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

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

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

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  1. 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 Rensslear Polytechnic Institute Troy, NY, 12180 laheyr@rpi.edu 19June, 2003 Arlington, VA

  2. THE TEAM • RUSSIA • Ufa • Robert I. NIGMATULIN • Iskander Sh. AKHATOV • Naila K. VAKHITOVA • Raisa Kh. BOLOTNOVA • Andrew S. TOPOLNIKOV • Marat A. ILGAMOV • Kazan • Alexander A. AGANIN • USA • RPI • Richard LAHEY, Jr. • Robert BLOCK • Francisco MORAGA • ORNL • Rusi TALEYARKHAN • Colin D. WEST • Jeing S. CHO

  3. SPHERICAL SHOCK WAVE CONVERGENCE AND CUMULATION Initiation of a Spherical Shock Waveby the Convergent Interface • Selfsimilar Cumulation • of the Spherical or Cylindrical Shock Wave • from the Infinity • Guderley, 1942; • Landau & Stanyukovich, 1955; • Nigmatulin, 1967 Focusing of the Spherical Shock Waveat the Center of the Bubble The Spherical Shock Waveafter the Reflectionfrom the Center of the Bubble

  4. tw~ 30s 6 days dtC ~ 30 ns 7 min dtF ~ 50 ps 0,7 s Specific Features ofSingle Bubble Sonoluminescence a • 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 = 5·10-11s tw Radius of the bubble a0 amin dtC ~ 10-8s t tw Tmax ~ 5000 K (adiabatic compression) Light Radiation dtF ~ 10-11s t

  5. Supercompression by Convergent Spherical Shock Wave Moss et al (Livermore National Laboratory, 1994) Radius of the Hot Plasma Core: 109 m = 1 nm Density: 10 g/cm3 = 104 kg/m3 Temperature: 106 K Time Duration:  1011 s = 10 ps No Thermonuclear Fusion

  6. HOW TO AMPLIFY THE SUPERCOMPRESSION? • AMPLIFING THE ACOUSTIC WAVE (pI  15-20 bar) • 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 • CLUSTER of the Bubbles

  7. Kinetic Energy of Convergent Flow around the Bubble (CFAB) p 15 bar(in SBSLp  1.5 bar) Rmax 500 – 800 mcm(in SBSLRmax 50 – 80 mcm) In our experiments: • the Kinetic EnergyKof CFAB is104 times higher • the maximum mass of the gas 103 times higher BUT the final mass of the gas in the Bubblemisonly 50-100times higher (because of the condensation) • K/m and Tmax is = 100 – 200 times higher than in SBSL It means that in our experiment we may getTmax (100-200)106 K

  8. Mass, Momentum, Energy Conservation Differential Equations Liquid a(t) • Mass Gas • Momentum • Energy

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

  10. MI-GRUNEIZEN EQUATIONS OF STATE - averaged heat capacity and Gruneizen Coefficient • pandpp– “cold” or potential internal energy and pressure due to intermolecular interaction • TandpT– thermal internal energy and thermal pressure • c - chemical internal energy

  11. LENNARD-JONES POTENTIAL pp = Rn – Am p = pp BORN-MAYERPOTENTIAL p V 1 V0 LIQUID PHASE (NONDISSOCIATED )

  12. SHOCK ADIABAT (D-u) FOR LIQUID ACETONE(Trunin, 1992) Non-dissociated Non-dissociated Dissociated Shock Wave Speed, D, km/s Cl MASS VELOCITY, U, km/s D U Dissociated Trunin, 1992 MASS VELOCITY, U, km/s D–Shock Wave Speed U – Mass Velocity after the Shock Wave

  13. SHOCK ADIABAT & ISOTHERMS (P-V) for D-Acetone (C3D6O) ●Trunin, 1992 6000 K NDis 5000 K Dis 4000 K 3000 K PRESSURE p, Mbar Dis 2000 K 1000 K NDis RELATIVE VOLUME, r0/r Isothermsof Vapor Shock adiabat of Liquid PRESSURE p, bar 0D =  (D – U) p – p0 = 0D U RELATIVE VOLUME, r0/r

  14. ISOTHERMS (P-V) & SATURATION LINE for D-Acetone Internal Energy and Evaporation heat Isotherms C C Vapor ENERGY , 105 m2/s2 PRESSURE p, bar Liquid Evaporation Heat (ig-il) RELATIVE VOLUME, r0/r TEMPERATURE, K

  15. 0.9 0.1 Td DISSOCIATION of GAS

  16. IONIZATION of DISSOCIATED GAS

  17. IONIZATION CONSTANTS

  18. THERMAL CONDUCTIVITY for acetone 0 . 0 8 Gas 6 1 0 Gas 5 1 0 0 . 0 6 ) ) K K 4 1 0 3 3 s s ( ( / / 0 . 0 4 m m 3 1 0 g g k k , , 2 1 0 g 0 . 0 2 0 l g l / g l 1 1 0 0 . 0 0 0 1 0 2 0 0 4 0 0 6 0 0 8 0 0 1 0 0 0 3 5 7 9 1 0 1 0 1 0 1 0 T , K T , K Liquid

  19. KINETICS OF FUSION

  20. Different Stages for Bubble Expansion and Compression • Low Mach Regime (M << 1) Rayleigh-Plesset + Thermal Conductivity Eqn • Middle & High Mach Regime (M ~ 1, and M >> 1)  Hydro Code a,m 500 BF Tg=Tg(t, r) pg=pg(t) Heat conducting,homobaric gas (M < 10-1) M >1 Tg=Tg(t, r) pg=pg(t, r) SBSL t, s 30

  21. Low Mach regime For GAS (vapor): For LIQUID: Rayleigh-Plesset equation

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

  23. Cluster Amplification Effect Void fraction Number of bubbles N=50 Maximum microbubble radius Radius of the cluster a, m R = 0.05 a 20 a = a = 400 mm 0max R = 4 mm 0 r = 0 r = 2mm r = 4mm r = 4mm r = 2mm t,s m r = 0 p, bar p,bar t = 32 s m m t, s r,mm

  24. LOW MACH (microsecond) STAGE

  25. LOW MACH (microsecond) STAGE

  26. Transition from LOW MACH to HIGH MACH STAGE (microsecond stage)

  27. HIGH MACH (nanosecond) STAGE 4 0 1 9 2 0 104 1 8 3 0 3 m m / 102 m g 2 0 k , , a t - t * r 1 6 2 0 1 0 1 7 1 6 0 1012 8 1 9 2 0 1010 1 8 4 108 s / m r a k 106 b , 0 t , d * / p 104 a d 1 7 t - t - 4 102 1 6 2 0 1 6 1 - 8 - 5 . 0 0 . 0 5 . 0 , n s t - t * 1 9 108 2 0 1 8 106 K , 1 7 * T 104 1 6 102 - 5 . 0 0 . 0 5 . 0 , n s t - t *

  28. HIGH MACH (nanosecond) STAGE

  29. PARAMETERS IN THE CENTER OF THE CORE

  30. LIQUID DISSOCIATION IMPACT 5 0 4 0 ] m k m 3 0 [ S U I D 2 0 A R 1 0 0 - 1 0 - 5 0 5 T I M E [ n s ] “Cold dissociation” because of the “super high pressure” (105 bar) in liquid needs 102 ns; “Super high pressure” in liquid (near the bubble interface) takes place 1 ns dissociated liquid non-dissociated liquid Вubble radiusevolution for deuterated acetone C3D6O;

  31. “COLD” ELECTRONS Te<< Ti (during 10-13 s) CV = 2000 m2/c2K, not 8000 m2/c2K

  32. Neutron production distributionand maximum density, temperature and velocity 0 . 1 6 Dr=0.132 nm Dr=0.256 nm 0 . 1 2 1 - m Dr=1.32 nm n 0 . 0 8 , r Dr=2.65 nm N Dr=5.29 nm 0 . 0 4 Dr=13.2 nm Dr=26.5 nm 0 . 0 0 100 101 0 2 0 4 0 6 0 8 0 1 0 0 r , n m , n m D r r* r 1010 0 . 1 6 0 0 . 1 6 F 4 . 0 T m a x 109 K N , r 0 . 1 2 - 4 0 0 0 . 1 2 x 3 . 0 a 108 m s T 1 / 1 - - m m m 107 & k n n 0 . 0 8 - 8 0 0 0 . 0 8 , , , 3 N u 2 . 0 m x 106 r r a m a x N / r N m g u m a x k 105 , 0 . 0 4 - 1 2 0 0 0 . 0 4 N x 1 . 0 a r m 104 r 103 0 . 0 0 - 1 6 0 0 0 . 0 0 0 . 0 10-2 10-1 100 101 102 103 10-2 10-1 100 101 102 103 10-1 102 , n m , n m r r

  33. INTERNAL GAS ENERGY AS THE SUM OF COMPONENTS

  34. Acetone =103 kg/m3 pT/p =104 kg/m3 TEMPERATURE, K

  35. LOW TEMPERATURE (condensation) EFFECT 2 5 0 3 2 0 0 a = 1.0 2 a = 0.1 1 5 0 Normalized neutron production, N/N273 1 0 0 MINIMUM MASS, mg min, ng 1 a = 0.1 a = 1.0 5 0 0 0 2 5 0 2 6 0 2 7 0 2 8 0 2 9 0 3 0 0 2 5 0 2 6 0 2 7 0 2 8 0 2 9 0 3 0 0 LIQUID TEMPERATURE, Tl0, K LIQUID TEMPERATURE, Tl0, K Minimum bubble mass and total number of emitted neutrons vs liquid temperature, T0

  36. 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 = 2.5·10-2, 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.

  37. a20/R0 = 0.03 Incompressible viscous Liquid Homobaric Van der Waals Gas Temporal dependences of the radius R of anair bubble in water, the sphericity distortiona2 /R and some bubble shapes just before the time of the collapsetc 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 = 0.001

  38. SUMMARY OF THE ANALYSIS Bubble Fusion (ORNL+RPI+RAS) Sonoluminescence (LLNL) Density: 20 - 80 g/cm3 Temperature: 108 K = 10 KeV Pressure: 1011 bar Velocity: 900 km/s 10 g/cm3 106K = 10-1 KeV Time Duration: 1013–1012 s = 101-100 ps Radius of the Fusion Core: 50 nm Number of nucleus: 20 • 109 10 ps 1-3 nm Fast Neutron & Tritium Production 10-1 - 10 per collapse

  39. FINDINGS • COLD LIQUID Effect • CLUSTER effect • NON-DISSOCIATION of Liquid • “COLD” Electrons” • SHARPENNING: • Node size for Fusion Core • r  0.1 nm <<a10 nm << a10 000 nm

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