Analysis of damaging effects of laser-plasma accelerated shrapnels on protecting glass shield

Analysis of the damage caused by laser plasma accelerated fragments of metal target was performed. Measured as well as calculated parameters of craters and shrapnel found in BK7 glass blastshield are presented. Method applied for the measurement of parameters of craters is described. Potential damage of optical elements by the so-called striking cores (high-velocity stable objects arising due to collapse of cones or some other target parts toward their axes) that can be generated in IFE related experiments is evaluated.


INTRODUCTION
Operation of the Inertial Fusion Energy (IFE) power plants and the experiments related to IFE can be accompanied by the formation of the high-velocity, high-density objects that can damage optical elements and/or other equipment unless some measures to prevent this are not taken [1][2][3][4][5].In many situations the effect of such objects on the equipment will be similar to that of the micrometeorites and space debris on the equipment operating in space.Below, we provide data from analysis of craters and target fragments (shrapnel) found in the BK7 protecting glass shield after interaction of ∼ 600 J laser pulse with the target with a cavity.We use the formulae from [6][7][8][9][10] to estimate the velocities of those shrapnel and to analyze possible damage of transparent optical elements of IFE power plants and experimental facilities by the so-called striking cores.

EXPERIMENTAL DATA AND THEIR ANALYSIS
Shrapnel generated in experiments employing high-energy lasers (generally with masses in the range from several micrograms to few tens or even hundreds milligrams) can reach energies sufficient to severely damage or to destroy a glass plate made of fused silica, BK7, or similar kinds of glasses with the thickness up to several millimeters.This may result in a serious damage or even destruction of the diagnostics and optical components located in the path of such objects when these components are not shielded or otherwise protected [1][2][3][4][5].
Below, an analysis of damaging effects of the laser-plasma accelerated Cu fragments on 8 mm thick, 315 mm in diameter, blastshield made of BK7 glass is presented.Blastshield originated from the Prague Asterix Laser System (PALS).Dominant part of the damage was caused during a single shot experiment using the so-called Reverse Pressure Acceleration (RPA) target schema (targets with a cavity) [11][12][13].Target, located a distance 50 cm away from the blastshield, was irradiated by the first a e-mail: martimi2@fjfi.cvut.czThis is an Open Access article distributed under the terms of the Creative Commons Attribution License 2.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.EPJ Web of Conferences harmonics (1315 nm) of PALS iodine laser with a pulse duration ∼ 350 ps, energy ∼ 600 J, and intensity ∼ 6 × 10 14 W/cm 2 , cavity facing laser.
For estimation of the volume (and mass) of the material removed from selected craters their replicas were prepared.This was done by plasticine pressed into the craters using a very thin protective plastic foil (not affecting the craters' replicas shape).The foil constitutes not more than 3% of the total volume of each crater.This way, replicas of a reasonably good accuracy and reproducibility were obtained.Minimal dimensions of the structure recordable by this method with required precision and reproducibility were estimated to be of the order of 0.1 mm in diameter.For the scope of this work objects of diameter higher then 1 mm were analyzed.Plasticity of the plasticine allows for a careful removal of the reliefs (corresponding solely to the crater) from the plasticine subbase and a subsequent formation of this subtracted material into a sphere.Diameters of those spheres were estimated with precision of about 0.05 mm using the photography of such sphere positioned on the ruler.This procedure represents relatively fast and accurate method for estimation of the parameters of relief structures.Some of examined craters were of very irregular shape.The biggest crater maximum diameter was ∼ 1.4 cm, while its depth was ∼ 0.2 cm.The shape of the craters was close to cones with the angle at the base (the blastshield surface) varied from about 4 to 22 degs.The aspect ratio of measured craters, i.e. the ratio of the crater's diameter to its depth, varied from ∼ 27 (smaller craters) to ∼ 5 (larger craters), the corresponding interpolation gave dependance D cr /P cr = 130 • D cr [mm] −1.6259 for aspect ratio and D cr [mm] = 3 • V cr [mm 3 ] 0.2821 for crater diameter.From examination of the blastshield it was found that several smaller craters contained remains of shrapnel sealed in the glass.The measured as well as calculated parameters of those shrapnel and the corresponding craters are shown in table 1.It was found that their masses varied from circa 0.03 mg to 0.8 mg, assuming the density presented in table 1.It shall be noted that the abrasive nature of glass can reduce volume (mass) of metallic fragments during their interaction with glass.When estimating the shrapnel velocities, the diameter of the crater D cr created in the glass with density glass in the situation when the vector of the projectile velocity is perpendicular to the glass surface was described using the equations [7], all substituted in cgs units.
For the borosilicate glass CMX, the ratio of the predicted to the actual values of D cr is in the range of about 0.2 to 3 [7].Eqs. ( 1) and ( 2) are the different approximations of the experimental data [6,7,10].The value of d p was chosen as a parameter providing the equality of the volume of the ball with such a diameter and that of the remains of shrapnel estimated using microscope.
Mechanical properties of BK7 glass were studied also using a 5.5 mm (22") caliber air gun in order to evaluate possible effect of collision of non-irradiated target with glass.For this purpose a 10 mm thick, 315 mm in diameter, BK7 shield was used.The velocity of projectile, measured at the distance corresponding to the actual distance of the tested blastshield, was about 122 m/s.The mass of the lead projectile m p used for the experiment (22" Diabole Boxer), was 0.858 ± 0.004 g, its kinetic energy was 6.4 J.No crater was created.The impact of the projectile caused three significant cracks going from the impact epicenter to the edge of the plate to the points where the blastshield was fixed.In the impact epicenter, the uncomplete circle of very weakly damaged glass surface, corresponding to the diameter of the projectile transformed after impact, became noticeable.Only antireflection coatings was possibly affected.During the impact the projectile was shrank to the length of about 1.7 mm from the original 8 mm.

THEORETICAL PREDICTIONS OF POSSIBLE DAMAGING EFFECTS OF STRIKING CORES
The failure of ignition of the fast ignition targets with the cones and the non-ignition experiments with such target can result in the formation of striking cores [3].They arise due to collapse of the metal cones, hemispheres and parts having some other shapes toward their axes with velocities that are not sufficient for formation of cumulative jets (see Refs. [3,[15][16][17]).The limitation on the velocity of collapse seems to restrict the maximum velocity of the striking cores, that can arise in the IFE experiments, by the value of about 3 to 5 km/s.In contrast with the cumulative jets, striking cores are not influenced by the hydrodynamic instabilities and, as a result, do not decay [3,[15][16][17].The large mass and the high stability of striking cores result in their high danger for the equipment [3].
When estimating the possible damage of the optical elements by the striking core, let us consider the situation when the striking core is formed from the whole material of the golden cone with the inner base radius r = 0.9 mm, the height h = 1.4 mm, and the wall thickness l = 30 m. Volume V cone of the material of this cone is about 1.4 × 10 −4 cm 3 .The choice of r and h is based partly on the example presented in Ref. [19] for the fast ignition, indirect compression, NIF-scale target.The thickness of the cone wall of this target equals to 30 m in the region near the tip and is about 190 m in the region near the base [19].Thus, the assumption used here corresponds to the relatively small value of V cone .The shape of the striking core will be determined by several factors (see also Refs.[15,17]).Let us assume that the damage of the optical element by the striking core is approximately the same as that caused by the spherical projectile with the same volume, density, and velocity.
According to Ref. [9], the depth P cr [cm] and the diameter D cr [cm] of the crater created by the spherical projectile with the diameter d p [cm], density p [g/cm 3 ] and velocity v p [km/s] in the fused silica in the situation when the vector of the projectile velocity is perpendicular to the surface of the glass are given by ( Here it is assumed that the thickness of the fused silica is sufficiently large, namely, at least about 2 to 3 times greater than P cr , and, therefore, the penetration of the projectile through it does not occur (see Ref. [8]).
In the experiments with the two-stage light gas gun launcher the ratio of the predicted value of P cr , corresponding to Eq. (3), to the actual one was in the range from about 0.4 to about 1.6, the ratio of 08011-p.3

Table 1 .
Parameters of Cu fragments found in smaller craters and parameters of smaller and larger craters.