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. Tokamak Operation (I):

Basic Tokamak Plasma Parameters (Wood 1.2, 1.3) Week 4. Tokamak Operation (II): Startup

Week 5. Tokamak Operation (III): Tokamak Operation Mode Week 7-8. Tokamak Operation Limits (I):

Plasma Instabilities (Kadomtsev 6, 7, Wood 6) Week 9-10. Tokamak Operation Limits (II):

Plasma Transport (Kadomtsev 8, 9, Wood 3, 4) Week 11. Heating and Current Drive (Kadomtsev 10)

Week 12. Divertor and Plasma-Wall Interaction

Week 13-14. How to Build a Tokamak (Dendy 17 by T. N. Todd)

Contents

Week 1. Magnetic Confinement

Week 2. Fusion Reactor Energetics (Harms 2, 7.1-7.5) Week 3. Tokamak Operation (I):

Basic Tokamak Plasma Parameters (Wood 1.2, 1.3) Week 4. Tokamak Operation (II): Startup

Week 5. Tokamak Operation (III): Tokamak Operation Mode Week 7-8. Tokamak Operation Limits (I):

Plasma Instabilities (Kadomtsev 6, 7, Wood 6) Week 9-10. Tokamak Operation Limits (II):

Plasma Transport (Kadomtsev 8, 9, Wood 3, 4) Week 11. Heating and Current Drive (Kadomtsev 10)

Week 12. Divertor and Plasma-Wall Interaction

Week 13-14. How to Build a Tokamak (Dendy 17 by T. N. Todd)

Contents

Neutron (14 MeV)

Blanket

Deuterium Tritium

Coolant

Tritium Lithium

Fusion Power Plant (FPP) System

What is required to light a fire in a stove?

n

T

?

³

×

× T t

n

Criterion required (fusion triple product) Deuterium

Tritium

Fuel: D, T

Amount/density:

Heat insulation:

Ignition temperature:

Fusion Reactor Energetics

J. D. Lawson

Fusion Reactor Energetics

• Fundamental requirement of a fusion reactor system

τ_b: burning time

ò ò

ò ÷÷ >

ø ö çç è

- æ

÷÷ ø ö çç è

= æ

÷÷ ø ö çç è

æ

^{b b}

b

dt dt dt dE

dt dt dE

dt dE

in out

net

t t

t

0 0

*

*

0

*

0

Considering the time variations of power (Particularly for pulsed systems)

*

0

*

*

=

_out

-

_in

>

net

E E

E

*: referring to the entire

reaction volume

The overall net energy should be larger than the total energy externally supplied to sustain fusion reactions and associated processes subtracted from the total recovered energy

) ( )

,

( r t d

³

r E

^*

t

E

_out

V

out

=

ò r

Fusion Reactor Energetics

ò

ò = + - - -

b b

o E

th rad

n fu

aux o

th

E dt

E E

E E

dt dt

dE

^t

t

t

*

*

*

*

*

*

*

• Fusion Plasma Energy Balance

*

*

in in

aux

E

E = h

c fu

alpha

E f

E

_*

=

*

( )

^*

*

1

_{c fu}

n

f E

E = -

f_c: alpha particle fraction of fusion product energy Thermal energy content in the total plasma volume

ò

+ +

=

+

=

b

o E

th rad

n in

fu aux

out

E dt E

E E

E E

E

t

t

*

*

*

*

*

*

*

*

ò ò

ò ÷÷ >

ø ö çç è

- æ

÷÷ ø ö çç è

= æ

÷÷ ø ö çç è

æ

^{b b}

b

dt dt dt dE

dt dt dE

dt dE

in out

net

t t

t

0 0

*

*

0

*

0

Time Temperature

Energy Confinement Time

t

_E

• t

_E

is a measure of how fast the plasma looses its energy.

• The loss rate is smallest, t

_E

largest

if the fusion plasma is big and well insulated.

1/e

Time Temperature

Energy Confinement Time

t

_E

1/e

Time Temperature

Energy Confinement Time

power heating

applied

energy stored

=

»

¶ - ¶

=

in in

E

P

W t

P W

t W

Fusion Reactor Energetics

ò

ò ÷ ÷ - -

ø ö ç ç

è

æ +

=

b b

o E

th rad

fu c o p

th

E dt

E E

Q f dt dt

dE

^t

t

t

*

*

*

*

*

1

p c

o E

th rad

fu

f Q

E dt E

E

b

1

*

*

*

*

+ +

=

ò

t

If, steady state

t

• 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

= h

=

Plasma Q-value (fusion multiplication factor):

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

ò

ò = + - - -

b b

o E

th rad

n fu

aux o

th

E dt

E E

E E

dt dt

dE

^t

t

t

^*

*

*

*

*

*

*

→ What are requirements of a fusion reactor?

( )

^*

*

1

_{c fu}

n

f E

E = -

Fusion Reactor Energetics

• Ignition

Energy viability of the fusion plasma:

actual self-sustaining engineering reactor condition with no heating power

Considering a D-T plasma with Q_p→ ∞,

ò

+

>

b

o E

th rad

fu

c

E dt

E E

f

t

t

*

*

*

*

¥

®

=

_p

in in

fu

Q

E E

*

*

h

1 0

*

*

*

*

*

>

-

÷ -

÷ ø ö ç ç

è

æ +

= ò

ò

b b

o E

th rad

fu c o p

th

E dt

E E

Q f dt dt

dE

^t

t

t

Fusion Reactor Energetics

) (

) ( )

, (

) , (

*

* 3

t t E t

r t r r E

d

E th E

th

V

ò t r = t

r

ò ò ò ò

ò ú ú

û ù ê ê

ë

é + +

>

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

t t t

t ( , ) ) , ) (

( )

,

(

³

3

,

r

r r

e e

i br

br

A n n Z kT

P =

²

ú

û ù ê ë

´ é

»

^-

s eV

J A

_br

m

3

10

38

6 . 1

e

y

e cyc net

cyc

A n B kT

P =

²

A

cyc

» 6 . 3 ´ 10

^-20

[ JeV

^-1

T

^-2

s

^-1

]

volume integrated

+ ò

>

b

o E

th rad

fu

c

E dt

E E

f

t

t

*

*

*

*

Fusion Reactor Energetics

*

) (

2 ) 3 , ( )

, , ( )

,

,

(

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 t

+ + +

>

e i j T

n

E

_{th j j j}

, , 2

3

.

= =

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

Charged particle self-heating power > loss powers

(radiation + plasma transport)

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

nT P

P P

f

_{c,dt dt}

t

_E*

³ (

_br

+

_cyc^net

) t

_E*

+ 3

n T B T A

T A Q v

f n T

cyc dt br

dt dt c dt

E

s y

t

₂

,

*

4

) ( ) 3

(

-

> -

³ <

no energy conversion efficiency contained n_i = n_e = n, T_i = T_e = T

Plot?

• 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.

Fusion Reactor Energetics

Why?

n T B T A

T A Q v

f n T

cyc dt br

dt dt c dt

E s y

t ₂

,

*

4 ) ( ) 3

(

-

> -

³ <

• 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

Fusion Reactor Energetics

n T B T A

T A Q v

f n T

cyc dt br

dt dt c dt

E s y

t ₂

,

*

4 ) ( ) 3

(

-

> -

³ <

<σv>_dt ∝ T ² at 10-20 keV but ~constant above 50 keV

Fusion Reactor Energetics

*

1

*

=

=

_p

in in

fu

Q

E E h

• Break-even (scientific)

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

1 0

*

*

*

*

*

>

-

÷ -

÷ ø ö ç ç

è

æ +

= ò

ò

b b

o E

th rad

fu c o p

th

E dt

E E

Q f dt dt

dE

^t

t

t

Fusion Reactor Energetics

• Lawson criterion from the original paper

– reactor criterion: energy viability of the entire plant

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

Fusion Reactor Energetics

19

• Lawson criterion from the original paper

– deriving some criteria which have to be satisfied in a power producing system by considering power balance for systems in which the reaction products escape, defined as “pulsed systems” by Lawson.

– The gas is heated instantaneously to a temperature T, this temperature is maintained for a time t, after which the gas is allowed to cool.

– The energy released by the reaction appears as heat generated in the

walls of the apparatus (blanket), and thus has to be converted to electrical, mechanical or chemical energy before it can be fed back into the gas

with efficiency η.

– Assumptions:

considering bremsstrahlung radiation only (Spitzer 1956) (cyclotron radiation neglected)

neglecting conduction loss entirely

energy used to heat the gas and supply the radiation loss regained as useful heat

– introducing R: ratio of the energy released in the hot gas to the energy supplied

-3 2

/ 1 2

34

watts cm 10

4 .

1 n T

P

_B

= ´

^-

*

*

*

th rad

aux

E E

E = +

*

*

/ E E

R =

Fusion Reactor Energetics

• Lawson criterion from the original paper

– Condition for a system with net power gain

( R + 1 ) > 1

h

Variation of R with T for various values of nt for T-D reaction

in aux in

out

E E

E h

*

*

*

> =

h 1 3

3 >

+ + +

nkT tP

nkT tP

tP

B B R

h nkT nkT tP

tP

tP

_{R B} ^B

3

3 +

>

+ +

Total output energy after a pulse

> input energy for heating and

*

*

*

*

*

*

th rad

aux

fu aux

out

E E

E

E E

E

+

=

+

=

( )

*

1

*

*

+ >

aux fu aux

in

E

E h E

Energy required to heat the gas to a temperature T

( ) P n kT nt

kT n P

nkT tP

tP k

T n T n tP

tP E

R E

B R B

R

i e i i B

R aux

fu

/ 1 3

/

3 / 3

2

3

²

2

*

*

= +

» + +

+

=

=

Fusion Reactor Energetics

• Lawson criterion from the original paper

– Conclusion:

For a successful thermonuclear reactor not only has the temperature to be sufficiently high, but also the reaction has to be sustained for a sufficient time. The reason for this is that the organized energy used to heat the gas is ultimately degraded to the temperature of the walls of the apparatus and, consequently, sufficient thermonuclear energy must be released during each heating cycle to compensate for this degradation.

Fusion Reactor Energetics

• Lawson criterion

*

*

*

*

th th rad

rad fu

fu

out

E E E

E = h + h + h

*

*

*

th rad

in

in

E = E + E

h

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 >

conduction loss

η_fu < 4/5 in DT fusion?

Fusion Reactor Energetics

in th rad

th th rad

rad fu

fu

E E E

E

E h h h

h

*

*

*

*

*

+

>

+ +

*

*

*

*

*

)

(

_{fu rad th rad th}

out

in

h E + E + E > E + E

h

th rad fu

E l E

l l l

l l

out

= , = , ,

å å h

h

• Lawson criterion

average conversion efficiency

= ò

V l E

l

P r d r

E

^* _*

( r )

³

t

global energy terms

- output electric energy (recoverable energy) > required input energy

*

*

in

out

E

E >

*

*

*

*

th th rad

rad fu

fu

out

E E E

E = h + h + h

*

*

*

th rad

in

in

E = E + E

h

Fusion Reactor Energetics

) 3 (

) 3

(

_{* *} ³ _*

3

r P P nT d r P nT

d

_{E br}

V V

br E fu

E out

in

h ò t + t + > ò t +

h

nT T

n T n r

E

_th

(

_{i i e e}

) 3 2

) 3

( r = + =

Assuming, Bremsstrahlung only

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

*

÷ ÷ > +

ø ö ç ç

è

æ < > + +

+ s t t t

h d h

Assuming, homogeneity throughout the plasma volume V

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

T Q A

T v

n T

out br in ab

ab ab

out in

out in E

) 1

) ( 1

( 4

) (

) 1

( 3

*

h d h

h s h

h t h

- + -

>

<

> - h

_in

h

_out

» 1 / 3

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

*

h d h

h s h

h t h

- + -

>

<

> -

- Practical energy break-even condition for confinement parameter nτ

_E

in a fusion

reactor of electric power plant

1

out

=

h

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 Homework:

Problems 8.6

Q=1.14

Status of the Tokamak Research

Q = 1 Q = ∞

Status of the Tokamak Research

Status of the Tokamak Research

Ignition condition

s bar

s keVm T

n

_E

×

=

´

³

^-

5

10

3

^{21 3}

t

bar atm 1 . 01325

1 =

_<σv>

dt ∝ T ² at 10-20 keV → nτ_{E *}T ²⁹

s keVm T

n

₀

t

_{E 0}

³ 5 ´ 10

^{21 -3}

with realistic profiles:

• Present machines produced significant fusion power:

- TFTR (USA) ~10 MW in 1994

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

Status of the Tokamak Research

• DT-Experiments only in

- JET

- TFTR

Status of the Tokamak Research

• DT-Experiments only in - JET

- TFTR

• with world records in JET:

- P

_fusion

= 16 MW - Q = 0.65

Q_tot ?

Status of the Tokamak Research

• Progress in fusion can be compared with the computing

33

Homework

- Problems 8.4

(submission until the next Wednesday)