Fusion Reactor Technology I

(1)

F usion Reactor Technology I

(459.760, 3 Credits)

Prof. Dr. Yong-Su Na

(32-206, Tel. 880-7204)

(2)

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

Ohmic Heating

(7)

φ

_p

+

_p _p

=

_p

= −

p

I I R V

L

• Total change in magnetic flux needed to induce a final current

f p f i

p p t

ind

l I

k a R R

I L

f

dt

⎥ ⎦

⎢ ⎤

⎣

⎡ ⎟ + −

⎠

⎜ ⎞

⎝

≈ ⎛

=

Δ φ ∫

0

φ μ

⁰ ⁰

ln 8

⁰

2 2

[ 1 . 65 0 . 89 ( 1 ) ]

ln +

₉₅

−

≈ q

l

_i

4 . 0

0

,

0

≈

=

Δ φ

_res

C

_E

μ R I

_p^f

C

_E

t d R

t

I

p f p

burn

= ′

Δ φ ∫

0

• Additional magnetic flux needed to overcome resistive losses during start up

• Further change in magnetic flux needed to maintain I_p after start up

internal inductance

Ejima coefficient

OH

v

B

r Δ

≈ Δ φ π

²

• Technological limit to the maximum value of B_OH

Tokamak is inherently a pulsed device.

Ohmic Heating

(8)

8

: Neoclassical resistivity

2 2 1

1 ⎟⎟

⎟

⎠

⎞

⎜⎜

⎜

⎝

⎛

⎟ ⎠

⎜ ⎞

⎝

− ⎛

=

R r

s n

η η

] /

[

²

2

W m

j P

_Ω

= j ⋅ E = η

• Ohmic heating density

η_s: Spitzer resistivity

) 1 2

/(

) ) / ( 1 ( )

(

2 0 2

2 0

+

=

−

=

v j

j

a r j

r

j

^v

⎥ ⎥

⎦

⎤

⎢ ⎢

⎣

⎡

⎟⎟ ⎠

⎜⎜ ⎞

⎝

⎛ − + −

=

+1 2 2 0

2

0

1 1

) 1 (

) 2 (

v

a r r

v j r a

B μ

θ Ampère’s law

0 0 0

0

1 , 2 /

/ ,

/

_θ _φ

μ

φ

RB q q v j B Rq

aB

q

_a

=

_a

= + =

⎟ ⎠

⎜ ⎞

⎝ ⎛ −

⎟⎟ ⎠

⎜⎜ ⎞

⎝

= ⎛

0 0

2

0 2

2 1 2 1

q q

R q j B

a

μ

φ

Ohmic Heating

,

2

∑ ∑

=

s

s s e

e s

s s

eff n n Z

n Z n Z

Z_s: charge number for the s-type ion

) 3 /

, 2 / (

/

10

8

²

3

8

= =

×

≈

⁻

Z

_eff

T

_e

r a R a

η

(9)

Ohmic Heating

Magnetic field limited by engineering

→ compact high-field tokamak

2 2

/ 3 5

2

) 2 / (

10 1 0

.

1 ⎟⎟

⎠

⎜⎜ ⎞

⎝

⎥ ⎛

⎦

⎢ ⎤

⎣

⎡

⎟⎟ −

⎠

⎜⎜ ⎞

⎝

× ⎛

=

Ω

=

R B q

q q T

j Z P

o a

o

eff φ

η

q_a limited by instabilities

R j B

R j B a

a R j

aB a

R I aB RB

q aB

p a

0

0 2 0 0

2 2 2 2

μ

μ π

π μ π

μ

φ

φ φ

φ θ

φ

<

>

=

- Z_eff limited by radiation losses

- High T required for enough fusion reactions

(10)

L

E

P

nT =

= 3 / τ

5 4 5

2

0

10

8

7 .

2 ⎟⎟

⎠

⎜⎜ ⎞

⎝

⎟⎟ ⎛

⎠

⎜⎜ ⎞

⎝

× ⎛

= R

B q

nq T Z

a E

eff

τ

φ

2 / ) 10 /

( n

²⁰

a

²

E

= τ

5 4

87 .

0 B

_φ

T =

5 .

=1

Zeff q_aq_o =1.5

Alcator scaling

Average temperatures above ~ 7 keV are necessary before alpha heating is large enough to achieve a significant fusion rate.

Ohmic Heating

2 2

/ 3 5

2

) 2 / (

10 1 0

.

1 ⎟⎟

⎠

⎜⎜ ⎞

⎝

⎥ ⎛

⎦

⎢ ⎤

⎣

⎡

⎟⎟ −

⎠

⎜⎜ ⎞

⎝

× ⎛

=

Ω

=

R B q

q q T

j Z P

o a

o

eff φ

η

It seems unlikely that tokamaks that would lead to practical reactors can be heated to thermonuclear temperatures by Ohmic heating!

(11)

259-Car Autobahn pile-up near Braunschweig,

largest in German history:

(20 July 2009)

Neutral Beam Injection

- More than 300 ambulances, fire engines and police cars

rushed to the scene to tend to the 66 people injured in the crash.

- The crash was blamed on cars aquaplaning on puddles and a low sun hindering drivers.

(12)

Neutral Beam Injection

259-Car Autobahn pile-up near Braunschweig,

largest in German history:

(20 July 2009)

(13)

13 Andy Warhol http://www.nasa.gov/mission_pages/galex/20070815/f.html

Plasma

NBI

Neutral beam

Neutral Beam Injection

• Supplemental heating by energy transfer of neutral beam to the plasma through collisions

• Requirements

- Enough energy for deep penetration - Enough power for desired heating

- Enough repetition rate and pulse length > τ_E - Allowable impurity contamination

(14)

Beam particles confined⇓

Collisional slowing down⇓

Injection of a beam of neutral fuel atoms (H, D, T)

at high energies (E_b > 50 keV)*

Ionisation in the plasma⇓

Neutral Beam Injection

* E_b = 120 keV and 1 MeV for KSTAR and ITER, respectively

B H,D,T

(15)

Neutraliser

D

D D₂

Low

temperature D plasma,

5 eV

Ion source

D⁺, e^-

100 kV -3 kV 0 kV Extraction acceleration grids

D⁺ D⁺ D₂⁺

Beam dump

B

D⁺

Deflection magnet

Vacuum valve

Beam duct

Ex) W7-AS: V=50 kV, I=25 A, power deposited in plasma: 0.4 MW

•

Generation of a Neutral Fuel Beam

Neutral Beam Injection

(16)

•

Ion Source

(17)

•

Ion Acceleration

(18)

•

Ion Neutralisation

(19)

•

Ion Deflection

(20)

•

Neutral Injection

(21)

•

JET NBI System

(22)

•

JET NBI System

(23)

23

•

JET NBI System

JET with machine and Octant 4 Neutral Injector Box

(24)

•

JET NBI System

Octant 4 Neutal Injector Box

(25)

•

Ion source

• Requirements

- Large-area uniform quiescent flux of high-current ions

- Large atomic ion fraction (D⁺, D^-) > 75 % → adequate penetration - Low ion temperature ( << 1 eV ) to minimize irreducible divergence

of extracted ion beams due to random thermal motion of ions

(26)

•

Ion source

• Ion generation

- Positive ion generation by electric discharge

D D

e e D

e D

e e D D

e D

+

→ +

+ +

→ +

+ + +

→ +

+ +

3 2

2

2 2

2

Electron attachment (Double electron capture)

M: alkali or alkali-earth metal vapor (Cs, Rb, Na, Sr, Mg)

+

−

+ +

−

− +

−

+

→ +

+

→ +

+

→ +

+

→ +

+

→ +

M D

D Cs

surface cathode

D

D Cs

surface cathode

D

D D

e D

h D

e D

0 0

0

* 2

) (

ν

Radiative attachment in high density gas (E_binding = 0.75 eV) Dissociative electron attachment by electric discharge (~eV)

Surface production by electric discharge (~100 eV range)

- Negative ion generation

(27)

• 3-lens system

Positive electrode

V₁

Negative electrode

V₂

Earth electrode

potential lines

Grid system at ASDEX Upgrade

0.5m 0.2m

•

Beam Forming System: Extraction and steering

2

1

V

V >>

Source Plasma

- Ion extraction + acceleration + minimum beam divergence (≤ 1°)

(28)

•

Ion sources

RF Source

0.4 - 0.8 m

Cathodes difficult to replace, finite life time Duopigatron

(29)

N N N N

fast slow fast gas

D D

D

⁺

+

₂

→ +

₂⁺

- Charge exchange:

- Re-ionisation:

N D + N D → N N D

⁺

+ D + e

⁻

fast gas fast gas

2 2

- Efficiency: (outgoing NB power)/(entering ion beam power)

•

Neutraliser

(30)

- Negative ion beam development in JT-60U

(31)

•

Ion Beam Dump and Vacuum Pumps

• Beam dump

- Deflect by analyzing magnet - Minimize reionisation losses

- Prevent local power dump at undesirable place (~kW/m²) - Possible application to direct energy conversion

• Pumping

- Minimise reioninsaton losses

- Prevent cold neutral particles from flowing into reactor plasma - Liquid He cryopumps ( ~10⁶ l/s for ~MW system)

(32)

32

•

Energy Deposition in a Plasma

Andy Warhol

http://www.nasa.gov/mission_pages/galex/20070815/f.html

n: density

σ: cross section

NBI

beam energy

Attenuation of a beam of neutral particles in a plasma Charge exchange:

D

_fast

+ D

⁺

→ D

⁺_fast

+ D

Ion collision:

D

_fast

+ D

⁺

→ D

_fast⁺

+ D

⁺

+ e

Electron collision:

D

_fast

+ e → D

_fast⁺

+ e + e

(33)

33

•

Energy Deposition in a Plasma

Neutral Beam Injection

Ex. beam intensity:

( / λ )

exp

) ( )

(

0

x

I

v x N x

I

_b _b

−

⋅

=

2

10

20

5 m

tot

⋅

−

σ =

3

1020

5⋅ ⁻

= m

n

m

n 1

_tot

0 . 4

≈

= σ λ

In large reactor plasmas, beam cannot reach core!

tot b

b

N x n x

dx x

dN ( ) = − ( ) ( ) σ

Penetration (attenuation) length

keV E_b₀ = 70

Charge exchange:

D

_fast

+ D

⁺

→ D

⁺_fast

+ D

Ion collision:

D

_fast

+ D

⁺

→ D

_fast⁺

+ D

⁺

+ e

Electron collision:

D

_fast

+ e → D

_fast⁺

+ e + e

Attenuation of a beam of neutral particles in a plasma

(34)

•

Energy Deposition in a Plasma

4 ) /

( ) (

) (

10 5

. 5 1

3 17

Z a m

n amu A

keV E

Z

n

_eff

b eff

tot

× ≥

=

≡

_γ ₋ _γ

λ σ

General criterion for adequate penetration

γ eff

b

AnaZ

E ≥ 4 . 5 × 10

⁻¹⁹

Charge exchange:

D

_fast

+ D

⁺

→ D

⁺_fast

+ D

Ion collision:

D

_fast

+ D

⁺

→ D

_fast⁺

+ D

⁺

+ e

Electron collision:

D

_fast

+ e → D

_fast⁺

+ e + e

(35)

•

Energy Deposition in a Plasma

Charge exchange:

D

_fast

+ D

⁺

→ D

⁺_fast

+ D

Ion collision:

D

_fast

+ D

⁺

→ D

_fast⁺

+ D

⁺

+ e

Electron collision:

D

_fast

+ e → D

_fast⁺

+ e + e

(36)

] [keVs

ˆ 1 10

71 .

1 ¹

2 / 3

18 −

− ⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

⎟⎟⎠

⎜⎜ ⎞

⎝ +⎛

×

=

b c e

b b e

T A P n

ξ ξ ξ

3 /

)

2

( 8 ˆ . 14

i i

e b

c

Z A

T

= A ξ

Neutral Beam Injection

•

Slowing down

- Critical energy: The electron and ion heating rates are equal

81 4

/ 3

, 6

ln

2

²

1 2

3 2 2

1

2 1 2

3 2

0 2 3

2 1 4 2 2

1

≈

⎟ =

⎟ ⎟

⎠

⎞

⎜ ⎜

⎜

⎝

⎛ Λ +

=

+

=

−

i e b

b e

b

b e b

e

i e

b

m m A

Z C C

T A

m e Z n

P P

dt P d

π ξ

ξ ε

π

ξ

²

2 1

b b

b

= m v

ξ

(37)

e b

/ T ˆ ξ

Ion heating fraction

3 /

)

2

( 8 ˆ . 14

i i

e b

c

Z A

T

= A ξ

•

Slowing down

Critical energy

] [keVs

ˆ 1 10

71 .

1 ¹

2 / 3

18 −

− ⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

⎟⎟⎠

⎜⎜ ⎞

⎝ +⎛

×

=

b c e

b b e

T A P n

ξ

(38)

38

1. ξ_b > ξ_c: Slowing down on electrons no scatter

v_||

v ⊥

v_b

v_||

v

⊥

v_b 2. ξ_b < ξ_c: Slowing down on ions

scattering of beams

1

0 ξ_b/ξ_c ¹⁰ Fraction of initial beam energy

going to ions

Neutral Beam Injection

•

Slowing down

after before

(39)

B Tangential injection

Radial (perpendicular, normal) injection

• standard ports

• shine-through

• particle loss

B

∇ B

. Radial injection:

•

Injection Angle

(40)

B Tangential injection

Radial (perpendicular, normal) injection

•

Injection Angle

KSTAR NB shine-through armor

Neutral Beam Injection

(41)

41

Better heating efficiency

. B I_p

Worse heating efficiency

Projected

particle drifts

- At low magnetic fields heating efficiency depends on NBI direction.

- Best injection angle for maximum penetration and minimum orbital excursion = 10-20° off perpendicular in co-injection direction

•

Injection Angle

Neutral Beam Injection

r B

v

F = e × _θ = −ˆ r

B v

F = e × _θ = ˆ

outward shift of orbit center inward shift → bad drift orbits

→ energetic ion loss to wall/limiters

(42)

• JET

• ASDEX Upgrade

Fusion Reactor Technology I