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 19 June, 2003 Arlington, VA

THE TEAM RUSSIA USA Ufa RPI ORNL Kazan 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

SPHERICAL SHOCK WAVE CONVERGENCE AND CUMULATION Initiation of a Spherical Shock Wave by 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 Wave at the Center of the Bubble The Spherical Shock Wave after the Reflection from the Center of the Bubble

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

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

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

Kinetic Energy of Convergent Flow around the Bubble (CFAB) p  15 bar (in SBSL p  1.5 bar) Rmax  500 – 800 mcm (in SBSL Rmax  50 – 80 mcm) In our experiments: the Kinetic Energy K of CFAB is 104 times higher 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) K/m and Tmax is = 100 – 200 times higher than in SBSL It means that in our experiment we may get Tmax  (100-200)106 K

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

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

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 - averaged heat capacity and Gruneizen Coefficient

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

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

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

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

DISSOCIATION of GAS 0.1 0.9 Td

IONIZATION of DISSOCIATED GAS

IONIZATION CONSTANTS

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

KINETICS OF FUSION

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

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

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

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

LOW MACH (microsecond) STAGE

LOW MACH (microsecond) STAGE

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

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

HIGH MACH (nanosecond) STAGE

PARAMETERS IN THE CENTER OF THE CORE

LIQUID DISSOCIATION IMPACT - 1 5 T I M E [ n s ] 2 3 4 R A D U S m k “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 radius evolution for deuterated acetone C3D6O;

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

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

INTERNAL GAS ENERGY AS THE SUM OF COMPONENTS

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

LOW TEMPERATURE (condensation) EFFECT LIQUID TEMPERATURE, Tl0, K MINIMUM MASS, mg min, ng 5 2 3 1 6 7 8 9 a = 1.0 a = 0.1 a = 0.1 a = 1.0 2 5 6 7 8 9 3 1 Normalized neutron production, N/N273 LIQUID TEMPERATURE, Tl0, K Minimum bubble mass and total number of emitted neutrons vs 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 = 2.5·10-2, 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.

Incompressible 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 = 0.001

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 106 K = 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

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