Fusion Reactor Technology I

F usion Reactor Technology I

(459.760, 3 Credits)

Prof. Dr. Yong-Su Na

(32-206, Tel. 880-7204)

Week 1. Magnetic Confinement

Week 2. Fusion Reactor Energetics (Harms 2, 7.1-7.5)

Week 3. How to Build a Tokamak (Dendy 17 by T. N. Todd) Week 4. Tokamak Operation (I): Startup

Week 5. Tokamak Operation (II):

Basic Tokamak Plasma Parameters (Wood 1.2, 1.3) Week 7-8. Tokamak Operation (III): Tokamak Operation Mode Week 9-10. Tokamak Operation Limits (I):

Plasma Instabilities (Kadomtsev 6, 7, Wood 6) Week 11-12. Tokamak Operation Limits (II):

Plasma Transport (Kadomtsev 8, 9, Wood 3, 4) Week 13. Heating and Current Drive (Kadomtsev 10)

Week 14. Divertor and Plasma-Wall Interaction

2

Contents

Week 1. Magnetic Confinement

Week 2. Fusion Reactor Energetics (Harms 2, 7.1-7.5)

Week 3. How to Build a Tokamak (Dendy 17 by T. N. Todd) Week 4. Tokamak Operation (I): Startup

Week 5. Tokamak Operation (II):

Basic Tokamak Plasma Parameters (Wood 1.2, 1.3) Week 7-8. Tokamak Operation (III): Tokamak Operation Mode Week 9-10. Tokamak Operation Limits (I):

Plasma Instabilities (Kadomtsev 6, 7, Wood 6) Week 11-12. Tokamak Operation Limits (II):

Plasma Transport (Kadomtsev 8, 9, Wood 3, 4) Week 13. Heating and Current Drive (Kadomtsev 10)

Week 14. Divertor and Plasma-Wall Interaction

3

Contents

Fusion Reactor Energetics

4

*

0

*

*

=

_out

−

_in

>

net

E E

E

∫ ∫

∫ ⎜⎜ ⎝ ⎛ ⎟⎟ ⎠ ⎞ =

^τ

⎜⎜ ⎝ ⎛ ⎟⎟ ⎠ ⎞ −

^τ

⎜⎜ ⎝ ⎛ ⎟⎟ ⎠ ⎞ >

τ

o out o in

o net

dt dt dt dE

dt dt dE

dt

dE 0

*

*

*

∫

∫

^b

= + − − −

^b

o E

th rad

n fu

aux o

th

E dt

E E

E E

dt dt

dE

^τ

τ

τ

^*

*

*

*

*

*

*

*

*

in in

aux

E

E = η

c fu

n

f

E

E

_*

= 1 −

*

*

*

*

fu c n

fu

E f E

E − =

• Fusion Plasma Energy Balance

• Fundamental requirement of a fusion reactor system

Considering the time variations of power

τ_b: burning time

Fusion Reactor Energetics

5

∫

∫ ⎟ ⎟ − −

⎠

⎞

⎜ ⎜

⎝

⎛ +

=

^b

b

o E

th rad

fu p c

o

th

E dt

E Q E

f dt dt

dE

^τ

τ

τ

^*

*

*

*

*

1

) 0 ( )

(

^*

*

*

th b

th o

th

dt E E

dE

b

= −

∫ τ

τ

p c

o E

th rad

fu

f Q

E dt E

E

b

1

*

*

*

*

+ +

=

^τ

∫ τ

If, steady state

• 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.

*

*

*

*

in in

fu aux

fu

p

E

E E

Q E

= η

=

Plasma Q-value (fusion multiplication factor):

measure for how efficiently an energy input to the plasma is converted into fusion energy

∫

∫

^b

= + − − −

^b

o E

th rad

n fu

aux o

th

E dt

E E

E E

dt dt

dE

^τ

τ

τ

^*

*

*

*

*

*

*

Fusion Reactor Energetics

6 E

e e i i e

e net cyc e

e i br i

i dt dt c

T n T T n

n P T

n n P T

n P

f τ

) (

2 ) 3 , ( )

, , ( )

,

,

(

+ + +

=

e i j T

n

E

_{th j j j}

, , 2

3

.

= =

) (

) ( )

, (

) , (

*

* 3

t t E t

r t r r E

d

E th E

th

V

∫ τ

^GG

= τ

∫ ∫ ∫ ∫

∫ ⎥ ⎥

⎦

⎤

⎢ ⎢

⎣

⎡ + +

=

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 τ τ

τ ( , ) ) , ) (

( )

,

(

³

3

, G

G G

e e

i br

br

A n n Z kT

P =

²

⎟⎟ ⎠

⎜⎜ ⎞

⎝

× ⎛

≈

⁻

s eV

J A

_br

m

3

10

38

6 . 1

e

ψ

e cyc net

cyc

A n B kT

P =

²

A

_cyc

≈ 6 . 3 × 10

⁻²⁰

( JeV

⁻¹

T

⁻²

s

⁻¹

)

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

volume integrated

In a steady state, homogeneous plasma, local D-T fusion ignition condition

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

∫

+

=

^b

o E

th rad

fu

c

E dt

E E

f

τ

τ

^*

*

*

*

What is required to light a fire in a stove?

n

T

≥ ?

⋅

⋅ T τ

n

Criterion required Deuterium

Tritium

Fuel: D, T

Amount/density:

Heat insulation:

Ignition temperature:

Fusion Reactor Energetics

Lawson Criterion

7

Fusion Reactor Energetics

8

nT P

P P

f

_{c,dt dt}

τ

_E*

≥ (

_br

+

_cyc^net

) τ

_E*

+ 3

n T B T A

T A Q v

f n T

cyc dt br

dt dt c dt

E

σ ψ

τ

₂

,

*

4

) ( ) 3

(

−

> −

≥ <

*

1

*

=

=

_p

in in

fu

Q

E E η

• Ignition

Energy viability of the fusion plasma:

actual self-sustaining engineering reactor condition with no heating power

no energy conversion efficiency contained

• Break-even (scientific)

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

E e e i i e

e net cyc e

e i br i

i dt dt c

T n T T n

n P T

n n P T

n P

f τ

) (

2 ) 3 , ( )

, , ( )

,

,

(

+ + +

=

∞

→

=

_p

in in

fu

Q

E E

*

*

η

- Charged particle self-heating power > loss powers (radiation+plasma)

<σv>_dt ∝ T ² at 10-20 keV → nτ_E*T

Status of the Tokamak Research

• n = 10²⁰ m^-3: T ~ 30 keV, nτ_E* ~ 2.7x10²⁰ m^-3s, τ_E* ~ 2.7 s

• Ignition contours tend towards infinity as T approaches T_crit due to high cyclotron radiation.

Fusion Reactor Energetics

10

• Lawson criterion

– reactor criterion: energy viability of the entire plant

Proceedings of the Physical Society (London), B70, 6 (1957)

Fusion Reactor Energetics

11

• Lawson criterion

*

*

*

*

th th rad

rad fu

fu

out

E E E

E = η + η + η

*

*

*

th rad

in

in

E = E + E

η

Power loss

- The recoverable energy from a fusion reactor must exceed the energy which is supplied to sustain the fusion reaction.

*

*

in

out

E

E >

Fusion Reactor Energetics

12 in

th rad

th th rad

rad fu

fu

E E E

E

E η η η

η

^*

+

^*

+

^*

>

^*

+

^*

*

*

*

*

*

)

(

_{fu rad th rad th}

out

in

η E + E + E > E + E

η

th rad fu

E l E

l l l

l l

out

= , = , ,

∑

∑ η

η

• Lawson criterion

average conversion efficiency

∫

=

V l E

l

P r d r

E

^*

τ

_*

( G )

³ global energy terms - output electric energy > required input energy

Fusion Reactor Energetics

13

) 3 (

) 3

(

_{* *} ³ _*

3

r P P nT d r P nT

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 = + =

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

T Q A

T v

n T

out br in ab

ab ab

out in

out in E

) 1

) ( 1

( 4

) (

) 1

( 3

*

η η

δ η σ

η

η τ η

− + −

>

<

> −

Assuming, Bremsstrahlung only

Assuming, homogeneity throughout the plasma volume V

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

3 /

≈ 1

out in

η

η

14

Fusion Reactor Energetics

• Lawson criterion

T Q A

T v

n T

out br in ab

ab ab

out in

out in E

) 1

) ( 1

( 4

) (

) 1

( 3

*

η η

δ η σ

η

η τ η

− + −

>

<

> −

- Practical energy break-even condition for confinement parameter nτ_E in a fusion reactor of electric power plant

15

Fusion Reactor Energetics

• Lawson criterion

- No particular fusion design was necessary in the derivation of this criterion.

- Although it does not contain all relevant processes such as cyclotron radiation, it is a useful and widely employed criterion.

- For commercial power applications, it would be necessary to exceed the minimum Lawson limit by perhaps a factor of ten or better.

Homework:

Problems 8.6

Q=1.14

Status of the Tokamak Research

Status of the Tokamak Research

Status of the Tokamak Research

bars

keVs m

T n

_E

5

10

3

^{21 3}

=

×

≥

⁻

τ

Ignition condition

• Present machines produce significant fusion power:

- TFTR (USA) ~10 MW in 1994

- JET (EU) 16 MW (Q=0.64) in 1997

Status of the Tokamak Research

Status of the Tokamak Research

• DT-Experiments only in - JET

- TFTR

• with world records in JET:

- P

_fusion

= 16 MW

- Q = 0.65

• Progress in fusion can be compared with the computing power and particle physics accelerator energy.

Status of the Tokamak Research