Can time-like shocks

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Can time-like shocks

ignite the pellets in the

National Ignition Facility?

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L.P. Csernai, Minneapolis 2013 2

& Dieter Schneider, LLNL, Talk at GSI 2013

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Sun-surface - plasma

The picture was made using the Swedish Solar Telescope on the Canary Island of La Palma. The filaments' newly revealed dark cores are seen to be thousands of kilometers long but only about 100 kilometers wide.

Resolving features 100 kilometers wide or less At optical wavelengths,

these images are sharper than even current space- based solar observatories can produce. Recorded on 15 July 2002

Viscosity/Scaling are important to extrapolate to other scales !

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Stability of the core/crust HS.

• Landau-Lifsitz: mechanical stability is limited  V2,

rocket engine- gas-turbine- accidents,

• Fusion device instabilities

• Solved by Bethe /Los

Alamos publ. - Zeldovich, Raiser: High Temp.

phenomena

Hypersurface

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RT – instabilities in Tokamak

• The figure

above shows three-

dimensional isosurfaces of the pressure as the instability develops along ridges

dominantly

aligned along

the ambient

magnetic field.

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Shocks, Detonations, Deflagrations

…

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Next movie:

blue flame is stable,

red/yellow is

fluctuating and

turbulent.

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-1 +1

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-1

+1

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Aside: Taub-adiabat and Rayleigh line

Taub [‘48]

missed the sign

=> was not

applicable for

freeze- out.

The Rayleigh line is a straight line in the [P,X] plane. It gives the locus of final states “2” if the initial state “1” is known. The slope, j, is given by the current across the front.

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Aside: Taub-adiabat and Rayleigh line

Comparing the two equations for the current, j , :

So, we obtain the Taub adiabat :

The locus of the possible final states, “2”, lies on the Taub adiabat.

If the initial state and the EoS of the final state is known the Taub

adiabat with the Rayleigh line determine the final state.

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Stability, Reynolds number

- kinematic viscosity

- viscosity - density

- length - velocity

In an ideal fluid any small perturbation increases and leads to turbulent flow. For stability

sufficiently large viscosity and/or heat conductivity are needed!

Re < 1000 - 2000

(Calculations are also stabilized by numerical viscosity.)

Interesting and important: in RFD detonation fronts are stabilized by radiation and heat conductivity. E.g. :

- Rocket propulsion

- Implosion, fission- and fusion reactions

- Heavy Ion reactions

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Welding flames:

Again: blue flame is stable

& focused, red/yellow is

wider, fluctuating and

turbulent.

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Preventing turbulence

The

instability of

deflagratio n- (flame-) front is not desirable at

supersonic fronts.

With

increasing temperatur e the

radiation becomes dominant and

stabilizes

the flame

front.

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Shocks

• Rankine and Hugoniot’s description was

generalized to relativistic flow by A. Taub in 1948 [A. Taub, Phys. Rev. 74 (48) 328.]

• This work was used to describe Mach shock cones and shock compression in early works.

These fronts were causally connected.

• Based on Taub’s work, fronts “propagating super-luminously” were considered non-

physical. E.g. [ Landau & Lifshitz: Fluid

dynamics]

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L.P. Csernai 30

Phase Transitions in Shocks

• Detonation, through a non causally connected hyper-surface (i.e. with time-like normal)

seemed to be necessary to complete the phase transition. [N.K. Glendenning & T. Matsui &, Phys. Lett 141B (1984) 419.]

• Tetsuo Matsui, Berkeley discussions.

• Taub’s work was incomplete and could be generalized  rapid transitions are possible.

• We tried to publish it in PRL, 3-4 rounds, 84, 85,… referees claimed it is acausal, so, it did not work.Tetsuo gave it up. … maybe this is not possible, even if no mistake is found. …

• I had to find an example to show it is

unavoidable. I did in 86. PRL turned down: “it is

trivial” (?!)  went to another journal.

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Detonations

• $ others who know about detonations.

• Zel’dovich & Raiser: High T. Phenomena (1970)

• Igor, Zel’dovich’s former grad. student, then at the Kurchatov Institute, Igor Mishustin, .. understood the work.

• Thus, the work on the existence of time-

like detonations was published in 1987:

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Published in Russian and English

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Shock adiabat Detonation adiabat

Timelike h.surface

Detonation adiabat (*) and the Rayleigh line

(*) Taub adiabat or

Rankine-Hugoniot adiabat

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The example was a simple analytic model of a radiation dominated implosion.

This could come up in a pellet fusion experiment, or in other highly

energetic implosion where radiation is dominating.

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Burning and

radiating

outside shell

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Interestingly in Heavy Ion physics the space-time picture of hadronization and freeze out of

expanding and cooling QGP is very similar.

Recognized also in

[LV. Bravina et al., PL 354B (95)192.]

Thus, if the process is rapid, i.e. sudden

hadronization and freeze out, then it can be

described by the same formalism.

But can the

hadronization be a rapid

process ???

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Conclusions

• To avoid instabilities do not compress the fuel more than absolutely necessary. Avoid ablator!

• Make the irradiation faster, (~picosecond) , so that the fuel is heated up in a time needed for the light (or other beam) to cross the target.

In this short time not mechanical or pressure instabilities will occur.

• Make the target transparent enough so that the beam can just reach the opposite side of the target.

• Make the opacity such that all the beam energy is absorbed in the target, so it is not wasted.

• This goal is quite different from the present one, which focuses only

on compression.

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END

Thank you!

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Viscosity vs. T has a minimum at the 1

^st

order phase transition.

This might signal the phase transition if viscosity is measured.

At lower energies this was done.

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L.P. Csernai, Minneapolis 2013 42 Helium (NIST)

Water (NIST) QGP (Arnold, Moore, Yaffe)

This phenomenon can help us to detect experimentally the critical point:

η can be determined from (i) fluctuation of flow parameters and from (ii) scaling properties of flow parameters.

[Prakash, Venugopalan, .]

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KHI  ROTATION

KHI

_2.4 fm

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