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 TEAM

USA•RPI

•Richard LAHEY, Jr.•Robert BLOCK

•Francisco MORAGA

•ORNL•Rusi TALEYARKHAN

•Colin D. WEST•Jeing S. CHO

RUSSIA•Ufa

•Robert I. NIGMATULIN

•Iskander Sh. AKHATOV•Naila K. VAKHITOVA

•Raisa Kh. BOLOTNOVA•Andrew S. TOPOLNIKOV

•Marat A. ILGAMOV

•Kazan•Alexander A. AGANIN

SPHERICAL SHOCK WAVE CONVERGENCE AND CUMULATION

Initiation of a Spherical Shock Waveby the Convergent Interface

Focusing of the Spherical Shock Waveat the Center of the Bubble

The Spherical Shock Waveafter the Reflectionfrom the Center of the Bubble

Selfsimilar 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 m

• Adiabatic bulk compression gas temperature Tmax ~ 5000 K (?!)

• Cold water effect

• Noble gas effect

• Extremely short light flashes tF ~ 50 ps = 5·10-11s

Lig

ht

Rad

iati

on

Tmax ~ 5000 K (adiabatic compression)

tF ~ 10-11s

t

Rad

ius

of t

he

bu

bb

le

a

t

t

a0

amin

t

t~ 30s 6 daystC ~ 30 ns 7 mintF ~ 50 ps 0,7 s

13

00 a

a

T

T minmax

tC ~ 10-8s

Supercompression by Convergent Spherical Shock Wave

Moss 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

3maxRpK

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 )10050(

104

= 100 – 200 times higher

It means that in our experiment we may get Tmax (100-200)106 K

.,,,,,n

g

ggg T

TTTpp

ue

00

2

2

,0urrr

1t

22

,0rp

rurr

1u

t22

2

,

rT

rrr

peurrrt

e 22

22

11

Gas

Liquid

a(t)

Mass, Momentum, Energy Conservation Differential Equations

•Mass

•Momentum

•Energy

INTERFACIAL BOUNDARY CONDITIONS (r = a(t))

juaua gg

gSg

Sg

TR

TjTTT

ρ20.45][

g

g

g T

p

TTp

Rj

s

2α

ljr

T

rT g

g

Mass:

Momentum:

Energy:

Kinetics of phase transition (Hertz-Knudsen-Langmuir Eqn):

au

appg

μ4σ2

pS(T) – saturation pressure, l – evaporation heat

- accommodation (condensation) coefficient

- (Labuntsov, 1968)

- intensity of phase transition

cTp

TcpTc VTVT ,

Tp ppp

MI-GRUNEIZEN EQUATIONS OF STATE

d

d, p2

ppp p

• 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

andVc - averaged heat capacity and Gruneizen Coefficient

1),(

07.19,Pa10535.4,0 ,Pa10757.9

,/sm10048.6,K)/(sm8.1516

m/s1189,kg/m858

87

225)(22

03

0

llll

chlV

bKCA

c

C

,1exp1

0

1

0

3/10

3/2

0

KCbAp p

0000

3/10

01exp

3 KCb

b

Ap

BORN-MAYER POTENTIAL

LIQUID PHASE (NONDISSOCIATED )

LENNARD-JONES POTENTIAL

pp = R n – A

m

p = 011

11

mn

m

Q

n

R

pp

V 1

p

V0

Vp p

p d

d

SHOCK ADIABAT (D-u) FOR LIQUID ACETONE(Trunin, 1992)

Trunin, 1992

D – Shock Wave Speed

U – Mass Velocity after the Shock Wave

DU

Sh

oc

k W

ave

Sp

eed

, D, k

m/s

Cl

MASS VELOCITY, U, km/s0 2 4 6 8 1 0

0

2

4

6

8

1 0

Dissociated

Non-dissociatedNon-dissociated

MASS VELOCITY, U, km/s0 1 0 2 0 3 0 4 0

0

1 0

2 0

3 0

4 0

Dissociated

1 0 1 0 1 0 1 0 1 0 1 0

-2 -1 0 1 2 3

4

Г

P p

3

3

-2 1 0

-4 1 0

L iqN D isD is

0

0 .6 6 70 .1 1 3

RELATIVE VOLUME, /

SHOCK ADIABAT & ISOTHERMS (P-V) for D-Acetone (C3D6O)Isotherms of Vapor

PR

ES

SU

RE

p,

ba

r

Shock adiabat of Liquid

RELATIVE VOLUME, 0/0 .0 0 .2 0 .4 0 .6 0 .8 1 .0

0 .0

0 .1

0 .2

0 .3

0 .4

0 .5

pp

0 .4 0 .6 0 .8 1 .0

0 .0 0

0 .0 3

0 .0 6

pP

● Trunin, 1992

Dis

NDis

PR

ES

SU

RE

p,

Mba

r

6000 K

4000 K

3000 K

2000 K

1000 K

5000 K

NDis

Dis

0 D = (D – U)

p – p0 = 0 D U

5 0 8 K

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 3

1 2

1 1

1 0

9

8

7

6

5

4

3

2

1

0

1 0 K

1 0 K

1 0 K

1 0 K

1 0 K

1 0 K

1 0 K

8

7

6

5

4

3

3

2 7 3 KN D is

D is

ISOTHERMS (P-V) & SATURATION LINE for D-Acetone

TEMPERATURE, K

EN

ER

GY

,

105

m2

/s2

Evaporation Heat (ig-il)

Liquid

Vapor

Internal Energy and Evaporation heat

RELATIVE VOLUME, /

PR

ES

SU

RE

p,

ba

r

Isotherms

K)J/(kg9.129 ,kg/kmol64,kg/m309,K508 3critcrit gRMT

2 0 0 3 0 0 4 0 0 5 0 0 6 0 0

1 2

8

4

0

C

1 0 1 0 1 0 1 0

0

2 0

4 0

6 0

5 0 8 K

0 1 2 3

1 0 0 0 K

4 0 0 K

C

DISSOCIATION of GAS

207.25,Pa10585.3

,0,Pa10403.2

,333.0,667.0

K)/(sm 0.1940

d

d

8

7

22

V

2

dd

dd

dd

Vd

Tdd

Td

dT

d

pdp

d

Td

pdd

chd

Td

pdd

bK

CA

c

p

Tc

p

ppp

226chd0 /sm1027.6ε

dgkT

T

TTm

Tmmmm

mpmpp

mm

d

k

kk

ggdg

ddgg

ddgg

, eV, 01.4

,)5(tanh)(5

tanh5.0

),( ,1

,

,

028.24,Pa10784.1

,Pa107435.1,Pa100.4

,9000.0,9394.0,113.0

K)/(sm8.1516

d

d

9

97

22

V

2

gg

gg

ggg

Vg

Tgg

Tg

gTg

pgp

g

Tg

pgg

chg

Tg

pgg

bK

CA

c

p

Tc

p

ppp

225chg /sm106.048ε

1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0T ,

0 .0

0 .5

1 .0

md

K

0.1

0.9

Td

,)5(tanh)(5

tanh5.0

O7; O6, O5, O4, O3, O2, O1, D1; C6; C5, C4, C3, C2, C1,

oxygen. - )(16116

deuterium, - )( 1262

carbon, - )( 36312

weight molecular64

energy)ionization(

6416

СO

6412

DD

6436

СC

7

1j

OjOjO6416

D1D1D6412

6

1j

CjCjC6436(ch)

i

(ch)i

)ch(i

)ch(0d

)ch(d

:ODС 63

k

kk

k

kkkk

T

TTm

k

M

M

M

M

mTRmTRmTRTRm

IONIZATION of DISSOCIATED GAS

eV 739.3

eV, 138.1 eV .0490

eV, 13.91 eV 392.0

eV, .4177 eV .4964

eV, .9445 eV .8947

eV, .1953 eV .3823

eV, 13.69eV 11.26

K),/(sm 6.519 , K)/(sm 8.692

eV 13.60

K),/(sm 4157

O7

O6C6

O5C5

O4C4

O3C3

O2C2

O1C1

22O

22C

D1

22D

T

TT

TT

TT

TT

TT

TT

RR

T

R

IONIZATION CONSTANTS

0.1,273T

,609.0,169.0

,1T

T1

0l

0l0l

0l0l0ll

K

Ksm/kg 3

Liquid

2 0 0 3 0 0 4 0 0 5 0 0, K

0 .0 0

0 .0 4

0 .0 8

0 .1 2

0 .1 6

0 .2 0

, kg

m/(

s K

)

3l

T

Gas

200 400 600 800 1000, K

0.00

0.02

0.04

0.06

0.08

, kg

m/(

s K

)3

T

g 0.5K

Ksm/kg 3

,T

,.

,T

T

g

g

gggg

273

10238

11

0

30

000

Gas

, K/

,k

g m

/(s

K)

10 10 10 10T

g

g0

3

10

10

10

10

10

10

10

6

5

4

3

2

1

0

3 5 7 9

0g0

570 .g

750 g

THERMAL CONDUCTIVITY for acetone

21

213

HT

nHeDD

,dd,vσ22

1 Vt

tVJNnJ

1-26g

1-g

1-26

kg1056.0μ 6N

kmol64μ kmol1002.6

v

weightmolecular number, Avogadro

velocity, thermalnucleus deuterium themessection ti cross theofproduct averaged

A

A

N

N

D

, K

<

v >

m /

s3

1 0

1 0

1 0

1 0

1 0

1 0

-2 1

-2 4

-2 7

-3 0

-3 3

-3 6

1 0 1 0 1 0 1 0 1 06 7 8 9 1 0

T

D -D

D -T

neutrons, emitted of number

intensity, emissionneutron

N

J

KINETICS OF FUSION

,23CDCO atoms D ofion concentrat g6

g

n ΑΝ

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

t, s

Tg=Tg(t, r)pg=pg(t)

Heat conducting,homobaric gas(M < 10

-1)

Tg=Tg(t, r)pg=pg(t, r)

M > 1

NumberMach gC

aM

30

SBSL

BF

K)/(sm 22 2000VlVl c,Tc

119129 .c

Rc.R

TRp,Tc

Vg

gVgg

ggVg

K),J/(kg

ε

l

Iarl pp

t

a

t

aa

ρd

d

2

3

d

d2

2

2

constkg/m 3 858l

1lC

aM

For GAS (vapor):For GAS (vapor):

For LIQUID:For LIQUID:

Rayleigh-Plesset equationRayleigh-Plesset equation

Low Mach regime

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