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
Richard T. Lahey, Jr
Rensslear Polytechnic Institute
Troy, NY, 12180
19 June, 2003
Arlington, VA

2. 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

3. 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

4. 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 days
dtC ~ 30 ns min
dtF ~ 50 ps ,7 s
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  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 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 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  ( )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
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

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

12. 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

13. 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

14. 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

15. DISSOCIATION of GAS
0.1
0.9 Td

16. IONIZATION of DISSOCIATED GAS

17. IONIZATION CONSTANTS

18. 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

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 a
= 0.05 R 20
a = a = 400 mm
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

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- 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

28. HIGH MACH (nanosecond) STAGE

29. PARAMETERS IN THE CENTER OF THE CORE

30. 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 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;

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

32. 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

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
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

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[ {3.5lg(R/R0) + 1.5|lg(R/R0)|}].
Incopmpressible viscous liquid, homobaric Van-der-Waals gas.

37. 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

38. SUMMARY OF THE ANALYSIS
Bubble Fusion (ORNL+RPI+RAS)
Sonoluminescence (LLNL)
Density: 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 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  nm