I ntroduction to Nuclear Fusion
(409.308A, 3 Credits)
Prof. Dr. Yong-Su Na
(32-206, Tel. 880-7204)
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
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
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
• 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
)
2( m c Q
ab= − Δ
abMass Defect Energy of Nuclear Reaction e
d b
a + → +
reactants products
) (
)
(
d e a bab
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
ac
2+ E
k,b+ m
bc
2= E
k,d+ m
dc
2+ E
k,e+ m
ec
2Mass 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
• 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
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)
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 42 12 . 9
3
+ → + +
MeV Be
He
He
4 71 . 6
3
+ → +
MeV Li
Be
70 . 06
7
+ β
−→ +
6
K 10 15 ×
≤
Sun
Fusion in Nature
MeV N
p
C
131 . 9
12
+ → +
MeV C
N
131 . 5
13
→ + β
++ ν +
MeV N
p
C
147 . 6
13
+ → +
MeV O
p
N
157 . 3
14
+ → +
MeV N
O
151 . 8
15
→ + β
++ ν +
MeV C
p
N
125 . 0
15
+ → + α +
MeV p 2 2 25 . 1
4 → α + β
++ ν +
K Tstar ≥13×106
•
CNO (Carbon-Nitrogen-Oxygen) CycleFusion 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
Fusion in Nature
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.
Physical Characterisation of Fusion Reaction
r r q F
c aq
a3b0
,
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
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
Physical Characterisation 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)
Physical Characterisation of Fusion Reaction
Max Born (1882-1970) George Gamow
(1904-1968)
Fusion Reaction Cross Sections
• Beam-target collisions (Binary interactions) - For fixed target
- For moving target
2 /
,
,
1 1 121
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
BE
E A
/12
( ) =
−σ
Gamow theory (1938)Fusion Reaction Cross Sections
• 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 bv v
b a ab
ab v v v v F v F v d v d v
v
a b
3
) 3
( )
− (
−
=
>
<σ
∫ ∫
σab b
a
fu
N N v
R = < σ >
( )
( )
a b a a b b a bv 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 xx
v M v
F →
Thermodynamic equilibrium
dx n n E
dn1 = −
σ
12( ) 1 2v v dn
dn dt dn
dRfu ≡ d (− ) = 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
Both species at the same temperatures
Fusion Reaction Rate Parameter
(Reactivity or σ-v Parameter)
Fusion Fuels
•
Possible fusion reactionsMeV 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 + 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
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
stgeneration
- 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
Fusion Fuels
• D-T reaction: 1
stgeneration
- Tritium breedingThe 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 Li92.58% of natural Li
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
• 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 + He → p + α +
MeV 1
.
3
→ + + + 12
+ He n p α t
MeV 3
. + 14 +
→ d α
• 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
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
• 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 d → 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 Rdd,t=Rdt
MeV 1
. + 4 +
→
+ d t p d
MeV 2
.
3
+ + 3
→
+ d He n
d
• Catalyzed-D cycle (CAT-D Mode)
D-D Burn Modes
MeV 2
. 43 2
2 2
6 d → 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
• 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 + He → p + p + α
D- 3 He Fusion
MeV 3
.
3
→ + + 18
+ He p α
d
• 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
t→3 + 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
D- 3 He Fusion
36
D- 3 He Fusion
years He
t→3 + 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
Beam-target Fusion
• Beam-target collisions (Binary interactions)
• loss energy >> fusion energy
• Fusion by beam-target collisions are not proper for practical
dt
scatt