When an intense laser pulse is loaded upon solids, very high impact pressure can be generated on the surface. In this letter, we simulate this process through one-dimensional particle-in-cell simulation and find that the pressure as high as 0.13 TPa can be generated after the laser pulse with intensity 1015 W/cm2 and 5 picosecond duration is injected upon a nanometer solid-density plasma. The peak pressure is shown to be resulted from an energetic high-density plasma bunch, produced through plasma implosion under extremely high light pressure.

How to produce extremely high pressure is of critical importance in high-pressure physics, which can find wide applications in material science,1–4 astrophysics5,6 and laser fusion7–9 etc. Generally there are two kinds of high pressure, i.e. static10,11 and dynamic.12–16 In the past decades, the generation of dynamic high pressure by intense lasers has attracted much attention due to its low cost, short experimental period and easiness to control.17–20 The whole process of the laser loading upon a solid can be divided into two consecutive stages. The first stage is formation of the strongly heated and highly pressurized frontal layer through the energy absorbtion from the laser pulse. This stage is usually described by the hydrodynamics model.21,22 The second stage is the generation of shock wave and its evolution in the solid target, which can be simulated by molecular dynamic (MD) method.13 In the first stage, the hydrodynamic model can describe the physical phenomena in the nanosecond (ns) time scale and micrometer (μm) length scale. Recently, due to the fast development in the controlling of short intense laser pulses and the fabrication of nanometer (nm) targets, people are beginning to consider the laser loading with the picosecond (ps) or femtosecond (fs) laser pulses upon sub-micrometer films. For this new situation, hydrodynamic simulation meets great challenges since the single-particle dynamics begins to play an important role in the interactions. To appropriately describe the particle dynamics, the particle-in-cell (PIC) simulation is an effective and efficient way. To the best of our knowledge, up to now, there is still no work to investigate the first-stage physics with PIC method. Hence, in this letter, we will focus upon exploring this stage in order to maximize the peak impetus pressure in the loading process and also to check the corresponding underlying physical mechanism. All the PIC calculations are carried out by the software package VORPAL23 developed by Tech-X company.

Fig. 1 shows the schematic diagram of our physical model, in which an intense ps laser pulse with intensity 1015W/cm2 propagating along the positive direction of x axis normally irradiates on the surface of a solid film, which is described by a pre-formed solid-density plasma, so called pre-plasma. The pre-plasma is comprised of singly-charged carbon ions and electrons with the mass ratio mi/me = 21893, where mi and me are the ion and electron masses, respectively. The plasma impact pressure was calculated by its microscopic definition,

p d I d t d A = i , ν i x > 0 n i m ν i x 2 ,
(1)

where dI is the total particle momentum impinging upon an area dA in a time duration dt, ni is the number density of particles with the velocity νi, νix is x component of velocity and m is particle mass. In relativistic conditions, Eq. (1) can be written as,

p = i , ν i x > 0 n i γ i m 0 ν i x 2 = m 0 c 2 i , ν i x > 0 n i u i x 2 γ i c 2 = m 0 c 2 n | u x > 0 u x 2 γ c 2
(2)

where m0 is the rest mass of the particle, c is light speed in vacuum, n | u x > 0 is the number density of particles moving along the positive x direction and denotes the corresponding average. γ = 1 / 1 ν 2 / c 2 is the Lorentz factor and u x = γ ν x .

FIG. 1.

Schematic diagram of the physical model. The laser wavelength is λ = 0.4 μm and the pulse duration is τ 5 ps. The thickness of the pre-plasma is d 80nm.

FIG. 1.

Schematic diagram of the physical model. The laser wavelength is λ = 0.4 μm and the pulse duration is τ 5 ps. The thickness of the pre-plasma is d 80nm.

Close modal

Obviously, for a fixed thickness, if the pre-plasma density is too low, the laser pulse will go through the target with little energy deposition in the plasma. Otherwise, if it is too high, the laser field will be reflected before it reaches the rear surface. In both cases, it is impossible to generate high impact pressure in the rear surface. There must exist an optimal pre-plasma density to maximize the pressure. Through intensive calculations, we find that, when a linear polarized plane wave pulse with intensity I = 1015 W/cm2 and pulse duration τ = 5 ps is injected upon a pre-plasma with initial density n 0 = 2 n c = 1.393 × 10 28 m−3, thickness d = 0.2 λ and initial temperature T0 = 1000 K, we can acquire 0.1 TPa magnitude of extremely high pressure in the target rear surface. To investigate how this high pressure is generated, we plot the spatial and temporal evolution of the corresponding electron density, ion density and plasma pressure, respectively in Fig. 2.

FIG. 2.

Spatial and temporal evolution of (a) electron density, (b) ion density, and (c) plasma pressure, respectively. The laser pulse starts to interact with the target at t = 0 ps and leaves the target at t 5 ps. The pre-plasma target sits between x = 0 λ and x = 0.2 λ .

FIG. 2.

Spatial and temporal evolution of (a) electron density, (b) ion density, and (c) plasma pressure, respectively. The laser pulse starts to interact with the target at t = 0 ps and leaves the target at t 5 ps. The pre-plasma target sits between x = 0 λ and x = 0.2 λ .

Close modal

From Fig. 2, it can be easily observed that, when the laser pulse reaches the target at t = 0 ps, the front surface of the pre-plasma target begins to be compressed by the intense light pressure, which is around 33 GPa. As the laser field pushes into the deep of the plasma, the energy density of the plasma in the laser wavefront increases rapidly until it gets to a critical point at t 3 ps, when a jet of plasma is running backward, which subsequently generates a powerful recoil force to compress the frontal plasma violently. This is why we can see an energetic high-density plasma bunch running forward (see Figs. 2(a) and 2(b)). At t 5 ps, this plasma bunch arrives at the target rear surface and makes the plasma pressure reach its peak value around 0.13 TPa.

To check how the high pressure takes place, in Fig. 3 we present the temporal evolution of the forward-propagating maximum plasma impact pressure pf, the light pressure pl and the backward-propagating plasma impact pressure pb at the same spatial point where the maximum pf takes place. It is easy to see that pf reaches its peak value ( 0.15 TPa) at t 3.1 ps. Before 3.1 ps, there are some interesting things happening, which relates to the competition between pl and pb, which will be explained as follows.

FIG. 3.

The temporal evolution of the forward-propagating plasma impact pressure pf, the light pressure pl and the backward-propagating plasma impact pressure pb at the spatial point, where the maximum pf occurs. The simulation parameters are as same as Fig. 2.

FIG. 3.

The temporal evolution of the forward-propagating plasma impact pressure pf, the light pressure pl and the backward-propagating plasma impact pressure pb at the spatial point, where the maximum pf occurs. The simulation parameters are as same as Fig. 2.

Close modal

As the laser reaches the target frontal surface at t=0 ps, the plasma begins to be compressed by the light pressure. Hence the forward- or backward-propagating electromagnetic energy will face stronger and stronger stopping power from the strongly compressed plasma until it is reflected at t 0.5 ps, when pl changes sign. Fig. 4 gives the space-time evolution of pb and pf, which shows that, from 0.5 ps to 1.5 ps, the peak pressure keeps staying at x = 0.025 λ . After 1.5 ps, the reflected laser becomes lessened, namely pl begins to decrease. The position of the peak plasma impact pressure starts to move further into the target interior. Finally from 2.3 ps, no reflected light can be observed, which means the incident laser fields have finished its first strong kicking of the plasma, which should be responsible for the continuous increase of pf, as can be seen from Fig. 3. After this kicking, the laser pulse starts to push the plasma again in the forward direction.

FIG. 4.

The temporal-spatial evolution of pf, pl and pb at the point, where the maximum pf occurs. The simulation parameters are as same as Fig. 2.

FIG. 4.

The temporal-spatial evolution of pf, pl and pb at the point, where the maximum pf occurs. The simulation parameters are as same as Fig. 2.

Close modal

The next critical moment comes at t 3.0 ps, when we observe a backward-running plasma jet, which implicates an outbreak of the plasma implosion, as shown in Fig. 2. This makes pb increase quickly and soon surpassed the forward-directed light pressure. The backward-running plasma jet provided a second violent kick to the forward-propagating plasma, which prompts the exponential increase of pf and quickly reaches its peak value 0.15 TPa at t 3.1 ps. From t 3 ps to t 5 ps, the light pressure is getting smaller and smaller while the backward-propagating plasma pressure keeps high, which implicates that the light has lost the driving power to compress the plasma. Now it is the recoil of the backward-running plasma jet that drives pf to its peak value and remains the high level for about a period of 2 ps. It is interesting to note that the time evolution of pb and pf is very similar, which strongly supports the observation that the peak pressure at this stage is resulted from the plasma implosion. After the implosion, the plasma bunch keeps moving to the rear surface of the target. Even though pf decreases slightly at the rear surface, it is still as high as 0.13 TPa. By simple calculation from the traveling distance and time, the mean velocity of the energetic plasma bunch can be estimated to be around 5.83 × 10 4 m/s.

It is crucial important to note that, the mechanism of the high pressure generation discussed so far is quite similar to the plasma block generation based on the skin layer acceleration by nonlinear forces (SLANF),9,24,25 which has been investigated by both theoretical24,26,27 and experimental28–31 work. As we know, SLANF is of great importantce to the PW-ps laser induced plasma block-ignition,9 where the reaction is realized by the proton fusion with the isotope of borons,7–9 i.e. p-11 B reaction. The biggest advantage of using the plasma block in this fusion scheme lies in its ultrahigh particle density, which can be millions of times higher than that obtained by classical accelerators. The accelerated plasma block related to SLANF has been found experimentally by Sauerbrey based upon the Doppler shift of the reflected laser pulse after irradiating a 300 fs-terawatt laser pulse upon solid target.28 Hence, from another viewpoint, the implosion-induced plasma bunches, which run along or against the laser propagation direction, could also be regared as a clear demonstration of SLANF. We plan to do more detailed explorations about this issue in the future.

In summary, through one dimensional PIC simulation, we have investigated the dynamics of the high impact pressure generation when a picosecond laser pulse with intensity I=1015 W/cm2 is loaded upon a sub-micrometer solid-density plasma target. After optimizing the initial parameters of both the plasma and the laser fields, we have produced an impact pressure in the target rear surface as high as 0.13 TPa. We attribute the underlying mechanism to the recoil effect of the backward-propagating plasma jet, which directly results from the plasma implosion under intense high light pressure.

It should be reminded that in this work, we have only revealed how the implosion can lead to the generation of the high impact pressure in the rear surface of the thin plasma target. In practical laser loading applications, a thick solid target is usually attached to the rear surface of the pre-plasma target, which will absorb the energy imparted from the pre-plasma and then forms a intense forward-propagating shock pressure in the solid target. Our future work will focus upon studying the dynamic process of shock pressure generation in the solid target through MD method. Moreover, to generalize the present 1D calculations to high dimensions will also be our next task.

This work is supported by the National Natural Science Foundation of China under Grant No. 11274117.

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