Introduction to Fusion

Introduction to Fusion

• Fusion Reactions

• Thermonuclear Reactions

• Power Balance

• Ignition

• Tokamaks

• Tokamak Reactor

• Fuel Resources

• Tokamak Economics

• Tokamak Research

Why fusion is so difficult ?

Coulomb Barrier

Potential Energy vs. Nuclear Separation

Need only high energy beam?

Reaction Rates for Thermonuclear Fusion

Power Balance

E

H

n T

E v

V n P



³ 

4

1

  



Heating power per volume

-particle heating power

Energy losses:

Particle loss Radiation loss

Energy confinement time

H H

E

P

TV n

P

W  3

 

Ideal Breakeven and Lawson Criterion

s m n



• Ideal breakeven : perfect particle confinement, bremsstrahlung=fusion power

• Lawson criterion : no direct alpha heating

finite particle confinement, _p power station efficiency, =1/3

p br

p br

f

T P n

T P n

E v

n   

 3 ) ³

4

(1 ²      

1 1 ) 1

3 /(

) 3 4 /(

1

2











 



p br

f

T n n P

T E

v

2 / 1

2Z T

n P_br  _eff

Breakeven and Ignition Conditions



 v E

n

T



  12

P_H < 0

s m

n   1 . 5  10

At T=30keV,

H

H P

P P

E v

n

Q ^



4 1 ₂

 

 

Q = 1 : breakeven, Q =  : ignition

Ignition Condition : Triple Products





n _E T



  12 T 2

v 





keVs m

nT



Approach to Ignition

Constant confinement time

Ignition

) , ( 3 4

3 1 ²

T n E nT

v V n

nT P dt

d _H

  _ 







Approach to Ignition : Cordey Pass



 n T ^{n v E} nT

V P

E

H

 

 

4 1 )

,

(

3

Stability for Alpha Particle Heating at Ignition

0 )

1 4 (

1

4 ] ) 1 ( 1

3 [ 3

2

2 2



 





 











 

 





 

dT T v d

v T dT

d T T

v E n

T dT E

v n d

dT d n T

dt T n d

E E E E







 





 





condition for stability at ignition(P_H=0)

dT v d

v T dT

d T _E

E







 











Constant confinement time

) , ( 3 4

3 1 ²

T n E nT

v n

dt nT d

E

  _ 





E T

 1



at ignition(P_H=0)

Stabilizing Effect from Confinement Degrade

unstable

stable

E

T

 1



* Additional stabilizing factor : accumulation of ‘helium ash’

Toroidal Force Balance

• Radial force balance : OK

• Single charged particle motion : : outward drift motion

• Toroidally expanding forces

• outward toroidal magnetic pressure

• tire tube force from plasma pressure Need poloidal field !

Hoop force from poloidal field need to be balanced as well

Shafranov’s formula for the vertical field required for the toroidal force balance

8 ) 2 ln

( 3

4 a

R l

R

B I _p ^{i o}

o p o

v  



 





Concept of Tokamak

Inductive Current Drive and Ohmic Heating

• Plasma current drive

• Ohmic heating : resistive heating

Magnetic Field Coils for Tokamak

• Roles of PF coils

• ohmic heating

• position control

• plasma shaping

Plasma Confinement

Separation between Plasma and Vacuum Vessel

• Energy confinement time: size, density, plasma current, etc

• Ohmic(Alcator) scaling : ~ na² ~ naR²q^0.5

• L-mode scaling : ~ I_pR^1.75/P^0.5

• Impurities --> radiation losses H-mode (ASDEX, 1982)

• Impurity control and helium ash removal

• cause radiation losses and fuel dilution

• solved by magnetic divertor : localized power density limitation

Structure :

Principal Components of Tokamak Reactor

Current drive

Heat removal Tritium breeding Neutron shielding

Ash removal Heat removal Heat recovery

Conversion from Thermonuclear Power to Electric Power

Rankine or Brayton cycles?

Direct energy conversion system ?

Fuel Resources

+4.8Mev -2.5Mev 7.4% ⁶Li

92.6% ⁷Li

Tokamak Economics

f o

f

N N B v T E

P 

(

/ 16 

) 

  

Plasma beta

Fusion power density

f f

f

RE n n v E

P  

  

Fusion Power Density

o i o

i i e

e

B

nT B

T n T

n



 

2 / 2 2

/

2

 



Then,

where

N  n / n

Technology of large S.C. coil

Nuclear physics

Plasma physics

Reaction Parameter, Beta and Cost

H H

E P

TV n P

W 3



 

How to increase beta?

H EP T

n 

  

• Plasma stability requires large plasma currents

aB I l_{i p}

N

 

Tokamak Reactor Parameters

• energy confinement time

• instability-induced plasma disruption

• toroidal magnetic field

• critical field allowed in superconductors

• magnetic stresses on the coil

Size and plasma current required for a reactor determined by

keVs m

nT



keVs m

I H

nT 

 6  10

) , (

2

a b a f R nT

I _p

E 



Goldston from power balance and enhancement factor

2 / 1 2 /

)1

3

( P

f I

H ^p

E 



E

P nT



 3

) , (

2 2

a b a f R nT

I H _p

E 

 MA

I_p  30H

a R B

B

s

 2





s o

p aB

I _





 2 mT

RB_  65H Trade-off between size and magnetic field

Tokamak Reactor Power





 E n v RdS RE ^an v rdr

P 0

2 2

2

2   



)

1 ˆ(

ˆ 2

2

a T r

n

nT  

MW n T

Rab

P ₂₀ )² ˆ² 10

( ˆ 1

2

15 . 0

 



thermonuclear power density

Pressure profile

T2

v 



Greenwald density limit : n(10²⁰m^-3)<I(MA)/πa²

Tokamak Research History

• z-pinch to tokamak : strong toroidal field increase stability, T_e=1keV (1960s)

_E~milliseconds, T_i ~ a few hundred eV

• anomalous electron transport, _E~100 milliseconds in 1980s, _E~na² --> larger size

• heating : ohmic heating (plasma resistivity

~ T_e^-3/2), NBI and ICRF (T_i ~ several keV) in early 1980s, _E~P^-0.5

• H-mode of ASDEX : divertor, heating

• Instability : disruption, sawtooth, _limit

• TFTR and JET : T_i >30keV, DT >10MW I_p up to 7MA, _E~second (JET)

• toward Ignition

Beam-Fusion vs. Thermonuclear Fusion