Supersonic plasma jet interaction with gases and plasmas

Transcription

1 ICPP 2008 FUKUOKA september 11, 2008 Supersonic plasma jet interaction with gases and plasmas Ph. Nicolaï 3.5 ns 8.5 ns 13.5 ns He 15 bars 2 mm CELIA, Université Bordeaux 1 - CNRS - CEA, Talence, France

2 Co-authors C. Stenz, X. Ribeyre, V. Tikhonchuk CELIA, Université Bordeaux 1 - CNRS - CEA, Talence, France A. Kasperczuk and T. Pisarczyk Institute of Plasma Physics and Laser Microfusion, Warsaw, Poland L. Juha, E. Krousky, K. Masek, M. Pfeifer, K. Rohlena, J. Skala Institute of Physics AS CR, Prague, Czech Republic J. Ullschmied Institute of Plasma Physics, Prague, Czech Republic D. Klir, J. Kravarik, P. Kubes, M. Kalal Czech Technical University, Prague, Czech Republic

3 Motivations Issues relevant to astrophysical objets Collimation and propagation of jets over long distance Interaction of these jets with suroudding media X-ray emission of these jets Issues relevant to the inertial fusion joints surface bumps fill tubes, ) Test for large multi D radiation hydrodynamic codes Clumpy HH jet Hartigan 2006

4 Convergent plasma flows produce jets (radiative collapse) Multi-beams X-rays Z-pinch B laser laser X Jet laser laser X Jet Jet X conical target holhraum wire array laser laser Jet These jets can be scaled to astrophysical conditions D. Farley et al, Phys. Rev. Lett. 83, 1982 (1999) J Foster et al,phys. Plasma 9, 2251 (2002) S. Lebedev et al, Astrophys. J 564, 113 (2002) D. Ryutov et al, Astron. Astrophys. 518, 821 (1999) Foam-filled cone target B. Loupias et al, Phys. Rev. Lett. (2007)

5 Jet formation using a single laser beam The experiment was carried out at the PALS iodine laser facility: low energy, simple and reproducible conditions target jet 600 µm Laser E 100 J t 300 ps Experimental electron density distribution Mach number : M = Length : L = 3-4 mm Velocity : U = 500 km/s duration τ 10 ns The jet is produced due to the radiative cooling of plasma Competition between expansion time and radiation cooling time Confirmed by 2D radiation magneto hydrodynamic code This jet can also be scaled to astrophysical parameters Ph. Nicolaï et al, Phys. Plasmas 13, (2006), T. Pisarczyk et al, ibid, (2006)

6 Experimental setup The experiment was carried out at the PALS iodine laser facility The laser beam: E ~ 100, λ = μm, t = 300 ps, R = 300 μm L L L L The gas puff : Argon or helium gas. Presssure ~2-40 bars The plasma density profiles were obtained by means of a 3-frame interferometric system (3ω) The plasma X-ray emission were obtained by means of a 4-frame X-ray pinhole camera (.01-1kev)

7 Structure and evolution of the working surface Shadowgraphic and interferometric images 0.5 argon (10b) t = 4ns bow shock t = 7ns Cu copper jet laser marks t =10ns density accumulation narrow tip nozzle other shot reverse shock copper jet t = 7ns laser marks Detailed structure with three sequential snapshots Very good reproducibility shot after shot

8 Structure and evolution of the working surface X-ray images [10 ev 1 kev] 2 mm bow shock (a) Cu jet noze 0 ns 5 ns 10 ns 30 tilt density accumulation (b) 2 mm 0 ns 5 ns 10 ns Good correspondence between X-ray images and interferograms bow shock, Cu jet, narrow tip and density accumulation

9 Effect of Ar gaz pressure on the working surface shadowgraphic images copper jet bow shock 0 bar 2 bars 5 bars reverse shock bow shock reverse shock 15 bars laser marks Gas pressure strongly modifies the working surface shape from an arrow form to a more spherical shape The decrease of the WS thickness linked to radiation losses

10 Effect of Ar gaz pressure on the working surface 2 mm (a) 8 ns 2 bars 2 mm 13 ns (b) 9 ns 10 bars 14 ns X-ray images confirm the change of the WS shape For 10 bars Ar, hydrodynamic instabilities appear in the WS

11 Bow shock position and density ratio For each pressure, several shots have been done improving confidence mean value (mm) Bow shock position 10 ns 7 ns 4 ns gas pressure (bar) By balancing the momentum fluxes at the jet head and at bow shock ρ (v v ) ρ v 2 2 jet jet bs gas bs one can estimate the bow shock velocity v v 1+ bs jet η ( 1/2 ) 1 with η = ρ ρ jet gas A pressure increase induces a shorter propagartion length The relative velocities between 4ns and 10 ns, corresponding to the density plateau, equal 140 km/s (15 bars), 185 km/s (10 bars), 210 km/s (5 bars) Given the jet velocity ~ 400 km/s, the density ratio, η, varies between 0.3 (15 bars) and 1.2 (5 bars) The Working Surface thickness decreases as gas pressure increases, from 0.85 mm to 0.5 mm for 7 ns. After 10 ns, the W.S. becomes thinner.

12 Effect of He gas pressure on the working surface Cu 10 bars 15 bars WS He 20 bars reverse shock bow shock 30 bars 0.1 nozzle copper jet Contrary to Ar plasma, He gas pressure variation does not induce significant change in the WS shape: the radiation losses are small The WS thickness slightly decreases as the gas pressure increases and the distance of the Cu jet propagation through gas decreases

13 X-ray images for various HELIUM gaz pressures 9.5 ns 10.5 ns 2 mm 10 bars 20 bars 9.5 ns 2 mm 8.5 ns 30 bars 40 bars One does not have the agreement of the X-ray images with previous shadowgrams Emission just arises from copper material - bow shock in He gas is not visible The shape remains the same similitude with the low Ar gas pressure

14 Bow shock position and W.S. thickness (mm) ns 7 ns * * * * * * * * * bow shock Mach disk working surface thickness gas pressure (bar) A pressure increase induces a shorter propagation length, 20 The relative velocities varies between 270 km/s (15 bars) and 195 km/s (40 bars) which involve a density ratio between 4 (15 bars) and 1 (40 bars) The working surface thickness exceeds 1 mm for all pressures indicates more adiabatic conditions in the interaction zone

15 Estimate of Radiation losses For a plane slab of thickness d, the cooling time writes : Energy density * d ρ d C T Z+1 v -3 1 τ c = = = f ( τ) T κ m radiation flux 2FR A where f (τ) is a function of the optical depth τ = dρκ m κ m = mean Planck opacity 15 = 4 π 0 κ 3 u ν u e du hν with u = T cm 2 /g κ argon ν helium ρ = 4 10 / g cc T = 100 ev ν (ev) 2 Ar : κm = 79cm / g τc 2ns 2 He : κm =.089cm / g τc 2 µ s from bremsstrahlung emission Ar : τ c He : τ 450 ns 3 s c µ to be compared with the jet propagation time ~ 5 ns Drake, High-Energy-Density Physics, Springer, 2006 Tsakiris JQSRT Vol. 38, No 5, pp. 353 (1987)

16 0. 4 ns bow shock interface 7 ns 10 ns copper Structure and evolution of the working surface Simulation* correctly reproduces interaction zone laser marks Helium gas, pressure ~ 10 bars interface copper helium interface bow shock 0. - bow shock reverse shock reverse shock reverse shock Simulation allows to identify physical processes : bow shock in gas, reverse shock in copper jet, laser absorption, The gas behind the bow shock remains warm implicating a large W.S. Helium gas induces an adiabatic evolution of the w.s. *PH Maire et al, SIAM JSC 29, 1781 (2007), J. Breil et al, J. Comp. Phys. 224, 785 (2007)

17 Effect of gaz pressure on Working Surface Helium gas [7 ns] 7 b bow shock 15 b bow shock 30 b bow shock 0. - interface copper helium reverse shock interface helium reverse shock copper interface laser marks reverse shock The working surface shape remains the same As Cu jet propagation through gas decreases as gas pressure increases (lateral and longitudinal expansions are reduced) Simulation images agree with experiment

18 Structure and evolution of the working surface X-ray images [10 ev 1 kev] 7 bars 15 bars 30 bars tilt ns 2 mm 10.5 ns 20 bars 30 bars Only copper plasma emits X-rays The bow shock propagation through helium gas does not appear The copper jet form remains (more or less) identical

19 Structure and evolution of the working surface 0. - copper argon 10ns tip reverse non adiabatic case : argon gas argon copper 10ns tip reverse laser marks 3 bars shock 6 bars shock w.s. 12 bars tip argon 0. As the pressure increases as the w.s. form changes a narrow tip appears for high pressure The interaction zone structure strongly differs from the helium case. Formation of a dense/thin shell due to radiative cooling which reduces temperature behind the «bow» shock The argon gas accumulation in shell may lead to hydrodynamic instabilities Blondin et al, Astrophys. J, 360, 370 (1990)

20 Structure and evolution of the working surface X-ray images [10 ev 1 kev] 3 bars 6 bars 2 mm ns Conformity between previous density distributions and X-ray images Shape change Density accumulation and nose cone also observed in X-ray image

21 Similarity conditions Can the experiment be scaled to an astrophysical jet?

22 Conclusion Supersonic jet study using a 100J single laser beam facility Adiabatic or cooling jet structures observed by changing gas composition These structures are correctly simulated by our 2D radiation hydrocode These jets verify the similarity criteria and apply to astroϕ conditions More details in ref; Ph. Nicolaï et al, Phys. Plasmas 15, (2008)

23 The numerical tool We use the 2 D radiative magneto-hydrodynamic code, CHIC* second order cell centered Lagrangian scheme ALE scheme unstructured meshes classical or nonlocal thermal conduction nine points scheme thermal coupling detailled radiation transport LTE or NLTE opacities real Equation of State (QEOS and Sesame) 3D ray tracing for laser propagation self-generated magnetic fields thermonuclear burn *PH Maire et al, SIAM JSC 29, 1781 (2007), *J. Breil et al, J. Comp. Phys. 224, 785 (2007)

24 The use Conditions of hydrocode One has to verify that the mean free paths are shorter than the dimensions of structures observed in experiment Fast copper ions are slowed down in collisions with the ions and e- of ambiant gas By using the NRL plasma formulary!, the collision frequencies read υ = 9.10 nzz Λ ( A + A ) A ε s 8 a /2 3/2 1 Cu a i a Cu Cu a Cu a Cu Cu υ nz Λ A T s /2 1 Cu e e Cu Cu e Cu e For our parameters; kinetic energy of Cu ion ε 50 kev, T~100 ev, ρ~10-4 g/cc 9 1 υ υ 4.10 Cu a Cu e s Given the jet velocity v Cu = 400 km/s, the m.f.p; λ = v /( υ + υ ) 50μ Cu Cu Cu a Cu e m The gas is not motionless (bow shock), and the relative velocity should be smaller. As! J. Huba, NRL, Washington DC, (2007) 4 λcu v if v v/2 λcu λcu /16

25 Energie balance : Helium gas case (15 bars) (J) Copper w/o gas kinetic energy thermal energy X-ray losses (ns) E las. = 100J (J) Without gas X-ray Copper with He gas kinetic Cu He thermal After 9 ns, 20% of the energy lost through X-ray emission, 66% transformed in kinetic energy and 11% in thermal energy. At the laser pulse end, thermal energy reaches 52% With helium gas After 9 ns, radiated energy (21%) and copper thermal energy (11%) remain the same. Only the copper kinetic energy is reduced (40%) and decreases with time. Energy lost by copper is transformed into kinetic (10%) and thermal (15%) energies of He gas (ns)

26 Energie balance : argon gas case (6 bars) (J) Copper w/o gas kinetic energy thermal energy X-ray losses (ns) E las. = 100J (J) Without gas thermal Copper with Ar gas kinetic Cu Ar X-ray (ns) After 9 ns, 20% of the energy lost through X-ray emission, 66% transformed in kinetic energy and 11% in thermal energy. With argon gas After 9 ns, radiated energy (30%) and copper thermal energy (15%) increase. The copper kinetic energy only represents 29%. Fast increase of argon energies for first ns then decrease due to X-ray losses Losses are greater than energy gain from copper material

27 Density maps obtained from interferograms unfolded with Abel inversion Helium gas pressure = 10 bars a b 3D view (10 ns) t = 10 ns c end of the density plateau d One accesses to the density range and a more detailed information

28 Bow shock position and W.S. thickness For each pressure, several shots have been done improving confidence mean value (mm) Bow shock position * * * * 10 ns 4 ns * * * * * on axis off axis (mm) * * 10 ns * * 7 ns bow shock mach disk * * * working surface thickness gas pressure (bar) gas pressure (bar) «Off axis» and «on axis» positions converge to the same value as the P increases the bow shock shape becomes spherical The triangular shape elongates with time at low pressure The Working Surface thickness decreases as gas pressure increases, from 0.85 mm to 0.5 mm for 7 ns. After 10 ns, the W.S. becomes thinner. P. Hartigan, Astrophys. J. 339, 987 (1989)

29 Experiment Effect of the target atomic number Experimental electron density distribution E = 100 J λ= μm R = 300 μm 400 ps pulse aluminium copper silver The jet is produced due to the radiative cooling of plasma