5-Fusion Reactor Requirement.pdf

I ntroduction to Nuclear Fusion

Prof. Dr. Yong-Su Na

2

What is requirement of a fusion reactor?

Discussion

Fusion Reactor

Neutron (14 MeV)

Blanket

Deuterium Tritium Lithium

Coolant

What is required to light a fire in a stove?

n

T

≥ ?

⋅

⋅ T τ

n

Criterion required (fusion triple product) Deuterium

Tritium

Fuel: D, T

Amount/density:

Heat insulation:

Ignition temperature:

J. D. Lawson

Fusion Reactor Energetics

https://www.euro-fusion.org/glossary/lawson-criteria/ 6

Why nτT?

• Fundamental requirement of a fusion reactor system

*

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

τ_b: burning time

∫ ∫

∫

^b_^dE_dt ^_^{ dt = b}_^{ dE}_dt ^_^{ dt − b}_^{ dE}_dt ^_^{ dt >}

in out

net

τ τ

τ

0 0

*

*

0

*

0 Considering the time variations of power

(Particularly for pulsed systems)

Fusion Reactor Energetics

6

• Fusion Plasma Energy Balance

*

*

in in

aux

E

E = η

( )

^*

*

1

_{c fu}

n

f E

E = −

c fu

alpha

E f

E

_*

=

*

f_c: alpha particle fraction of fusion product energy

∫

+ +

=

+

=

b

o E

th rad

n in

fu aux

out

E dt E

E E

E E

E

τ

τ

^*

*

*

*

*

*

*

*

∫ ∫

∫

^b

   dE dt    dt =

^b

   dE dt    dt −

^b

   dE dt    dt >

in out

net

τ τ

τ

0 0

*

*

0

*

0

Fusion Reactor Energetics

*

*

*

fu alpha

n

E E

E + =

*

*

*

*

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

Energy Confinement Time

Time Temperature

τ

_E

1/e

Time Temperature

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

• The loss rate is smallest, τ_{E largest}

if the fusion plasma is big and well insulated.

Energy Confinement Time

10

1 0

*

*

*

*

− − >

 





 



 + ∫

^b

o E

th rad

fu c

p

E dt E

E Q f

τ

τ

Fusion Reactor Energetics

∫ ∫

∫

^b

   dE dt    dt =

^b

   dE dt    dt −

^b

   dE dt    dt >

in out

net

τ τ

τ

0 0

*

*

0

*

0

*

0

*

*

*

*

*

+ − − − ∫

^b

>

o E

th rad

n fu

aux

E dt

E E

E E

τ

τ

Describe reactor criteria in terms of Q

_p

10

• Ignition

Energy viability of the fusion plasma:

actual self-sustaining engineering reactor condition with no heating power

∫

+

>

^b

o E

th rad

fu

c

E dt

E E

f

τ

τ

^*

*

*

*

∞

→

=

_p

in in

fu

Q

E E

*

*

η

Fusion Reactor Energetics

1 0

*

*

*

*

− − >

 





 



 + ∫

^b

o E

th rad

fu c

p

E dt E

E Q f

τ

τ

) (

) ( )

, (

) , (

*

* 3

t t E t

r t r r E

d

E th E

th

V

∫ τ   = 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

,



 

e e

i br

br

A n n Z kT

P =

²

e

ψ

e cyc net

cyc

A n B kT

P =

²

Volume integrated

[

^{1 2 1}

]

10

20

3 .

6 ×

^{− − − −}

≈ JeV T s

A

_cyc

 

 



× 

≈

⁻

s eV

J A

_br

m

3

10

38

6 . 1

Fusion Reactor Energetics

∫

+

>

^b

o E

th rad

fu

c

E dt

E E

f

τ

τ

^*

*

*

*

12

*

) (

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 τ

+ + +

>

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

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

(

−

> −

> <

nT P

P P

f

_{c,dt dt}

τ

_E*

> (

_br

+

_cyc^net

) τ

_E*

+ 3

n_i = n_e = n, T_i = T_e = T

Plot?

Fusion Reactor Energetics

n T B T A

T A Q v

f n T

cyc br

dt dt

dt c dt

E σ ψ

τ ₂

,

*

4 ) ( ) 3

(

−

> −

> <

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

Fusion Reactor Energetics

14

*

1

*

=

=

_p

in in

fu

Q

E E η

• Break-even (scientific)

The total fusion energy production amounts to a

magnitude equal to the effective plasma energy input

^.

Fusion Reactor Energetics

1 0

*

*

*

*

− − >

 





 



 + ∫

^b

o E

th rad

fu c

p

E dt E

E Q f

τ

τ

*

0

*

*

*

− − ∫

^b

>

o E

th rad

fu

c

E dt

E E

f

τ

τ

Q=1.14

Q = 1 Q = ∞

Status of the Tokamak Research

in D-D reactions

Ignition condition

16

s bar

keVs m

T n

_E

⋅

=

×

≥

⁻

5

10

3

^{21 3}

τ

bar atm 1 . 01325

1 =

Status of the Tokamak Research

https://www.euro-fusion.org/2011/09/progress-in-fusion