Hydrodynamic Instabilities

in Laser Plasmas

Cris W. BarnesP-24

July 3, 2002

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DEMONSTRATIONS•Why does water fall out of jar?

•Instability and stability

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Plasmas as Fluids•This talk is about “fluid dynamics”•But I’m a plasma physicist….

•Plasma fluids:– Unmagnetized

– No E or B fields

– Highly collisional

– Can be treated as single species (“no electron physics”)

– Generally caused by application of high energy density to near-solid material (such as by shock)

– (Can be) Compressible

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Fundamental Equations•Conservation of mass: particle balance•Conservation of momentum: force balance

(pressure balance)•Conservation of energy: energy balance

Ignoring time derivatives can define “hydrostatic equilibrium”.

Putting in time dependence and perturbing that equilibrium can analyze for stability.

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Examples of Rayleigh-Taylor• ICF

•Geophysics (material strength)

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Nonlinear behavior•What happens when ball hits floor?

•When mode amplitude is “significant fraction” of mode wavelength, the system become “nonlinear”.

•These instabilities generate “turbulence” and cause “mix”– ICF example

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Nano-technology (both foam production and precision machining) is an enabling technology for cylindrical implosion hydrodynamics

Mix Region

Foam Core

Outer Ablator

Increasingly Nonlinear Hydrodynamics

“Mix”

“Features”, both single and periodic

Direct-drive cylinder target for OMEGA

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Time resolved X-ray images provide substantial information from a single shot

polystyrene

C8H7Br

C8H6Cl2

CH2 foamphase reversal

l1.5 m initial amplitude; see trajectories, perturbation modal amplitudes, shock arrival, illumination asymmetry

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Ambiguous image center allows choice that reveals Fourier spectrum with fundamental (m=10), illumination imprint (m=4), and weak nonlinear coupling (m=6 & 14)

+*

Choose image center to reduce±1 sidebands around fundamental

Plotting Imaginary vs Real part of FFT for each mode for eachframe: see well-defined phases

Varying phase betweenm=10 and 4 and applyingmode-coupling simulates“odd-shaped” data

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More Stuff•Peter Wilson / Malcom Andrews Texas A&M

water tank experiment

This may be a “classic” field (Lords Kelvin and Rayleigh from the

Nineteenth Century) but cool stuff still possible today!

•Kelvin-Helmholtz•Richtmyer-Meshkov (impulsive)•Bell-Plesset (convergence matters)

CYLMIX and DNS calculations, and CYLART results from our own team

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We’ve established a useful, laser-based test bed for compressible convergent mix experiments• Implode cylinder with direct laser

irradiation• Hydrodynamically unstable at

plastic/Au and Au/foam interfaces (now using epoxy/Al)

• Shine x rays through cylinder• Measure radial extent of “mix

layer” of Au or Al into adjacent materials

• 1D experiment with Mach number ≈ 10, convergence ≈ 3, Pressure > 45 Mbars

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Experimental Results are compared to DNS (Direct Numerical Simulations) for different initial conditions

•Mix with rough initial conditions overwhelms end effects

•Differences exist between codes

•Both “bowing” and “filigree” exist

PETRA r-Z calculations

RAGE r-Z calculations

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rrZ

rrZ

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µm)

Time (ns)

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RageRage PetraPetra Experiment

We have made measurements of mix growth in time with rough surface finish•Done on different shots

(OMEGA backlighter limitations) but with the same type of target

•Growth consistent with linear after shock breakout, and with DNS simulations

22602 3.2 nsFrames 3c

18687 4.7nsFrames 2c

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Hydrodynamic Instability and Turbulent Mix

•Classic field of fluid dynamics studied world-wide at many institutions

8th International Workshop on the Physics of Compressible Turbulent Mixing was held in

Pasedena last December.•High Atwood number (“variable density,

inhomogeneous turbulence”), compressible (high energy density), convergent systems are at the forefront of challenging science at National Labs with new experimental and theoretical tools becoming available to study them.