1. Generation of high-pressure shocks in the LICPA-driven collider
J. Badziak
Institute of Plasma Physics and Laser Microfusion, Warsaw, Poland
Outline
Introduction
The LICPA-driven collider for generation of high-pressure shocks
Results of experiments and numerical simulations
Conclusions
Supplement

2. Generation of High-Pressure Shocks
Basic methods
Chemical explosion
Nuclear explosion
Hyper-velocity projectile – solid collision using:
light- gas guns
pulsed- power machines
laser drivers
Direct laser irradiations of a solid target
Generation of pressures in the sub-Gbar – Gbar range is possible with:
Nuclear explosions
Laser-based methods using multi-kJ lasers
Energetic efficiency of laser-based method used so far is very low:
the laser-to-shock energy conversion efficiency is below a few percent.
We proposed a principally new tool for high-pressure shock generation – the LICPA-driven collider – which allows for the shock generation with the energetic efficiency much higher than attainable with other methods known so far.

3. Experiment with NOVA laser at Lawrence Livermore National Laboratory
Generation of sub-Gbar-pressure shocks by the impact of a gold projectile
Experiment with NOVA laser at Lawrence Livermore National Laboratory
100kJ ten-beam NOVA laser
R. Cauble et al., Phys. Rev. Lett 1993
Using 10 ultraviolet beams of NOVA laser of total energy 25 kJ a planar shock of the pressure 0.75  0.2 Gbar was generated in the Au target impacted by Au flyer foil driven by laser-produced X rays.
The laser-to-shock energy conversion efficiency was below 1%.

4. Laser- Induced Cavity Pressure Acceleration (LICPA)
In the LICPA scheme, a projectile placed in a cavity is irradiated by a laser beam introduced into the cavity through a hole and accelerated along a guiding channel by the thermal pressure created in the cavity by the laser-produced plasma or by the photon pressure of the ultraintense laser radiation trapped in the cavity.
The cylindrical accelerator
The conical accelerator
The LICPA accelerator can (potentially) be driven by lasers covering a very broad range of laser energies (from 1J to 1MJ), intensities (from 1010 W/cm2 to 1023 W/cm2 or higher) and pulse lengths (from ns to subps) as well as laser wavelengths (from UV to IR) and repetition rates (up to multi – Hz); as a result, the accelerator can produce dense, fast and ultrafast projectiles of a wide variety of parameters.
Badziak et al., Appl. Phys. Lett. 96, (2010), Phys. Plasmas 19, (2012)

5. The LICPA Accelerator Regimes of operation
The hydrodynamic regime L  Lc / pl ~ 0.01 ns 10 ns, IL ~ 1010  1017 W/cm2
A projectile is driven by the hydrodynamic (thermal) pressure of hot plasma produced and confined in the accelerator’s cavity vp < 5  108 cm/s (vp limited by R – T instabilities)
The photon pressure regime L  10ps, IL > 1020 W/cm Acceleration of the projectile is predominantly due to the photon pressure of laser radiation trapped in the cavity vp > 109 cm/s (up to relativistic velocities)
The „mixed” regime L ~ 0.01 ps 100 ps, IL ~ 1017  1020 W/cm Both the photon pressure and the hydrodynamic pressure of very hot plasma (with thermal and hot electrons) can contribute to the acceleration process vp ~ 108  1010 cm/s 5

6. Potential Advantages of the LICPA Accelerator
projectile velocities up to the relativistic ones
very high energetic acceleration efficiency up to > 50%
possibility of acceleration of massive projectiles of a mass up to 10-2 g
various kinds of accelerated projectiles: macroparticles, ion beams, plasma jets
the accelerator seems to be scalable to high laser energies and intensities

7. The Hydrodynamic LICPA Accelerator The kilojoule PALS laser facility
LICPA Experiment at PALS
The kilojoule PALS laser facility
Wavelength: 1.315mm (1w) or 0.438mm (3w) Energy: 1kJ (1w) , 0.4kJ (3w) Pulse duration: 250 – 350 ps
Peak power: 3TW (1w) , 1.5TW (3w) Intensity: up to 5 x 1016 W/cm2

8. The Hydrodynamic LICPA Accelerator
LICPA Experiment at PALS
Measurement schemes
Targets (accelerators)
Laser:
EL=50 – 500J, tL = 0.3 ns
IL = 1014 – 1016 W/cm2
1w and 3w beam
LICPA
AA (ablative acceleration)
Diagnostics:
crater measurements
interferometry
scintillators (neutron and hard X-rays)
ion diagnostic (collectors, Thomson parabola)
optical streak camera
X-ray streak camera
Projectiles:
CH foil: 10, 20, 30 mm CD2 foil: 25, 50 mm Al disc: 10, 20, 50, 75 mm Au disc: 3um

9. acceleration efficiency [%]
Acceleration of a Dense Plasma Projectile in the LICPA Accelerator LICPA experiment at PALS
Parameters of the gold plasma projectile at the accelerator exit estimated from various measurements
EL  200J, mp = 4mg
Projectile parameter
mean velocity [km/s]
kinetic energy [J]
acceleration efficiency [%]
LICPA
interferometry
146 ± 8
39 ± 5
19.0 ± 2.9
ion diagnostic
estimation 1
135 ± 15
34 ± 8
16.9 ± 3.8
estimation 2
> 29 ± 6
>14.4 ± 3.3
streak camera
137 ± 7
35 ± 4
15.1 ± 1.8
acceleration
Ablative
< 60
< 7
< 3
35 ± 10
2.3 ± 1.3
1.2 ± 0.7
The measurement set-up included 3 parts:
three-frame interferometric system,
multi-collector ion detection system
streak camera
The mean velocity of plasma projectile driven by LICPA reaches 140 km/s and is by a factor 4 higher than that for the AA(ablative acceleration) scheme.
The (energetic) acceleration efficiency in the LICPA scheme is by a factor 15 higher than that in the AA scheme and reaches ~ 15 – 19 % which is the highest value achieved so far with the use of lasers or other drivers.

10. Acceleration of a Dense Plasma Projectile in the LICPA Accelerator
2D spatial profiles of density (a,e), temperature (b,f), pressure (c,g) and kinetic energy density (d,h) of plasma inside the accelerator channel in the intermediate and final stages of acceleration (2D PALE simulations, CH/Au projectile, EL = 200 J )
The plasma projectile driven by LICPA is fairly compact and dense (1 – 5 g/cm3) object, however its surface is not planar (probably due to R-T instabilities).
The temperature of the projectile is rather low (< 50eV) but its internal energy is relatively high (p ~ 0.5 Mbar) due to high projectile density.

11. The LICPA-driven Collider
Generation of high-pressure shocks with a single-beam LICPA-driven collider
The basic idea is to use LICPA to accelerate a projectile (heavy plasma macroparticle) to hyper velocities and to generate a strong shock wave by collision of the projectile with a solid target situated at the exit of the LICPA accelerator guiding channel.
Advantages of the metod:
very high energetic efficiency of acceleration (proved by experiments and simulations)
high density of the impacting projectile due to its compression in the channel (proved by simulations)
additional pushing the projectile during and after the collision by the ablative pressure still existing in the channel (proved by simulation)
no pre-heating of the target (suggested by simulations)
It is expected that the energy conversion efficiency from the laser to the shock will be by an order of magnitude higher than that in other laser-based methods used so far
Badziak et al., Phys. Plasmas 2015, Badziak et al., JINST 2016

12. The LICPA-driven Collider Two-beam colliders
The shock wave collider
In the two-beam collider the pressure, density and temperature produced in the target can be considerably higher than for the case of one-beam collider
The plasma jet collider
The plasma jet collider can be useful e.g. for laboratory astrophysics research

13. Generation of High-Pressure Shocks in the LICPA-driven Collider LICPA experiment at PALS
A scheme of the experimental set-up for measurements of the projectile (Al disc) velocity and the crater produced by the projectile - massive target collision in the LICPA-driven collider
CH # 5 mm
Al # 10 mm (2g)
Al # 20 mm (4g)
Al # 50 mm (10g)
Al # 75 mm (15g)
Results of measurements performed for the LICPA accelerator were compared with the ones for the AA scheme

14. Generation of High-Pressure Shocks in the LICPA-driven Collider LICPA experiment at PALS
Replicas of craters produced in the massive Al target by the impact of 4 mg Al projectile accelerated in the LICPA-driven collider or the AA-driven collider or by the direct irradiation of the target by laser beam. EL = 200 J.
Craters produced in the massive target by the projectile accelerated in the LICPA accelerator are much larger and deeper than those produced by the macroparticle driven by AA or by the direct irradiation of the target by laser beam. It indicates that energy and pressure of the shock generated in the LICPA-driven collider are also much higher than the ones for the cases (b) and (c).

15. Generation of High-Pressure Shocks in the LICPA-driven Collider LICPA experiment at PALS
The volume and depth of craters produced in the massive Al target by the Al projectile driven by LICPA or AA as a function of the projectile mass. The red circles and the blue squares – results of measurements, the green diamonds – results of numerical simulations using the 2D PALE code
The results of the numerical simulations are in fairly good agreement with the results of measurements  parameters of the shock obtained in the simulations are expected to be in agreement with those in the experiment.
Badziak et al., Phys. Plasmas 2015

16. Generation of High-Pressure Shocks in the LICPA-driven Collider Results of simulations with the 2D PALE code for conditions relevant to the PALS experiment
2D spatial profiles of density (a) and pressure (b) inside the massive Al target at the moment when the pressure attains a maximum value. CH/Al20mm target, EL = 200 J.
The shock front is flat over 2r 200 mm.
The maximum density in the shock is 14.3 g/cm3 and the shock velocity is 80 km/s
The pressure in the shock front reaches 144 Mbar and a maximum pressure behind the front approaches 290 Mbar.
These parameters of the shock are much higher than those for the case of projectile driven by AA or the direct laser irradiation

17. Generation of High-Pressure Shocks in the LICPA-driven Collider Parameters of the shock generated in the massive target inferred from the crater measurements by 2D PALE simulations
Parameters of the shock generated in the massive Al target by the projectile impact as a function of the thickness (mass) of the accelerated disc
Both the maximum pressure and the pressure at the shock front depend on the disc thickness (the projectile mass) and they achieve highest values for the disc with an optimum thickness (hd 10 mm).
For the disc with the optimum thickness the maximum pressure reaches 540 Mbar and the pressure at the shock front achieves 340 Mbar. These pressures are by an order of magnitude higher than the ones produced, at comparable laser energy, with the methods known so far.
Badziak et al., Phys. Plasmas 2015

18. Generation of High-Pressure Shocks in the LICPA-driven Collider LICPA Experiment at PALS
The volumes of craters and the maksimum pressure of shocks produced in the Al massive target by the impact of the CH projectile accelerated in the LICPA scheme and the AA scheme
Both the crater volumes and the shock pressures produced in the LICPA-driven collider are by a factor 20 or more higher than in the AA scheme.
The crater volume and the shock pressure generated in the LICPA-driven collider very weakly depend on the laser wavelength (excluding the shock pressure for 3w, 300J for which case the pressure is smaller than for 1w; the reason for this is a rapid decrease in density of the projectile during acceleration which is caused by too small areal density of the projectile for the highest energy of the 3w beam).

19. Generation of High-Pressure Shocks in the LICPA-driven Collider
The volume (a) and depth (b) of craters, produced in the massive Al target by the impact of a gold projectile accelerated in the LICPA-driven collider or in the AA scheme, as a function of the distance from the irradiated CH/ Au target to the massive target. EL  200J, mp = 4g.
At any distance between the irradiated CH/Au target and the impacted Al target the volume of crater produced in the LICPA collider is tens times larger than the one for the AA scheme.
It means that the shock energy in the LICPA collider is also ten times higher than that in the AA scheme.

20. Generation of High-Pressure Shocks in the LICPA-driven Collider
The volume (a) and depth (b) of craters, produced in the massive target (Al or Cu) by the impact of a 4g gold projectile accelerated in the cylindrical or conical LICPA-driven collider as a function of laser energy.
The volumes of the craters produced in the conical collider are slightly larger than in case of the cylindrical collider in spite
of the fact that the diameter of the conical channel outlet is by a factor 2 smaller than that of the cylindrical one. Since the
area of the impacting projectile in the conical collider is 4 times smaller, the maximum pressure of the shock generated in
this collider is expected to be a factor 4 higher than in the cylindrical collider.

21. Generation of High-Pressure Shocks in the LICPA-driven Collider
Observation of a fast shock in a dense Al plasma generated by the gold plasma projectile impact
1. The plasma projectile leaving the accelerator channel
2. The shock in plasma generated by the impact of the projectile into Al 20mm foil
The velocity of the projectile impacting Al 20mm foil approaches ~ 150 km/s.
The shock propagates in the dense Al plasma with the average velocity ~ 80 km/s. The maxim shock velocity is expected to be > 100 km/s.

22. Generation of High-Pressure Shocks in the LICPA-driven Collider
2D spatial profiles of pressure inside massive targets of various densities at the moment when the pressure attains a maximum value. 4ug gold projectile, EL = 200J (2D PALE simulations).
For all targets the shock is relatively flat over 2r  150 µm and the shock pressure is in the sub-Gbar range inspite of the fact that laser energy is rather low, only 200 J.

23. Generation of High-Pressure Shocks in the LICPA-driven Collider
2D spatial profiles of temperature inside massive targets of various densities at the moment when the pressure attains a maximum value. 4ug gold projectile. EL = 200J (2D PALE simulations).
For all targets the shock is relatively flat over 2r  150 µm.
The temperature in the shock reaches values from ~ 250 eV for CH to ~ 400 ev for Au.

24. Generation of High-Pressure Shocks in the LICPA-driven Collider
2D spatial profiles of pressure inside massive targets of various densities at the time of 5ns after
the projectile impact. 4ug gold projectile, EL = 200J (2D PALE simulations).
During propagation in the target, the shock transfers its energy to the target and expands also in the radial direction. As a result, the shock pressure decreases.
The shock velocity is the highest for the target of lowest density.

25. Generation of High-Pressure Shocks in the LICPA-driven Collider
2D spatial profiles of temperature inside massive targets of various densities at the final stage (t=1000ns) of crater formation in the target. 4ug gold projectile. EL = 200J (2D PALE simulations).
The crater size increases with a decrease in the impacted target density.

26. Generation of High-Pressure Shocks in the LICPA-driven Collider
The temporal dependence of the maximum shock pressure inside massive targets of various densities impacted by a 4ug gold projectile. EL= 200J (2D PALE simulations).
The shock is formed very fast and the peak pressure in the shock is achieved within ~ 200 ps after the impact.
The pressure in the sub-Gbar range in the target is observed for the period of ~ 1 ns.

27. Generation of High-Pressure Shocks in the LICPA-driven Collider
The spatial profiles of pressure and density along the shock propagation axis (at r = 0) for the moment when the pressure reaches a peak value. 4ug gold projectile. EL= 200J (2D PALE simulations).
The compressed material with the pressure in the sub-Gbar range occupies ~ 10 – 20 um.
There is no preheating of the target material in front of the shock.

28. Generation of High-Pressure Shocks in the LICPA-driven Collider Parameters of the shock generated by a gold projectile in massive targets of various densities inferred from 2D PALE simulations. EL = 200J
Maximum shock pressure increases with an increase in the target density and for the high-density targets it reaches 500 Mbar.
The shock velocity and laser-to-shock energy conversion efficiency increase when the target density decreases and for the low-density targets the conversion efficiency attains a very high value ~ 20% . This value is by an order of magnitude higher than in other laser-based methods used so far.

29. Generation of High-Pressure Shocks in the LICPA-driven Collider
Parameters of the shock generated by a gold projectile in the massive Al target as a function of laser energy (results of 2D PALE simulations)
The maximum shock pressure increases nearly linearly with laser energy and reaches 700 Mbar at EL = 200J. The pressures in the sub-Gbar range are reached at EL > 50 J.
The laser-to-shock energy conversion efficiency at the moment when the shock pressure attains the peak value depends weakly on laser energy and attains ~ % .

30. Conclusions
A novel, efficient tool for generation of high-pressure shocks – the LICPA-driven collider – has been proposed and investigated experimentally and numerically.
It has been demonstrated that in the LICPA-driven collider with a 200J laser a gold projectile of the mass of 4 ug can be accelerated to 140 km/s with the energetic efficiency > 15%. The projectille parameters seem to be sufficient to produce sub-Gbar shocks in any solid materials.
It has been demonstrated that by collision of Al projectile - accelerated in the cylindrical LICPA-driven collider - with a massive Al target a strong shock of the pressure in the sub-Gbar range is generated with laser energy as low as 200J. So far such pressures were attainable only with multi-kJ lasers.
The shock pressure increases with an increase in the impacting projectile density and using a gold projectile enables us to increase the pressure by a factor ~ as compared to the case when low-density (e.g. CH, Al) projectile is used.
The shock pressure can be further increased by the use of the conical LICPA-driven collider instead of the cylindrical one. In the conical collider, the pressures up ~ 1Gbar seem to be attainable with laser energy as low as 200 J.
The above results suggest that using a multi-kJ laser as a LICPA driver, multi-Gbar quasi-planar shocks might be generated in the collider. Demonstrating such extremely strong shocks would open up a way towards energy efficient DT fusion ignited by the impact of LICPA-driven projectiles.
On the other hand, the pressures up to tens of Mbar could be produced in the collider with low-energy (~ 10 J) lasers accessible on the market. In particular, it would open up the possibility of conducting research in high energy-density science, including the EOS studies, also in small laboratories.

31. Supplement
Studies of dense matter in extreme conditions at pressures above 100 Mbar – the idea of the experiment on EU-XFEL
The laser beam of an optical nanosecond laser injected into the cavity of the LICPA-driven collider irradiates a projectile (e.g. Au disc) covered by a CH ablator and produces a hot plasma in the cavity. The pressure of the plasma accelerates the projectile to a high velocity (> 100 km/s) in the guiding channel of the collider. The accelerated projectile collides with a solid target placed at the guiding channel outlet. Due to the projectile impact a strong shock is generated and a high pressure is produced in the target. The target material compressed by the shock is diagnosed by the X-ray beam of the XFEL laser. The VISAR device placed behind the target records a disturbance of the target rear surface generated by the shock and enables us to determine the shock velocity in the target.