to zero pressure, travels back in the material at the corresponding sound velocity C s .
Whether we obtain vaporization of the material on the target rear side or not depends on the final state of the material after decompression. In principle, we must then draw the relaxation curve and superimpose it on the phase diagram in figure 2. If we do so, we discover that the shock compression of Al to 2 Mbar will lead to an unloading that ends at zero pressure above the evaporation curve of Al (curve c in figure 2). Instead shock compression of Al to 1.2 Mbar will lead to an unloading that ends at zero pressure below the evaporation curve of Al. Despite the small difference in pressure, the two shocks therefore produce dramatically different effects and they may therefore be termed as the case of strong shock pressure and the case of small shock pressure.

Detailed hydrodynamics simulations
In order to get a more quantitative description of the involved phenomena we performed numerical simulations using the hydrodynamics codes MULTI [7] and MULTI 2D [8]. Figure 3 shows the typical density profiles obtained in a 6 µm thick Al-target irradiated at various pedestal laser intensities (in all cases the temporal laser profile is flat-top). Figure 4 shows a time-position plot of the results of the simulation at a laser intensity of 5 × 10 12 W cm −2 (a case with no plasma creation on the target rear side). We see indeed that the density profile on the rear side remains steep (unlike the front side).
However, the simulation in figure 4 shows another effect related to laser prepulses: after the breakout of the shock (here taking place about 0.6 ns after the beginning of irradiation with the 1.5 ns long laser pedestal), the whole target begins to move with a velocity of about 2U (as we said before). At 1 ns after shock breakout, the target has already moved almost by 10 µm. Of course the displacement will be larger for higher laser intensities (larger shock pressures) and for thinner targets (earlier shock breakout time, less mass to be moved). Often a very tight focus is realized in this kind of experiment, in order to obtain a greater intensity, which usually implies a very short depth of focus. Therefore, in same cases, the target may go out of focus due to its motion, and this can be a further reason for inefficient proton generation.
Note that the target motion, as shown in figure 4, is characterized by a series of accelerations every time the shock breaks on the target rear. It is also clear, however, that the overall behaviour, on a longer time scale, shows a parabolic trend that is characteristic of a constant acceleration. Indeed, it can be shown that the target displacement is approximately given by Figure 5. Propagation and breakout of a shock wave driven in a 6 µm Al target by a 10 12 W cm −2 pedestal with a 10 µm diameter focal spot. The red line represents the position of the shock front. The light grey region is unperturbed Al. Darker grey is the shocked Al (at the edge of the spot, the shock is very weak, or negligible, the shock velocity corresponds to the sound velocity in unperturbed Al, and the degree of compression approaches 1). Along the axis of the laser beam, instead, shock compression and shock velocity reach their maximum.
a distance that must be compared with the typical depth of focus: where we have introduced the F-number of the system, the divergence of the laser beam and the diffraction-limited divergence.

Two-dimensional effects and proton beam deviation
Until now, we have only considered one-dimensional (1D) hydrodynamics effects. These may lead to the formation of a plasma gradient on the target rear side and also to target defocusing (due to target displacement after shock breakout). In reality, due to the small lateral dimension of the laser focal spot, two-dimensional (2D) effects in shock propagation and in target deformation are very important. To achieve this goal, we have performed hydro simulations using the code MULTI 2D [7]. Figure 5 shows the propagation and breakout of a shock wave driven in a 6 µm Al target by a 10 12 W cm −2 pedestal with a 10 µm diameter focal spot. Here, the intensity on the target varies with the (radial) position. Therefore, at each point, we obtain a different shock pressure and shock velocity and the shock breakout time will be different. Also, after shock breakout, the local displacement 8 velocity (2U) of the target rear side will be different because the local fluid velocity is also different being larger at the centre and smaller at the edges of the spot.
2D effects in hydrodynamics lead to a deformation of the target. This is particularly interesting in the case of weak shocks, which do not lead to the formation of a plasma phase on the target rear side. In this case, the local deformation acts to change the local target normal and thereby may produce a deviation of the accelerated proton from the perpendicular to the 'unperturbed' target surface. If the fast electrons travelling in the material, and creating the space charge at the target rear side, are directed along the normal to the target surface, this may only result in an increased divergence of the proton beam. In many cases, however, the fast electrons are not travelling along the normal, but rather along the laser beam axis. For instance, if a laser beam (main picosecond pulse) is incident at an angle on the target surface, then fast electrons may still be produced normally to the surface or along the laser beam axis depending on the particular generation mechanism that is dominant in the experiment. In the case of resonant absorption, fast electrons will be mainly directed along the target normal. If instead ponderomotive effects are dominant, fast electrons will be mainly directed along the laser beam axis. In general, the two absorption mechanisms may be acting at the same time and will lead to the generation of different fast electron populations, the more energetic ones usually being related to ponderomotive effects.
The question of which is the dominant mechanism for laser absorption (and for fast electron generation) is a complicated matter and is still open to debate. While on the basis of simple scaling laws, one would expect ponderomotive effects to dominate at intensities larger than a few times 10 19 W cm −2 , the situation is indeed far more complex. For instance, recent measurements [9] show temperatures consistent with the scaling expected from resonant absorption still at very high intensities. Actually this depends not only on the scale length of the preplasma but also on the focusing conditions (from the experimental point of view, with tight focusing there is always a range of incident angles on targets and the conditions for resonant absorption may be different from what one expects with simple 'planar' laser beams). Also deformation of the front surface (due to ponderomotive pressure, plasma expansion and other effects) may change the interaction conditions. A more detailed discussion is outside the scope of the present paper, which aims to study the effects on proton emission, rather than going too deep into the mechanisms of fast electron generation. However, we would like to point out that estimating which acceleration mechanism dominates is important and must be addressed also at the experimental level. Developments in diagnostics techniques and analysis, like the important one contained in [10], may indeed help to address such a problem at the experimental level. Figure 6 shows the sequential illustration of proton acceleration in a shocked target following the general scheme we have just described.
Also note that interesting features are expected to appear in the case of stronger shocks, which may vaporize the material near the centre of the shock front but not at the edges. In this case, acceleration of protons may be completely prevented from the central region. Nearby, however, the strong will be weaker and the target will be deformed but not vaporized. Proton acceleration may still be produced here leading to the formation of an annular emission region.

Experimental results
Experimental results obtained with the Lund laser system [11,12] indeed show all the features previously described. The diagnostics simply consisted of CR-39 detector plates with an aluminium filter mask placed before it to enable the measurement of both the proton spatial and energy distributions. This is shown together with the expected proton pattern in figure 7(a) (assuming a beam directed along the target normal and with divergence decreasing with increasing proton energy). Figures 7(b)-(d) show examples of the actual patterns observed in the experiments, together with plots of the deviation from the target normal to the laser direction versus proton energy (degrees versus MeV) for different parameters of the experiment (target thickness, pedestal level and pedestal duration). We see that deviation is larger when we expect so according to the physical picture described in the previous paragraphs, i.e. when the target is thin and the laser pedestal is intense or long. In all these cases, the shock has the time to burn through and deform the rear surface of the target, while the shock itself remains low enough not to cause the vaporization of the material and the formation of a plasma with sufficient extension on the rear side.
Results obtained by changing the target material confirm the effect. For instance, we have compared 6 µm targets of Cu and Al. The shock speed increases with laser intensity, but is lower in Cu than in Al, due to the greater density of Cu as shown by equation (2). The lower shock speed in Cu makes shock effects less important. Indeed, experimental results (figure 8) show that in comparable conditions, deviation is smaller for Cu than for Al.
Finally, the shock model also allows one to calculate the beam deviation for higher energy protons, those related to the faster electrons, generated by ponderomotive forces and directed along the laser beam axis. (Let us recall that the angle of emission of protons is different for different proton energies because only higher energy protons are emitted from a smaller region with a narrower angular distribution. Therefore, they are more sensitive to surface deformation.) Indeed we can simply calculate the emission direction as the target normal at the point where the laser axis intersects the rear surface. Figure 9 compares the prediction of the model with experimental results showing the proton beam deflection versus pedestal duration. The lines through the images on the right indicate the target normal direction. (a) The effect of changing the target thickness from 12 to 6 µm while keeping the pedestal duration constant (1 ns more than its minimum value) and a contrast of 3 × 10 7 . (b) The effect of increasing the pedestal duration by 1 ns with a 6 µm target and a contrast of 3 × 10 7 . (c) The effect of decreasing the contrast (increasing the ASE level to 6 × 10 6 , corresponding to an estimated ASE intensity of 5 × 10 12 W cm −2 with a 6 µm target and minimum pedestal duration (≈ 1 ns) (data from [9]).
Note that although some papers (e.g. [13]) have predicted deviation of the proton emission direction, these were purely theoretical/numerical works that do not describe any experimental results. Also the context is very different, and does not refer to deviations produced by deformation of the target rear side due to the shock from a low-intensity prepulse.

Front side effects
The laser prepulse on the front side creates a 'preplasma' that may either improve or deteriorate laser absorption and affect the distribution of the generated fast electrons. The effects connected to the 'rear side', described in previous sections, clearly imply the need for reducing the prepulse. However, the complete absence of prepulse is also negative since it implies a reduced absorption, or in other words, the target behaves as a plasma mirror. Until recently, the laser prepulse was something that was not really controllable, but recent techniques (plasma mirrors, XPW) allowed improving the contrast up to 10 10 . It therefore becomes possible to do experiments with a controlled prepulse, obtained either by the prepulse associated with the main pulse or controlling by cutting it and replacing with another well-mastered secondary beam. In this way, it is possible to build a preplasma as desired in order to maximize absorption and shape the fast electron distribution. In this context, Andreev et al [14] suggest that the energy of the laser-generated protons peaks at L o /λ ≈ 4, where L is the characteristic scale length of the plasma profile.
From an experimental point of view, the obvious way to characterize preplasma is by performing interferometry. This was done, for example, in [15]. The experimental characterization of the preplasma, supported by computer hydrodynamics simulations, allows one to predict the evolution of the preplasma. However, at the same time, hydro simulations allow one to follow the evolution of the shock travelling in the target up to shock breakout (again such predictions can be corroborated by experimental measurements, as shown in figure 10). In turn this finally allows one to determine the minimum target thickness that is required to prevent shock breakout on the rear side. An example of how front and rear side predictions can be used together is shown in figure 10. The laser source used in the experiment was a CPA Ti:sapphire yielding 40 mJ on the target in 150 fs duration, resulting in a peak intensity on the target of 4 × 10 15 W cm −2 . We see that in order to obtain L/λ ≈ 4 (as predicted in [14]) a time delay of 80 ps was needed between the 'prepulse' and the main beam and that, in such conditions, the minimum allowable target thickness was ≈ 1.6 µm.   Actual measurement of proton energy versus the scale length of the front preplasma was performed by various groups. Figure 11 shows the measurements by Flacco et al showing some enhancement. However, firstly the enhancement was much smaller than was expected from simulations (∼17% against 50% predicted by Andreev et al) and, secondly, it was not always reproducible. This points to a different effect than that studied in [14].
Similar, but more robust, experimental results were obtained by McKenna et al [16,17] in an experiment at RAL. They observed not only a significant enhancement in proton energy (see figure 12) but also, in exactly the same conditions, an increase in conversion efficiency (proton number), implying an increased absorption of laser light.
However, the enhancement was taking place at a large scale length, in a range different from that predicted in [14]. In this case, an interferometric analysis of the interacting target showed the presence of laser beam channelling, or laser beam filamentation, in the 'preplasma' corona. Therefore, we are looking at the consequences of nonlinear interaction, which completely alters the laser intensity on the target and the interaction conditions.
We can therefore conclude that at the moment, the effect predicted in [14] is probably not observed yet, while nonlinear interactions in the plasma corona are also showing interesting consequences on proton generation, which probably deserves more careful studies in order to be routinely used in future experiments for laser-induced generation of protons.

Conclusions
In this paper, we have shown how the physics of laser-generated protons is complex and the effects induced by the low-intensity nanosecond prepulse may be very important. The state of the target material influences many aspects of the generation. The presence of prepulses is often negative. However, at very low intensities, which do not produce the vaporization of the material on the target rear side, a deformation of the target surface can be produced and used to deviate the proton beam. On the target front side, the scale length of the preplasma, in principle, allows one to control the amount of laser absorption and also the shape of the fast electron distribution function. Interesting measurements show the enhancement of the maximum proton energy when the laser beams channel in the preplasma corona.