Fusion Reactor Technology I

FF usion Reactor Technology I usion Reactor Technology I

FF usion Reactor Technology I usion Reactor Technology I

(459.760, 3 Credits) (459.760, 3 Credits)

P f D Y S N Prof. Dr. Yong-Su Na (32-206, Tel. 880-7204)

( , )

Contents Contents

Week 1 Magnetic Confinement

Contents Contents

Week 1. Magnetic Confinement

Week 2-3. Fusion Reactor Energetics

Week 4 Basic Tokamak Plasma Parameters Week 4. Basic Tokamak Plasma Parameters Week 5. Plasma Heating and Confinement Week 6 Plasma Equilibrium

Week 6. Plasma Equilibrium

Week 8. Particle Trapping in Magnetic Fields Week 9 10 Plasma Transport

Week 9-10. Plasma Transport

Week 11. Energy Losses from Tokamaks Week 12 The L and H modes

Week 12. The L- and H-modes Week 13-14. Tokamak Operation

2

Contents Contents

Week 1 Magnetic Confinement

Contents Contents

Week 1. Magnetic Confinement

Week 2-3. Fusion Reactor Energetics

Week 4 Basic Tokamak Plasma Parameters Week 4. Basic Tokamak Plasma Parameters Week 5. Plasma Heating and Confinement Week 6 Plasma Equilibrium

Week 6. Plasma Equilibrium

Week 8. Particle Trapping in Magnetic Fields Week 9 10 Plasma Transport

Week 9-10. Plasma Transport

Week 11. Energy Losses from Tokamaks Week 12 The L and H modes

Week 12. The L- and H-modes Week 13-14. Tokamak Operation

Fusion

Fusion Reactor Reactor EnergeticsEnergetics Fusion

Fusion Reactor Reactor EnergeticsEnergetics

• Fundamental requirement of a fusion reactor system

* 0

*

* = _out − _in >

net E E

E

∫ ∫

∫^{⎜⎛ ⎟⎞ τ ⎜⎛ ⎟⎞ τ ⎜⎛ ⎟⎞}

τ

dE d dE d

dE d

* 0

*

* ∫ ∫

∫^⎜_⎝^{⎛ ⎟}_⎠^{⎞ = ⎜}_⎝^{⎛ ⎟}_⎠^{⎞ − ⎜}_⎝^{⎛ ⎟}_⎠^{⎞ >}

o out o in

o net

dt dt dt dt

dt dt 0

• Fusion Plasma Energy Balance

∫

∫^{b dE}_dt^{th dt =Eaux +Efu −En −Erad −τb Eth dt}

τ

τ^*

*

*

*

*

*

*

• Fusion Plasma Energy Balance

Time variations of power considered

∫

∫

o E

o dt τ

*

*

in in

aux E

E =η E^*

power considered

c fu

n f

E

E_* =1− E^*_fu − E_n^* = f_cE^*_fu

*

*

fu

fu E

Q = E = Plasma Q-value

4

*

*

in in aux

p E E

Q η Plasma Q-value

Fusion

Fusion Reactor Reactor EnergeticsEnergetics Fusion

Fusion Reactor Reactor EnergeticsEnergetics

∫

∫^{b dE ⎜⎛ ⎟⎞ τb E}

τ _{* *}

1 ∫

∫ _⎟^{⎟ − −}

⎠

⎞

⎜⎜

⎝

⎛ +

=

o E

th rad

fu p

c o

th E dt

E Q E

f dt dt

dE

τ^*

*

1 *

τb

) 0 ( )

( ^*

*

*

th b

th o

thdt E E

dE

b = −

∫ ^τ

b *

τ

o E

th rad

fu

f

E dt E

E

b

1

*

*

*

*

+ +

= ^τ∫ _τ

If, steady state

p

c Q

f +

• if Q →∞ the fusion energy delivered to the plasma

• if, Q_p→∞, the fusion energy delivered to the plasma via the charged reaction products is seen to balance the total energy loss from the plasma

Fusion

Fusion Reactor Reactor EnergeticsEnergetics Fusion

Fusion Reactor Reactor EnergeticsEnergetics

⎤

⎡

b b b

t

τ τ τ E

) (G Considering a D-T plasma with Q_p→∞,

∫ ∫ ∫ ∫

∫ _⎥^⎥

⎦

⎤

⎢⎢

⎣

⎡ + +

=

b b b

o o E

th o

net cyc br

V dt

dt V

dt

c dt

t r

t r dt E

P P

r d dt

Q t r R r d

f τ ( , )

) , ) (

( )

,

( ³

3

, G G

kT Z

N N A

P ² ₋ ⎜⎛ m J ⎟⎞

A

3

10 38

6

1 Why effect of ions

e e

i br

br A N N Z kT

P = ² ≈ × ⎜⎜⎝ ⎟⎟⎠

s A_br 1.6 10 ³⁸ eV

eψ

e cyc net

cyc A N B kT

P = ² A_cyc ≈ 6.3×10⁻²⁰(JeV⁻¹T⁻²s⁻¹)

Why effect of ions not included in P_br and P_cyc?

Homework

) (

) ( )

, (

) , (

*

* 3

t t E t

r t r r E

d

E th E

th

V∫ τ ^{GG =}τ Volume integrated

e e i

i e

e net cyc e

e i br i

i dt dt c

kT N kT T N

N P

T N N P T

N P

f ( )

2 ) 3 , ( )

, , ( )

,

, (

+ + +

=

In a steady state, homogeneous plasma

E

y 2 τ

,

e i j kT N

E_{th j j j} , , 2

3

. = =

complex interrelation between the plasma density and its

6

• complex interrelation between the plasma density and its temperature as required for ignition

Fusion

Fusion Reactor Reactor EnergeticsEnergetics Fusion

Fusion Reactor Reactor EnergeticsEnergetics

• Lawson criterion

recoverable energy from a fusion reactor must exceed the energy supplied

d l

*

*

*

* E E E

E =η +η +η

during a representative time interval

– reactor criterion: energy viability of the entire plant

th th rad

rad fu

fu

out E E E

E =η +η +η

*

*

*

th rad

in

inE = E + E

η

in th rad

th th rad

rad fu

fu

E E E

E

E η η η

η ^* + ^* + ^* > ^{* + *} ηin

*

*

*

*

* )

( _{fu rad th rad th}

out

inη E + E + E > E + E

η

th rad fu

E l E

l

l l

out = , = , ,

∑

∑^η

η ^Average conversion

efficiency

E_l

∑ ^efficiency

Fusion

Fusion Reactor Reactor EnergeticsEnergetics Fusion

Fusion Reactor Reactor EnergeticsEnergetics

∫

= _{E l}

l P r d r

E^* τ _* (G) ³ Global energy terms

V

) 3

( )

3

( ³

3r P P NT d r P NT

d + + >∫ +

∫ ^{τ τ τ}

η η

Assuming, Bremsstrahlung only

) 3

( )

3

( _*P _*P NT d r _*P NT

r

d _{E br}

V V

br E fu

E out

in^η ∫ ^τ +^τ + >∫ ^τ +

η

NT T

N T

N r

E_th ( _{i i e e}) 3 2

) 3

(G = + =

e e i

i

th ( )

) 2 (

⎞

⎛

Assuming, homogeneity throughout the plasma volume V

NT T

N A NT

T N

A Q

N v N

E br

E br

E ab ab ab

b a out

in 3 3

1 ^*

2

* 2

* ⎟⎟⎠ > +

⎜⎜ ⎞

⎝

⎛ < > + +

+ σ τ τ τ

η δ η

Kronecker d introduced to account for the case of indistinguishable reactants

Q T v

N T

b b

out in

E ( )

) 1

( 3

* σ η η

τ > _{< >} ⁻

Kronecker-d introduced to account for the case of indistinguishable reactants

3 /

≈1

out inη η

8

T Q A

T v

out br in ab

ab ab

out

in (1 )

) 1

( 4

)

( η η

δ η σ

η − −

+

>

<

Fusion

Fusion Reactor Reactor EnergeticsEnergetics Fusion

Fusion Reactor Reactor EnergeticsEnergetics

• Ignition

Energy viability of the fusion plasma

NT P

P P

f_{c,dt dt}τ_E* ≥ ( _br + _cyc^net)τ_E* +3 Energy viability of the fusion plasma

N

T B T A

T A Q v

f N T

cyc dt br

dt dt dt

E σ ψ

τ _{* 2}

) ( ) 3

(

−

> −

≥ <

No energy conversion efficiency contained

T N A

Q

fc,dt dt br

4

• Break-evenBreak even

The total fusion energy production amounts to a magnitude equal to the effective plasma energy input.

* 1

*

=

= _p

in in

fu Q

E E η

Fusion

Fusion Reactor Reactor EnergeticsEnergetics

What is required to light a fire in a

Fusion

Fusion Reactor Reactor EnergeticsEnergetics

What is required to light a fire in a stove?

Fuel: D, T

n

Amount/density:

Heat insulation:

T

Deuterium

Ignition temperature:

≥ ?

⋅

⋅ T τ

n

Tritium

≥ ?

⋅

⋅ T τ

n

Criterion requiredLawson Criterion Criterion

10

Fusion

Fusion Reactor Reactor EnergeticsEnergetics Fusion

Fusion Reactor Reactor EnergeticsEnergetics

S h f G l d

• A.A. Harms, K.F. Schoepf, G.H. Miley, D.R. Kingdon,

„Principles of Fusion Energy“, Ch. 8 Homework: Problems 8.6

Status of the Tokamak Research Status of the Tokamak Research Status of the Tokamak Research Status of the Tokamak Research

Q=1 14 Q=1.14

Status of the Tokamak Research Status of the Tokamak Research Status of the Tokamak Research Status of the Tokamak Research

Status of the Tokamak Research Status of the Tokamak Research Status of the Tokamak Research Status of the Tokamak Research

Status of the Tokamak Research Status of the Tokamak Research Status of the Tokamak Research Status of the Tokamak Research

• Present machines produce significant fusion power:

- TFTR (USA) ~10 MW in 1994 TFTR (USA) ~10 MW in 1994

Status of the Tokamak Research Status of the Tokamak Research Status of the Tokamak Research Status of the Tokamak Research

• DT-Experiments only in - JET

TFTR - TFTR

• with world records in JET:

- P_fusion = 16 MW - Q = 0.65

Status of the Tokamak Research Status of the Tokamak Research Status of the Tokamak Research Status of the Tokamak Research

• Progress in fusion can be compared with the computingProgress in fusion can be compared with the computing