Week 1. Fundamentals of Nuclear Fusion I

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(1)

I ntroduction to Nuclear Fusion

(409.308A, 3 Credits)

Prof. Dr. Yong-Su Na

(32-206, Tel. 880-7204)

(2)

Week 1. Fundamentals of Nuclear Fusion I

- Present Status and Future Prospect Week 2. Fundamentals of Nuclear Fusion II

- Fusion Reactions

Week 3. Fundamentals of Nuclear Fusion III - Thermonuclear Fusion Conditions Week 4. Review of Plasma Physics

- Plasma Confinement, Transport, Equilibrium, and Stability

Week 5. Inertial Confinement Week 6. Magnetic Confinement

- Mirror, Pinches, and Stellarator

Contents

(3)

Week 9. Tokamaks I

- Plasma Equilibrium and Stability Week 10. Tokamaks II

- Plasma Transport

Week 11. Plasma Heating and Current Drive

- OH, NBI, RF, Adiabatic Compression, and Alpha Self-heating

Week 12. Plasma Wall Interaction

Week 13. Overview of Fusion Power Plants Week 14. Critical Issues in Fusion Researches

Contents

(4)

Week 1. Fundamentals of Nuclear Fusion I

- Present Status and Future Prospect Week 2. Fundamentals of Nuclear Fusion II

- Fusion Reactions

Week 3. Fundamentals of Nuclear Fusion III - Thermonuclear Fusion Conditions Week 4. Review of Plasma Physics

- Plasma Confinement, Transport, Equilibrium, and Stability

Week 5. Inertial Confinement Week 6. Magnetic Confinement

- Mirror, Pinches, and Stellarator

Contents

(5)

• Hydro-electric process

• Chemical reactions (combustion)

• Fission process

• Fusion process

• Total energy conservation including rest mass energy

out out

in

in

M E M

E + → +

heating

fuels

reaction energy

products reactor/

generator

Matter and Energy

(6)

)

2

( m c Q

ab

= − Δ

ab

Mass Defect Energy of Nuclear Reaction e

d b

a + → +

reactants products

) (

)

(

d e a b

ab

m m m m

m = + − +

Δ

Δmab < 0: exothermic or exoergic Δmab > 0: endothermic or endoergic

Einstein’s mass-energy relation

*

*

after before

E

E =

) (

) (

) (

)

( E

k,a

+ m

a

c

2

+ E

k,b

+ m

b

c

2

= E

k,d

+ m

d

c

2

+ E

k,e

+ m

e

c

2

(7)

Mass Defect Energy of Nuclear Reaction

ab b

k a

k

E Q

E

,

+

,

<<

2 2

,

,

2

1 2

1

e e d

d e

k d

k

ab

E E m v m v

Q ≈ + = +

For

e e d

d

v m v

m =

ab e

d d e

k ab

e d

e d

k

Q

m m

E m m Q

m

E m ⎟⎟

⎜⎜ ⎞

≈ +

⎟⎟ ⎠

⎜⎜ ⎞

≈ +

,

,

,

Momentum conservation for reactions with CM at rest

Ex) d-t fusion reaction

1 4

MeV 6

. 17

dt

= Q

MeV 6

. + 17 +

+ t n α

d

(8)

The amount of energy released when a particular isotope is formed.

The strength of the bonding is measured by the binding energy per nucleon where "nucleon" is a collective name for neutrons and

protons, sometimes called the mass defect per nucleon.

The difference in mass is equivalent to the energy released in forming the nucleus.

Binding Energy for an Assembled Nucleus

. . )

(A Z n X B E Zp + − →ZA +

2

)]

2

) (

[(

.

. E m Zm A Z m c mc

B ≡ −

X

p

+ −

n

= − Δ

Δm < 0: released energy

(exothermic or exoergic

(9)

Fusion in Nature

Fusion reactions by which stars convert hydrogen to helium - The PP (proton-proton) chain: in stars the mass of the Sun and less - The CNO cycle (Bethe-Weizsäcker-cycle): in more massive stars

Nobel prize in physics 1967

“for his contribution to the theory of nuclear reactions, especially his discoveries concerning the energy production in stars”

Hans Albrecht Bethe

(1906. 7. 2 – 2005. 3. 6)

(10)

Fusion in Nature

The PP (Proton-Proton) Chain

• Only 1.7% of 4He nuclei being produced in the Sun are born in the CNO cycle

MeV d

p

p + → + β

+

+ ν + 1 . 2 MeV He

d

p + →

3

+ 5 . 5

MeV p

He He

He

3 4

2 12 . 9

3

+ → + +

MeV Be

He

He

4 7

1 . 6

3

+ → +

MeV Li

Be

7

0 . 06

7

+ β

→ +

6

K 10 15 ×

Sun

(11)

Fusion in Nature

MeV N

p

C

13

1 . 9

12

+ → +

MeV C

N

13

1 . 5

13

→ + β

+

+ ν +

MeV N

p

C

14

7 . 6

13

+ → +

MeV O

p

N

15

7 . 3

14

+ → +

MeV N

O

15

1 . 8

15

→ + β

+

+ ν +

MeV C

p

N

12

5 . 0

15

+ → + α +

MeV p 2 2 25 . 1

4 → α + β

+

+ ν +

K Tstar 13×106

CNO (Carbon-Nitrogen-Oxygen) Cycle

(12)

Fusion in Nature

http://jcconwell.wordpress.com/2009/07/20/formation-of-the-elements/

http://eqseis.geosc.psu.edu/~cammon/HTML/Classes/IntroQuakes/Notes/earth_origin_lecture.html

Layers of Fusion in a Star

(13)

Fusion in Nature

(14)

Physical Characterisation of Fusion Reaction

a+b → (ab) → d+e+Qab

- ( ab ) : a complex short-lived dynamic state which disintegrates into products d and e .

→ The energetics are determined according to nucleon kinetics analysis, with nuclear excitation and subsequent gamma ray emission known to play a comparatively small role in fusion

processes at the energies of interest envisaged for fusion reactors.

(15)

Physical Characterisation of Fusion Reaction

r r q F

c a

q

a3b

0

,

4

1

= πε

a b

r r m G m

F

g,a

= −

a3 b

The electrostatic force caused by positively charged nuclei is very strong over long distances, but at short distances the nuclear force is stronger.

(16)

16

p t R d

q R q

U a b ~0.4MeVfor , , 4

) 1 (

0 0

0 = πε

Reflection and tunneling of an electron wavepacket directed at a potential barrier

A. B. Balantekin and N. Takigawa, 'Quantum tunneling in nuclear fusion', Rev. Mod. Phys. 70, 77 (1998).

V0

E <<

( )

e a

k k

a k

k T k

κ

κ κ

κ κ

κ

κ

2 2

2 0 2

0

2 2 2 0 2 2 0

2 2 0

4

sinh )

/ 2 (

) / 2 (

⎟⎟

⎜⎜

+

+

= +

0

Finite potential barrier

] 1 exp[

) Pr(

r b a

r v

q q tunneling v γ

Attractive strong nuclear force

Physical Characterisation of Fusion Reaction

(17)

Physical Characterisation of Fusion Reaction

(18)

By 1928, George Gamow had solved the theory of the alpha decay of a nucleus via tunneling. After attending a seminar by Gamow, Max Born recognized the generality of quantum-mechanical tunneling.

(Max Born, Nobel Prize in Physics 1954)

Physical Characterisation of Fusion Reaction

Max Born (1882-1970) George Gamow

(1904-1968)

(19)

Fusion Reaction Cross Sections

• Beam-target collisions (Binary interactions) - For fixed target

- For moving target

2 /

,

,

1 1 12

1

v v E m v

m

m = = =

CM

r

v v v E E

m

m = , =

1

2

, = dx

n n E

dn

1

= − σ

12

( )

1 2

- Fusion cross section for low energy ECM < U(R0) by quantum mechanical tunneling process:

E

e

B

E

E A

/

12

( ) =

σ

Gamow theory (1938)

(20)

Fusion Reaction Cross Sections

(21)

σ-v parameter

• Fusion reaction rate density

• Fusion power density

Fusion Reaction Rate Parameter (Reactivity or σ-v Parameter)

( )

a b a a b b a b

v v

b a ab

ab v v v v F v F v d v d v

v

a b

3

) 3

( )

− (

=

>

<σ

∫ ∫

σ

ab b

a

fu

N N v

R = < σ >

( )

( )

a b a a b b a b

v v

b a fu b

a

b a b

b b a a a b a v v

b a fu fu

v d v d v F v F v v v v N

N

v d v d v F N v F N v v v v R

a b a b

3 3

3 3

) ( ) (

) ( )

(

=

=

∫ ∫

∫ ∫

σ σ

) ( )

(

x x x

x

v M v

F

Thermodynamic equilibrium

dx n n E

dn1 = −

σ

12( ) 1 2

v v dn

dn dt dn

dRfud (− ) = 1 2σ12( )

2 3 2 2 2 2

1 3 1 1 1 1

) (

) (

v d v f n dn

v d v f n dn

=

=

f1,2: normalised distribution function

(22)

Both species at the same temperatures

Fusion Reaction Rate Parameter

(Reactivity or σ-v Parameter)

(23)

Fusion Fuels

Possible fusion reactions

MeV 4

.

7

3

6

→ + +

+ Li Be n d

MeV 0

.

7

+ + 5

Li p

MeV 6

. + 2 + +

p α t

MeV 3

. 22 2 +

→ α

MeV 0

.

3

4

6

→ + +

+ Li He α p

MeV 1

.

6

2

9

→ + +

+ Be Li

p α

MeV 6

. 0 2 + +

d α

MeV 7

. 8

11

→ 3 +

+ B α

p

MeV 3

. 11 2 + +

+ t n α t

MeV 9

. 12

3

2

3

He + Hep + α +

MeV 1

.

3

→ + + + 12

+ He n p α t

MeV 6

. + 17 +

+ t n α d

MeV 1

. + 4 +

+ d p t d

MeV 2

.

3

+ 3 +

n He

MeV 3

.

3

→ + + 18

+ He p α

d

(24)

Fusion Fuels

Choice of a fusion reaction as a fuel in a fusion reactor

- Availability of fusion fuels

- Requirements for attaining a sufficient reaction rate density

D-T reaction: 1

st

generation

- Considered for the first generation of fusion reactors

- Ample supply of deuterium: d/(p+d)~1/6700 in the world’s oceans, fresh water lakes, rivers

- Scarce of tritium: radioactive β decay with a half life of 12.3 years.

total steady state atmospheric and oceanic quantity produced by cosmic radiation ~ 50 kg

MeV 6

. + 17 +

+ t n α

d

(25)

Fusion Fuels

D-T reaction: 1

st

generation

- Tritium breeding

The 7Li(n,n’α)t reaction is a threshold reaction and requires an incident

neutron energy in excess of 2.8 MeV.

MeV 47

. 2 '

MeV 78

. 4

4 7

4 6

− + +

→ +

+ +

→ +

n He t

Li n

He t

Li

n

7.42% of natural Li

92.58% of natural Li

(26)

D-T Burn

( )

( )

( )

) , ( )

, ( ) , (

) , , ( ) , , (

) , , ( ) , , ) (

, ( ) , (

) , , ( ) , , (

) , , ( ) , , ( )

, (

3 3

3 3

3 3

*

*

3 3

t r v

t r N t r N

v d v d t v r f t v r f

v d v d v v

v v

t v r f t v r t f

r N t r N

v d v d v v

v v

t v r f t v r f N

N

v d v d v v

v v

t v r N t v r N t

r R

dt t

d

t d

t t

d d

t d

t d

t d

dt t

t d

d t

d

t d

t d

t d

dt t

t d

d t

d

t d

t d

t d dt t

t d

d dt

G G

G

G G G

G

G G

G G

G G G

G G G

G G

G G

G G G

G

G G

G G

G G G

G G

>

<

=

= −

=

=

∫∫ ∫∫

∫∫

∫∫

σ

σ σ

σ

d+t → n+

α , Q

dt

=17.6 MeV

dt dt

t d

dt dt

dt

r t R r t Q N r t N r t v r t Q

P ( G , ) ( G , ) ( G , ) ( G , ) ( G , )

>

<

=

= σ

(27)

• D-D reactions and side reactions

D-D Burn Modes

MeV 6

. + 17 +

+ t n α d

MeV 1

. + 4 +

+ d p t d

MeV 2

.

3

+ 3 +

n He

MeV 3

.

3

→ + + 18

+ He p α d

MeV 3

. 11 2 + +

+ t n α t

MeV 9

. 12

3

2

3

He + Hep + α +

MeV 1

.

3

→ + + + 12

+ He n p α t

MeV 3

. + 14 +

d α

(28)

• PURE-D Mode

D-D Burn Modes

MeV 1

. + 4 +

+ d p t d

MeV 2

.

3

+ 3 +

n He

Channel - t Channel - 3He

t dd d

t

dd

N v

R

,

2

,

= 2 < σ >

He dd d

He

dd

N v

R

3 3

, 2

,

= 2 < σ >

He t dd

dd

dd

v v

v

3

,

+ < >

,

>

=<

>

< σ σ σ

He dd t dd

dd

v v

v > ≈< > ≈ < >

< σ σ σ

2 1

,3

,

At temperatures of common interest

(29)

D-D Burn Modes

a1 a2 ax aNa

a1 a2

ax (ax,ax)

a1 a2 ax aNa

b1 b2

by (ax,by)

bNb

Interaction between Na a-type and

Nbb-type particles

ab b

a

ab N N v

R = <σ >

Interaction between Na a-type particles

aa a

aa a

a aa

N v N v R N

>

<

>

<

=

σ

σ 2

2 ) 1 (

2

(30)

• Semi-Catalyzed-D cycle (SCAT-D Mode)

D-D Burn Modes

dt t

d t

dd

d

v N N v

N

2

< σ >

,

= < σ >

2

Channel - t

Channel - 3He

MeV 6

. + 17 +

+ t n α d

MeV 9

. 24 2

5 dn +

3

He + α + p +

dt dd dt

t dd d

t

v v v

v N

N

>

<

>

≈ <

>

<

>

= <

σ σ σ

σ

4 1 2

1

,

reaction link

Providing Rdd,t=Rdt

MeV 1

. + 4 +

+ d t p d

MeV 2

.

3

+ + 3

+ d He n

d

(31)

• Catalyzed-D cycle (CAT-D Mode)

D-D Burn Modes

MeV 2

. 43 2

2 2

6 dn + α + p +

MeV 3

.

3

→ + + 18

+ He p

d α

MeV 1

. + 4 +

+ d t p d

MeV 2

.

3

+ + 3

+ d He n d

Channel - t

Channel - 3He

MeV 6

. + 17 +

+ t n α d

reaction link

reaction link

(32)

• General D-D initiated fusion linkage processes

D-D Burn Modes

) 6 . 14 ( )

7 . 3

3

(

p He

d + → α + )

1 . 3 ( )

0 . 1

( p

t d

d + → +

) 4 . 2 ( )

8 . 0

3

(

n He

d

d + → +

) 5 . 3 ( )

1 . 14

( + α

→ + t n d

) 3 . 1 ( )

0 . 5 ( )

0 . 5

( + + α

+ t n n

t

) 1 . 5 ( )

3 . 1 ( )

7 . 5

3

(

n p

He

t + → + α +

) 4 . 1 ( )

7 . 5 ( )

7 . 5

3

(

3

He + Hep + p + α

(33)

D- 3 He Fusion

MeV 3

.

3

→ + + 18

+ He p α

d

(34)

• An attainable “clean” fusion reaction, direct energy conversion - Tritium, neutron: problems of radiological safety,

first wall endurance, shielding and induced radioactivity

• Higher reaction temperature required

• More severe Bremsstrahlung radiation

• Scarce 3He: 3He/(3He+4He)~10-6 cf) Lunar Rock

D- 3 He Fusion

years He

t3 + β , τ1/2 =12.3 He

n d

d + → +3

d He He d He

d v N N

R p

He

d+3 → +α +18.3MeV, 3 =<σ > 3 3

(35)

D- 3 He Fusion

(36)

36

D- 3 He Fusion

years He

t3 + β , τ1/2 =12.3 He

n d

d + → +3

d He He d He

d v N N

R MeV p

He

d+3 → +α +18.3 , 3 =<σ > 3 3

2 , MeV 1

. 4

2 , ,

d t dd t

dd

v N R

p t d

d + → + + =<σ >

2 , MeV 2

. 3

2 ,

, 3

3 3

d He dd He

dd

v N R

n He d

d + → + + =<σ >

unclean side reactions

d He He

dd He d He

dd He d

N N v

v R

R 3

3 3

3 3

, ,

2< >

>

= <

σ σ

d He t

dd He d t

dd He d

N N v

v R

R 3 3 3

, ,

2 < >

>

= <

σ σ

Control on high temperature and

3He and d fuel ions

• An attainable “clean” fusion reaction, direct energy conversion - Tritium, neutron: problems of radiological safety,

first wall endurance, shielding and induced radioactivity

• Higher reaction temperature required

• More severe Bremsstrahlung radiation

• Scarce 3He: 3He/(3He+4He)~10-6 cf) Lunar Rock

(37)

Beam-target Fusion

• Beam-target collisions (Binary interactions)

• loss energy >> fusion energy

• Fusion by beam-target collisions are not proper for practical

dt

scatt

σ

σ >> 100

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