Deuterium-Deuterium Thermonuclear Fusion due to Acoustical Cavitation (Theoretical Analysis) Robert I. NIGMATULIN Ufa-Bashkortostan Branch of Russian Academy of Sciences - President [email protected]Richard T. Lahey, Jr Rensslear Polytechnic Institute Troy, NY, 12180 [email protected]19 June, 2003 Arlington, VA SONOLUMINESCENCE AND INDUCED FUSION WORKSHOP
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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 [email protected] Richard T. Lahey, Jr - PowerPoint PPT Presentation
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Deuterium-Deuterium Thermonuclear Fusion due to Acoustical Cavitation
(Theoretical Analysis)
Robert I. NIGMATULINUfa-Bashkortostan Branch of Russian Academy of Sciences
THERMAL CONDUCTIVITY EQUATIONS FOR HOMOBARIC BUBBLE (pg = pg(t)) IN INCOMPRESSIBLE LIQUID (l = const)
t
p
p
r
r
T
pu
trTtrRtpr
T
aa
up
t
p
t
p
r
Tr
rrr
Tu
t
Tcar
g
g
g
gg
gggg
ar
ggagg
ggg
gg
gggp
d
d
3
1
),(),()(,)1(33
d
d
d
d1: 2
2
const)(
,1
:2
22
2
l
lall
ll
ll
llr
auu
r
Tr
rrr
Tu
t
Tcar
g
g
g
gg
gg
T
p
T
Tp
Rjlj
r
T
r
T
juauaar
s
2
α,
:
Cluster Amplification Effect
Void fraction Number of bubbles N = 50Maximum microbubble radius
Radius of the cluster
12 17 22 27 32 37 42-150
-100
-50
0
50
100
450
500
0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 4,00
50
100
150
200
250
300
350
400
450
a,
p,bar
t, s
t, s
p, bar
t = 32 s
r, mm
12 17 22 27 32 37 421
10
100
r = 0r = 2 mmr = 4 mm
20
= 0.05
a = a = 4000 max m
R = 4 mm0
r = 0
r = 2 mm
r = 4 mm
R
LOW MACH (microsecond) STAGE
0.1,K273,kHz3.192,bar50,bar15 0L Tpp
0
2 0 0
4 0 0
6 0 0
8 0 0
, m
-4 0
0
4 0
8 0
1 2 0
1 6 0
,
bar
-8 0
-6 0
-4 0
-2 0
0
2 0
4 0
d /d
, m
/s
,
ng
0 1 0 2 0 3 0 4 0 , s
0 .0
0 .1
0 .2
0 .3
0 .4
, kg/
m
0 1 0 2 0 3 0 4 0 , s
2 5 0
2 6 0
2 7 0
2 8 0
2 9 0
3 0 0
, K
0 1 0 2 0 3 0 4 0 , s
0 .0 4
0 .0 6
0 .0 8
0 .1 0
0 .1 2
0 .1 4
, b
ar
3
g
t*
a a mTp*
**
t t
t
pI
1 0
1 0
1 0
1 0
1 0
1 0
1 0
3
2
1
0
-1
-2
-3
t
t 0
1 -3
4
5
67
8
9 -1 5
1 -3
45
67
8 -1 5
0.1,K273,kHz3.192
,bar50,bar15
0L
T
pp
LOW MACH (microsecond) STAGE
0 2 0 0 4 0 0 6 0 0 8 0 0 , m
0 .0
0 .1
0 .2
0 .3
0 .4
0 .5
, kg/
m
0 2 0 0 4 0 0 6 0 0 8 0 0 , m
-8 0
-6 0
-4 0
-2 0
0
2 0
4 0
, m
/s
0 2 0 0 4 0 0 6 0 0 8 0 0 , m
-2 0
-1 0
0
1 0
2 0
3 0
4 0
, ba
r
0 2 0 0 4 0 0 6 0 0 8 0 0 , m
2 5 0
2 6 0
2 7 0
2 8 0
2 9 0
3 0 0
, K
3
u Tp
r
r r
r
17
1
7
7
1 -3
1 72
8
2
8
8
28
3
3
3
4
4
4
4
5
5
5
5
6
6
6
6
μs05.28,μs76.22,μs46.14,μs86.9
,μs89.6,μs41.3,μs67.1,μs77.0
8765
4321
tttt
tttt
0.1,K273,kHz3.192
,bar50,bar15
0L
T
pp
Transition from LOW MACH to HIGH MACH STAGE (microsecond stage)
-1 .0 -0 .8 -0 .6 -0 .4 -0 .2 0 .0 , s
0
1 0 0
2 0 0
3 0 0
4 0 0 ,
m
-1 .0 -0 .8 -0 .6 -0 .4 -0 .2 0 .0 , s
-2 .0
-1 .6
-1 .2
-0 .8
-0 .4
0 .0
d /d
, k
m/s
0 2 0 0 4 0 0 6 0 0 , m
-1 .2
-1 .0
-0 .8
-0 .6
-0 .4
-0 .2
0 .0
, km
/s
-1 .0 -0 .8 -0 .6 -0 .4 -0 .2 0 .0 , s
0
2 0
4 0
6 0
8 0
1 0 0
, ng
0 2 0 0 4 0 0 6 0 0 , m
2 0 0
3 0 0
4 0 0
5 0 0
6 0 0
7 0 0
, K
ga a mT
p
t - t*
r0 2 0 0 4 0 0 6 0 0
, m
, ba
r
ut
1 0
1 0
1 0
1 0
1 0
1 0
4
3
2
1
0
-1
t - t* t - t*
9 -1 21 3
1 4
1 5
1 5
1 41 3
9 -1 2
9 -1 21 3
1 4
1 5
1 2
1 3
1 4
1 5
1 2 1 31 4
1 5
1 21 3
1 4
1 5
r r
μs03.0*,μs23.0*,μs52.0*,μs81.0*
,μs10.1*,μs28.1*,μs67.1*,μs01.30*
15141312
11109
tttttttt
ttttttt
0,1EOS
0.1,K273,kHz5.202,bar1000,bar40 0L
Tpp
-5.0 0.0 5.0 , ns
102
104
106
108
, K
3
*
*
*
t - t16 20
aa p
T
t - t*
t - t*
t
t - t16 20
1 6 1
0
10
20
30
40
, m
- 5 .0 0.0 5.0 , ns
-8
-4
0
4
8
d /d
, km
/s
102
104
, kg/m
1
102
104
106
108
1010
1012
, ba
r
7
1 8
1 92 0
1 6
1 7
1 81 9
20
s41.17* t
16
1 7
181 9
2 0
HIGH MACH (nanosecond) STAGE
HIGH MACH (nanosecond) STAGE
0 .0 1 .0 2 .0 3 .0 , m
, kg/
m
0 .0 1 .0 2 .0 3 .0 , m
, ba
r
0 .0 1 .0 2 .0 3 .0 , m
-1 5 0
-1 0 0
-5 0
0
5 0
1 0 0
, km
/s
0 .0 1 .0 2 .0 3 .0 , m
, K
3
r
p
r r
r
uT
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 0
5
4
3
2
1
0
1 1
9
7
5
1
1 0
1 0
1 0
9
7
3
1 0 3
1 0 5
1 61 71 8
1 92 0
1 61 7
1 8
1 9
2 0
1 61 7
1 9
1 8
2 0
1 61 7
1 8
1 9
2 0
0.1,K273,kHz3.192,bar50,bar15 0L Tpp
ps
ps,
ps
ps
ps
21 170
100
060
020
040
20
19
18
17
.tt
.tt
,.
,.
,.
tt
tt
tt
0 .0 0 .2 0 .4 0 .6
, bar
0 .0 0 .2 0 .4 0 .6 , p s
-8 0 0
-6 0 0
-4 0 0
-2 0 0
0
2 0 0 ,
km/s
0 .0 0 .2 0 .4 0 .6
, kg/
m
0 .0 0 .2 0 .4 0 .6
, K
*
*
*p 3
T
u *
0 .0 0 .2 0 .4 0 .6 * * , p s
0 .0
1 .0
2 .0
3 .0
4 .0
5 .0
6 .0
7 .0
N
t - t
t - t* *
1 7
1 8
1 92 0
2 1
1 7
1 8
1 9
2 02 1
1 7
1 8
1 92 0
2 1
2 0
2 1
1 71 8
1 9
1 7 1 8
1 9
2 0
2 1
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 2
1 0
8
6
4
2
0
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 0
6
5
4
3
2
1
0
-1
9
8
7
6
5
4
3
2
PARAMETERS IN THE CENTER OF THE CORE
-10 -5 0 5TIME [ns]
0
10
20
30
40
50
RA
DIU
S [m
km]
Вubble radius evolution for deuterated acetone C3D6O;
non-dissociated liquid
dissociated liquid
“Cold dissociation” because of the “super high pressure” (105 bar) in liquid needs 102 ns;
LIQUID DISSOCIATION IMPACT
“Super high pressure” in liquid (near the bubble interface) takes place 1 ns
“COLD” ELECTRONS
Te << Ti (during 10-13 s)
CV = 2000 m2/c2K, not 8000 m2/c2K
corefusion theof Radius - nm
productionneutron maximum theof Radius - nm
55
,11
Fr
r
Neutron production distributionand maximum density, temperature and velocity
0.0
1.0
2.0
3.0
4.0
N
10-1
, nmr100 101 10210-2
, nm
-1600
-1200
-800
-400
0
, km
/s
, nm
0.00
0.04
0.08
0.12
0.16
,
nm
r-1
max r
-1
uN N
r
umax
Nr
10-1 100 101 102 103
, nm
103
, kg/
m
&
,
K
0.00
0.04
0.08
0.12
0.16
3
max
max
T
r
max
Tmax
Nr
104
105
106
107
108
109
1010
10-2 10-1 100 101 102 103
, nm rF
0 20 40 60 80 100r*
0.00
0.04
0.08
0.12
0.16
,
n mr
-1N
r
r=0.132 nmr=0.256 nm
r=1.32 nm
r=2.65 nm
r=5.29 nm
r=13.2 nmr=26.5 nm
a
V
a
VV
fff
ttrJrrrJrtVJtN
0
2
0
2
0
111
d),(4dd4ddd a
r rrNN
0
d)( ttrJrN
f
r d),(4
1
0
2
INTERNAL GAS ENERGY AS THE SUM OF COMPONENTS
T , K
0 .0
0 .2
0 .4
0 .6
0 .8
1 .0
1 0 1 0 1 0 1 0 1 04 5 6 7 8
p,
T, d
, i
p
T
d
i
k g /m3 3
T , K
0 .0
0 .2
0 .4
0 .6
0 .8
1 .0
1 0 1 0 1 0 1 0 1 04 5 6 7 8
p,
T, d
, i
p
T
d
i
k g /m4 3
ii
dd
TT
ppidTp TTTTT ,,,,,,
Acetone
TEMPERATURE, K
pT/p
=104 kg/m3
=103 kg/m3
1 E + 2 1 E + 3 1 E + 4 1 E + 5 1 E + 6 1 E + 7 1 E + 8
0
0 .2
0 .4
0 .6
0 .8
1
1 .2
LIQUID TEMPERATURE, Tl0, K
MIN
IMU
M M
AS
S, m
g m
in, n
g
0
5
0
25 2 0 2 0 2 0 2 0 3 00
50
1 0
1 0
2 0
250
0
6 7 8 9 0
= 1.0
= 0.1
= 0.1
= 1.0
250 260 270 280 290 300
0
1
2
3
Nor
mal
ized
neu
tron
pro
duct
ion,
N/N
273
LIQUID TEMPERATURE, Tl0, K
LOW TEMPERATURE (condensation) EFFECT
Minimum 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 a2
0/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.
Temporal dependences of the radius R of an air 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 = 0.03
a20/R0 = 0.001
Incompressible viscous Liquid
Homobaric Van der Waals Gas
SUMMARY OF THE ANALYSIS
Density: 20 - 80 g/cm3
Temperature: 108 K = 10 KeV
Pressure: 1011 bar
Velocity: 900 km/s
Time Duration: 1013–1012 s = 101-100 ps
Radius of the Fusion Core: 50 nm
Number of nucleus: 20 • 109
Fast Neutron & Tritium Production 10-1 - 10 per collapse
10 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 << a 10 nm << a 10 000 nm