Deuterium-Deuterium Thermonuclear Fusion due to Acoustical Cavitation ( Theoretical Analysis)

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SONOLUMINESCENCE AND INDUCED FUSION WORKSHOP. Deuterium-Deuterium Thermonuclear Fusion due to Acoustical Cavitation ( Theoretical Analysis). Robert I. NIGMATULIN Ufa-Bashkortostan Branch of Russian Academy of Sciences - President nigmar@anrb.ru Richard T. Lahey, Jr - PowerPoint PPT Presentation

Transcript of Deuterium-Deuterium Thermonuclear Fusion due to Acoustical Cavitation ( Theoretical Analysis)

  • Deuterium-Deuterium Thermonuclear Fusion due to Acoustical Cavitation (Theoretical Analysis)

    Robert I. NIGMATULINUfa-Bashkortostan Branch of Russian Academy of Sciences- Presidentnigmar@anrb.ru

    Richard T. Lahey, JrRensslear Polytechnic Institute Troy, NY, 12180laheyr@rpi.edu

    19 June, 2003Arlington, VA

    SONOLUMINESCENCE AND INDUCED FUSION WORKSHOP

  • THE TEAMUSARPI Richard LAHEY, Jr.Robert BLOCKFrancisco MORAGA

    ORNLRusi TALEYARKHANColin D. WESTJeing S. CHO

    RUSSIAUfa Robert I. NIGMATULIN Iskander Sh. AKHATOVNaila K. VAKHITOVARaisa Kh. BOLOTNOVAAndrew S. TOPOLNIKOVMarat A. ILGAMOV

    KazanAlexander A. AGANIN

  • SPHERICAL SHOCK WAVE CONVERGENCE AND CUMULATIONInitiation of a Spherical Shock Wave by the Convergent InterfaceFocusing of the Spherical Shock Wave at the Center of the BubbleThe Spherical Shock Wave after the Reflection from the Center of the BubbleSelfsimilar Cumulation of the Spherical or Cylindrical Shock Wave from the Infinity Guderley, 1942; Landau & Stanyukovich, 1955; Nigmatulin, 1967

  • Specific Features ofSingle Bubble Sonoluminescence Equilibrium bubble size a0 ~ 3 5 mm Adiabatic bulk compression gas temperature Tmax ~ 5000 K (?!) Cold water effect Noble gas effect Extremely short light flashes dtF ~ 50 ps = 510-11sLight RadiationTmax ~ 5000 K (adiabatic compression)dtF ~ 10-11stRadius of the bubbleattwa0amintwdtC ~ 10-8s

  • Supercompression by Convergent Spherical Shock WaveMoss et al (Livermore National Laboratory, 1994) Radius of the Hot Plasma Core: 109 m = 1 nm Density: 10 g/cm3 = 104 kg/m3 Temperature: 106 K Time Duration: 1011 s = 10 ps

    No Thermonuclear Fusion

  • HOW TO AMPLIFY THE SUPERCOMPRESSION? GAS IN THE BUBBLE: CONDENSING VAPOR (VAPOR CAVITATION) - Minimizing Effect of Gas Cushioning - Higher Kinetic Energy of Convergent Liquid COLD LIQUID LARGE MOLECULES (ORGANIC) LIQUID Low Sound Speed in Vapor AMPLIFING THE ACOUSTIC WAVE (pI 15-20 bar) CLUSTER of the Bubbles

  • Kinetic Energy of Convergent Flow around the Bubble (CFAB)Rmax 500 800 mcm (in SBSL Rmax 50 80 mcm) p 15 bar (in SBSL p 1.5 bar)In our experiments: the maximum mass of the gas 103 times higher BUT the final mass of the gas in the Bubble m is only 50-100 times higher (because of the condensation)than in SBSL the Kinetic Energy K of CFAB is 104 times higher K/m and Tmax is = 100 200 times higherIt means that in our experiment we may get Tmax (100-200)106 K

  • GasLiquida(t)Mass, Momentum, Energy Conservation Differential EquationsMassMomentum Energy

  • INTERFACIAL BOUNDARY CONDITIONS (r = a(t)) Mass:Momentum:Energy:Kinetics of phase transition (Hertz-Knudsen-Langmuir Eqn):pS(T) saturation pressure, l evaporation heata - accommodation (condensation) coefficient- (Labuntsov, 1968)- intensity of phase transition

  • MI-GRUNEIZEN EQUATIONS OF STATE p and pp cold or potential internal energy and pressure due to intermolecular interaction T and pT thermal internal energy and thermal pressure c - chemical internal energy

  • BORN-MAYER POTENTIALLIQUID PHASE (NONDISSOCIATED )LENNARD-JONES POTENTIALpp = R n A mp = ppV 1 pV0

  • SHOCK ADIABAT (D-u) FOR LIQUID ACETONE(Trunin, 1992)Trunin, 1992D Shock Wave SpeedU Mass Velocity after the Shock WaveMASS VELOCITY, U, km/sDissociated

  • RELATIVE VOLUME, r0/rSHOCK ADIABAT & ISOTHERMS (P-V) for D-Acetone (C3D6O)Isotherms of VaporPRESSURE p, barShock adiabat of Liquid0 D = (D U)p p0 = 0 D U

  • ISOTHERMS (P-V) & SATURATION LINE for D-AcetoneTEMPERATURE, KENERGY , 105 m2/s2Evaporation Heat (ig-il)LiquidVaporInternal Energy and Evaporation heatRELATIVE VOLUME, r0/rPRESSURE p, barIsotherms CC

  • DISSOCIATION of GAS

  • IONIZATION of DISSOCIATED GAS

  • IONIZATION CONSTANTS

  • LiquidTHERMAL CONDUCTIVITY for acetone

  • KINETICS OF FUSION

  • Different Stages for Bubble Expansion and Compression Low Mach Regime (M > 1) Hydro Code a,m500t, sTg=Tg(t, r)pg=pg(t)Heat conducting, homobaric gas(M < 10 -1)Tg=Tg(t, r)pg=pg(t, r)M > 130SBSLBF

  • For GAS (vapor):For LIQUID:Rayleigh-Plesset equationLow Mach regime

  • THERMAL CONDUCTIVITY EQUATIONS FOR HOMOBARIC BUBBLE (pg = pg(t)) IN INCOMPRESSIBLE LIQUID (l = const)

  • Cluster Amplification EffectVoid fraction Number of bubbles N = 50Maximum microbubble radiusRadius of the cluster a,mmmmp,bart, st, sp, bart = 32 sr, mmr = 0r = 2 mmr = 4 mma 20= 0.05a = a = 4000 max mmR = 4 mm0r = 0r = 2 mmr = 4 mmR

  • LOW MACH (microsecond) STAGE

  • LOW MACH (microsecond) STAGE

  • Transition from LOW MACH to HIGH MACH STAGE (microsecond stage)

  • HIGH MACH (nanosecond) STAGE

  • HIGH MACH (nanosecond) STAGE

  • PARAMETERS IN THE CENTER OF THE CORE

  • ubble radius evolution for deuterated acetone C3D6O; non-dissociated liquiddissociated liquidCold dissociation because of the super high pressure (105 bar) in liquid needs 102 ns;LIQUID DISSOCIATION IMPACTSuper high pressure in liquid (near the bubble interface) takes place 1 ns

  • COLD ELECTRONS Te
  • Neutron production distributionand maximum density, temperature and velocity

  • INTERNAL GAS ENERGY AS THE SUM OF COMPONENTS

  • AcetoneTEMPERATURE, KpT/p=104 kg/m3=103 kg/m3

  • LOW TEMPERATURE (condensation) EFFECTMinimum bubble mass and total number of emitted neutronsvs liquid temperature, T0

  • Fig.1. Temporal dependence of the air bubble radius R and some bubble shapes in the course of a single-period harmonic pressure oscillation in water with p = 3 bar, /2 = 26.5 kHz, for a20/R0 = 2.510-2, R0 = 4.5 m . While plotting the shapes, the bubble radius was taken to be R0[1 + 0.3{3.5lg(R/R0) + 1.5|lg(R/R0)|}].Incopmpressible viscous liquid, homobaric Van-der-Waals gas.

  • Temporal dependences of the radius R of an air bubble in water, the sphericity distortion a2 /R and some bubble shapes just before the time of the collapse tc under harmonic forcing with p=5bar, /2=26,5 kHz for two values of the initial distortion. Convergent and divergent shock waves in the bubble are shown in figure (b). a20/R0 = 0.03a20/R0 = 0.001 Incompressible viscous LiquidHomobaric Van der Waals Gas

  • SUMMARY OF THE ANALYSISDensity: 20 - 80 g/cm3

    Temperature: 108 K = 10 KeV

    Pressure: 1011 barVelocity: 900 km/sTime Duration: 10131012 s = 101-100 ps

    Radius of the Fusion Core: 50 nm

    Number of nucleus: 20 109Fast Neutron & Tritium Production 10-1 - 10 per collapse10 g/cm3

    106 K = 10-1 KeV

    Bubble Fusion (ORNL+RPI+RAS)Sonoluminescence (LLNL)10 ps

    1-3 nm

  • FINDINGS

    COLD LIQUID Effect

    CLUSTER effect

    NON-DISSOCIATION of Liquid

    COLD Electrons

    SHARPENNING:Node size for Fusion Core r 0.1 nm