I ntroduction to Nuclear Fusion

I ntroduction to Nuclear Fusion

Prof. Dr. Yong-Su Na

1

2

What is nuclear fusion?

3

Matter and Energy

• Chemical reactions (combustion)

heating fuels

reaction energy products

E_out

m_out E_in

m_in

Matter-Energy Transformation

reactor/

generator

eV O

H O

H 3

2 1

2 2

2 + → +

K K J

eV J 11600

/ 10

38 . 1

10 6

.

1 1 ₂₈

19 =

×

= × ₋⁻

4

Matter and Energy

• Chemical reactions (combustion)

• Fission process

• Fusion process

• Total energy conservation including rest mass energy

• If Δm = M_out-M_in < 0, then we can get E_out > E_in.

out out

in

in M E M

E + → +

heating fuels

reaction energy products

E_out

m_out E_in

m_in

Matter-Energy Transformation

reactor/

generator

http://www.meteoweb.eu/2011/09/e- possibile-superare-la-velocita-della- luce-teoria-della-relativita-a-

rischio/88437/, Dec, 2014

5

Mass Defect Energy of Nuclear Reaction

e d

b

a + → +

reactants products

*

*

after before E

E =

) (

) (

) (

)

(E_k,a + m_ac² + E_k,b + m_bc² = E_k,d + m_dc² + E_k,e + m_ec²

Total energy

(

) (

)

) (

)

( _{d e a b}

ab m m m m

m = + − +

∆

ab b

k a

k E Q

E _, + _, <<

For

( ) ( )

[ ]

2

2

) (

m c

c m m

m m

Q

ab

e d

b a

ab

∆

−

=

+

− +

=

2 2

,

, 2

1 2

1

e e d

d e

k d

k

ab E E m v m v

Q ≈ + = +

6

Mass Defect Energy of Nuclear Reaction

2 2

,

, 2

1 2

1

e e d

d e

k d

k

ab E E m v m v

Q ≈ + = +

e e d

dv 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 d +t → n +α MeV

6 .

=17 Qdt

kg m

kg m

m m

n p

p n

27 27

10 674927

. 1

10 672621

. 1

−

−

×

=

×

=

≈



 



 +

= +



 



 +

= +



 



 +

= +

2 2

2 2 2

2 2

2

2 2

2 1 2

1

2 1 2

1

2 1 2

1

d d e

d e e d e

d e

d d d

e d e

d e

d d e

e d e d

e d

d

v m m v

m m m m

m m

v m m v

m m

m m

v m m

m m

m m

v m Derive! m

MeV 5

. 5 3

1 , MeV 5 14.1

4

,

,_n ≈ _dt ≈ _k ≈ _dt ≈

k Q E Q

E _α

eV O

H O

H 3

2 1

2 2

2 + → +

Fusion in Nature

• Nuclei are made up of protons and neutron, but the mass of a nucleus is always less than the sum of the individual masses of the protons and neutrons which constitute it.

• Binding energy: the amount of energy released when a particular nucleus is formed.

. . )

(A Z n X B E

Zp + − →_Z^A +

2

)] 2

) (

[(

.

.E m Zm A Z m c mc

B ≡ − _X − _p + − _n = −∆

Δm < 0: released energy

(exothermic or exoergic)

http://www.daviddarling.info/encyclopedia/B/binding_energy.html 7

Fusion in Nature

8

Sun producing 3.8x10²⁶ J/s equivalent to 4.3x10⁹ kg

Sun composed of proton (73%), He (25%), etc

How old is the sun?

How long is the sun’s lifetime?

Fusion in Nature

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)

• 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

http://www.nobelprize.org/nobel_prizes/physics/laureates/1967/bethe-bio.html 9

10

Fusion in Nature

One of the most impressive discoveries was the origin of the stars, that makes them continue to burn. One of the men who

discovered this was out with his girl friend the night after he realized that nuclear reactions must be going on in the stars in order to make them shine. She said “Look at how pretty the stars shine!” He said “Yes, and right now I am the only man in the

world who knows why they shine.” She merely laughed at him.

She was not impressed with being out with the only man who, at that moment, knew why stars shine. Well, it is sad to be alone, but that is the way it is in this world.

- The Feynman Lectures on Physics I, p.3-7

• 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

11

Fusion in Nature

• The PP (Proton-Proton) Chain

Step 1: Smash two protons together to make deuterium

MeV d

p

p + → + β ⁺ +ν +1.2

Positron: antiparticle of the electron-like an electron with charge of +1e

Neutrino: electrically neutral, weakly interacting elementary subatomic particle

http://burro.astr.cwru.edu/Academics/Astr221/StarPhys/ppchain.html

MeV n

p → + β ⁺ +ν − 0.782

12

Fusion in Nature

• The PP (Proton-Proton) Chain

Gamma ray: electromagnetic radiation of an extremely high frequency (very high energy photon)

MeV He

d

p + →³ +γ +5.5

Do Steps 1 and 2 again so to have two ³He nuclei.

Step 2: A proton crashes into a deuterium nucleus, making ³He

http://burro.astr.cwru.edu/Academics/Astr221/StarPhys/ppchain.html

13

Fusion in Nature

• The PP (Proton-Proton) Chain

MeV p

He He

He ^{3 4} 2 12.9

3 + → + +

Step 3: Mash two helium-3 nuclei together to make helium-4

http://burro.astr.cwru.edu/Academics/Astr221/StarPhys/ppchain.html

14

Fusion in Nature

MeV d

p

p + → + β ⁺ +ν +1.2 MeV He

d

p + →³ +γ +5.5

MeV p

He He

He ^{3 4} 2 12.9

3 + → + +

γ +

→ + He Be He ^{4 7}

3

ν β → + + ⁻ Li

Be ⁷

7

nucleosynthesis

PPII Chain (14-23x10⁶ K)

He He

p

Li ^{4 4}

7 + → +

PPIII Chain ( > 23x10⁶ K)

γ +

→ + p B

Be ⁸

7

ν β + +

→ Be ⁺ B ⁸

8

He He

Be ^{4 4}

8 → +

• The PP (Proton-Proton) Chain

http://csep10.phys.utk.edu/astr162/lect/energy/ppchain.html

10-14x10⁶ K

CX → years

15

Fusion in Nature

- Most of ⁴He nuclei being produced in the Sun are born in the PP chain (98.3%).

6K 10 15×

T_Sun ≤

• The PP (Proton-Proton) Chain

http://www.nasa.gov/mission_pages/galex/20070815/f.html

Why are other processes needed to explain stars?

16

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 +

• The CNO Cycle

K T_star ≥13×10⁶

17

Fusion in Nature

keV Be 92

8 −

→ +α α

MeV C

Be ¹² 7.367

8 +α→ +γ +

• The triple alpha process

18

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 the final stage of a massive star

19

Physical Characterization of Fusion Reaction

r r q F_{c a} q^a₃^b

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.

• As such, the main technical difficulty for fusion is getting the nuclei close enough to fuse.

20

Physical Characterization of Fusion Reaction

(

)

^{( )}

R R

p t R d

q R q

U

p b

a p

b a

15 3

/ 1 3

/ 1 0

0 0 0

10 7

. 1 3 . 1

,

, , for MeV 4

. 0 4 ~

) 1 (

× −

−

= +

≈

= πε

] 1 exp[

) Pr(

r b a

r v

q q tunneling ∝ v −γ

Reflection and tunneling of an

electron wave packet 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

Attractive strong nuclear force

Sun: 1.4x10⁶ eV

21

Physical Characterization of Fusion Reaction

• 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)

Max Born (1882-1970) George Gamow

(1904-1968)

22

Fusion Reaction Cross Sections

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

E B

ab e

E

E) A ^/

( = ⁻

σ Gamow theory

(1938)

0 2

2 / 1 2

/

1 /

2

., B πm Z Z e hε

const

A = = ⁻ _{r a b}

2 28 2

24 10

10

1barn = ⁻ cm = ⁻ m

23

Fusion Reaction Rate Parameter (Reactivity)

• Fusion reaction rate density

ab r

b a

fu N N v

R = <σ >

( )

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-v parameter

r b a

fu N N v

R ∝ v_r = v −_a v_b

24

Fusion Reaction Rate Parameter (Reactivity)

- Thermodynamic equilibrium - Both species at the same

temperatures

http://www.scienceall.com/jspJavaPopUp.do?classid=CS000140&articleid=611&bbsid=146&popissue=java

) ( )

( _{x x x}

x v M v

F →

25

Fusion Reaction Rate Parameter (Reactivity)

• Fusion reaction rate density

ab r

b a

fu N N v

R = <σ >

fu ab b

a fu

fu

fu R Q N N v Q

P = = <σ >

• Fusion power density

( )

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-v parameter

r b a

fu N N v

R ∝ v_r = v −_a v_b

26

Which fusion fuels to utilize for our

fusion reactor?

27

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 8

.

3 + + +1

→ He α n

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

3He+ He → p +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

28

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

http://www.scienceall.com/jspJavaPopUp.do?classid=CS000140&articleid=611&bbsid=146&popissue=java

29

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 (10 g out of 50 kg) - 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

Difference

between HWR and LWR?

30

D-T Fusion

• 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

MeV 6

. +17 +

→

+ t n α d

31

Fusion fuel microcapsule (micro balloon)

http://article.joinsmsn.com/news/article/article.asp?total_id=4570206&ctg=1100

The total lithium content of seawater is very large and is estimated as 230 billion tonnes, where the element exists at a

relatively constant

concentration of 0.14 to 0.25 parts per million (ppm).

Silvery-white lithium floating in oil)

D-T Fusion

Deuterium: 13-150 ppm

32

Fusion fuel microcapsule (micro balloon)

http://www.sciencetimes.co.kr/?news=%ec%8b%a0%ea%b8%b0%ed%9b%84%ec%b2%b4%ec%a0%9c%eb%a1%9c-

%eb%85%b9%ec%83%89%ea%b4%91%eb%ac%bc-%eb%9c%ac%eb%8b%a4

“한국광물자원공사가 발표한 ‘리튬시장 최근 동향 및 전망’이라는 보고서에 의하면 2016년 4월 6일자 리튬 가격은 2015년 1월 대비 약 270% 상승했다. 집계가 시작된 2007년 이후 명목 가격으로는 최고점에 있으며 8~9년 전 대비 370% 인상된 상태다.

리튬의 가격이 천정부지로 치솟는 이유는 스 마트폰 및 태블릿 등 IT 제품의 수요 덕분이다.

거기다 자동차 1대당 엄청난 양의 리튬이 사 용되는 전기자동차 시장의 활성화가 리튬 가 격의 인상을 더욱 부채질하고 있다.”

Li: 녹색광물. 전기차와 ESS의 2차전지에 사용됨.

D-T Fusion

전기자동차 및 재생에너지 분야의 성장으로 리튬 가격이 폭등하고 있다. 사진은 리튬 중 가장 많이 사용되는 탄산리튬.

33

) , ( )

, ( )

, ( )

,

( r t N r t N r t v r t

R









>

<

= σ

- Fusion reaction rate as a function of position and time

D-T Fusion

dt dt

t d

dt dt

dt

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

P (  , ) (  , ) (  , ) (  , ) (  , )

>

<

=

= σ

- Fusion power density

MeV 6

. + 17 +

→

+ t n α

d

34

D-D Fusion

• D-D fusion

- Possessing a much smaller power density

→ requiring a larger size for a specified total fusion power production

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

3He+ He → p +α +

MeV 1

.

3 → + + +12

+ He n p α t

MeV 3

. +14 +

→ d α

• Side reactions

35

D-D Burn Modes

• PURE-D Mode

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

ab b

a

fu N N v

R = <σ >

36

D-D Burn Modes

Fusion fuel microcapsule (micro balloon)

a₁ a₂ … a_x … a_Na

a₁ a₂

…

a_x (a_x,a_x)

… a_Na

a₁ a₂ … a_x … a_Na

b₁ b₂

…

b_y (a_x,b_y)

… b_Nb

Interaction between N_a a-type and

N_b b-type particles

ab b

a

ab N N v

R = <σ >

Interaction between N_a a-type particles

aa a

aa a

a aa

N v N v R N

>

<

≈

>

− <

=

σ

σ 2

2 ) 1 (

2

- To find the number of (x,y) combinations

37

D-D Burn Modes

Fusion fuel microcapsule (micro balloon)

dt t

d t

dd

d v N N v

N² <σ > _, = <σ >

2

Channel - t

Channel - ³He

MeV 6

. +17 +

→

+t n α d

MeV 9

. 24 2

5d → n+³He +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 R_dd,t = R_dt (triton fusion burn at a rate equal to its production rate)

MeV 1

. + 4 +

→

+ d t p d

MeV 2

.

3 + +3

→

+ d He n d

The relative tritium concentration in the fusing plasma may be small at low-to-medium temperatures but will increase for higher temperatures.

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

The bred tritium consumed almost immediately

38

D-D Burn Modes

• Catalyzed-D cycle (CAT-D Mode)

MeV 2

. 43 2

2 2

6d → n+ 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

39

D-D Burn Modes

• General D-D initiated fusion linkage processes

) 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 (

3He+ He → p + p +α

The connection reaction linkages vary with temperature and density.

40

D-

He Fusion

MeV 3

.

3

→ + + 18

+ He p α

d

41

D-

He Fusion

• 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 supply by nuclear decay of tritium

supply by d-d fusion reaction Lunar Rock

keV 6

.

3 + +18

→ He β ⁻ t

MeV 2

.

3 + + 3

→

+ d He n d

42

D-

He Fusion

43

D-

He Fusion

MeV 3

.

3

→ + + 18

+ He p α d

MeV 1

. + 4 +

→

+ d t p d

MeV 2

.

3

+ + 3

→

+ d He n d

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 for cleanliness

44

How to realise fusion on earth?

45

Beam target Fusion

46

Beam target Fusion

e d

b

a + → +

47

Beam target Fusion

• Beam-target collisions (Binary interactions)

- For fixed target - For moving target

2 /

,

, _{a a a}²

a v v E m v

m

m = = =

CM b

a

r v v v E E

m

m = , = − , = dx

n n E

dn_a = −σ_ab( ) _{a b}

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

Gamow theory (1938)

0 2

2 / 1 2 /

1 /

2

., B πm Z Z e hε

const

A = = ⁻ _{r a b}

E B

ab e

E

E) A ^/

( = ⁻

σ

v, E n_a, m

n_b

dx

48

Beam target Fusion

• Beam-target collisions (Binary interactions)

Scattering cross section?

49

Rutherford Scattering

Ernest Rutherford (1871-1937)

Nobel prize in Chemistry 1908

“It was quite the most incredible

event that has ever happened to me in my life. It was almost as incredible as if you fired a 15-inch shell at a

piece of tissue paper and it came back and hit you.” by Rutherford

50

Coulomb Scattering Cross Section

’

s

c

φ

1

r₀ m_b, q_b

m_a, q_a

v_r, m_r

A

c











  −



 



 



 



= 

−

2 1 sin

2

2 θmin

π

σ_s K

2 / 1 2

0 



 



= 

Ne kT_e

D

λ ε



 



= ⁻ 

D

K θ_min 2tan ¹ λ

51

Coulomb Scattering Cross Section

• loss energy >> fusion energy - ionisation, heating the target,

bremsstrahlung radiation, etc

• Projectiles slowed down to energies far below the Coulomb barrier

(370 keV in DT) rendering further fusion reactions most unlikely

• Fusion by beam-target collisions are not proper for practical energy-producing fusion reactors.

dt

scatt σ

σ >>100

Confinement needed!

52

Confinement for Fusion

http://rumd.org/

http://blog.naver.com/PostView.nhn?blogId=ofgrnkqn&logNo=90145273295&redirect=Dlog&widgetTypeCall=true http://desert.tistory.com/1991

53

Realisation of Nuclear Fusion

p t R d

q R q

U ^{a b} ~ 0.4 MeVfor , , 4

) 1 (

0 0

0 ⁼ πε

] 1 exp[

) Pr(

r b a

r v

q q tunneling ∝ v −γ

Thermonuclear fusion in a confined way:

Main approach to develop fusion energy

• Thermal conditions with high temperature needed for the high fusion reaction rate

• A sufficiently high temperature plasma needed to sustain in a practical reaction volume for a sufficiently long period of time.

Thermonuclear?