Prof. Dr. Yong-Su Na

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)

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

Objectives of the Tokamak Operation

• High <n

>/n

• High β

• High H

(y,2)

• Pulse length

Objectives of the Tokamak Operation

fishbones (q=1)

P_nbi (MW)

β_N

H₉₈ (y,2)

<n_e>/n_GW D_α

4xl_i

# 14521

• No sawteeth, good confinement, and β

~ 3.5, T

~ T

,

<n

>/n

~ 0.88, averaged over 3.6 seconds (~ 50 τ

).

Objectives of the Tokamak Operation

fishbones (q=1)

b_N

H₉₈ (y,2)

<n_e>/n_GW 4xl_i

~ 18 MW / m² ≤ 6 MW / m²

outer divertor

inner divertor

Small ELMs

(type II)

I_p (MA) ^{# 14521}

D_α

Basic Tokamak Variables

7

•

Cylindrical and local coordinates for a tokamak

• Aspect ratio: R₀/a ~ 3-5 ex) KSTAR: 3.6, ITER: 3.1

Basic Tokamak Variables

• Elongation: κ

• Triangularity: δ

• Squareness: ζ

•

Plasma equilibrium parameters

Basic Tokamak Variables

9

• Elongation

•

Plasma equilibrium parameters

a

= b

κ a

d c

2

= + δ

• Triangularity

( )

θ κ

θ δ

θ sin

sin

0

cos a Z

a R

R

=

− +

=

Basic Tokamak Variables

• Outer and inner squareness: ζ_o,i

•

Plasma equilibrium parameters

What is the squreness?

( )

( ^{θ ζ θ} )

κ

θ δ

θ

2 sin sin

sin sin

cos

,

1 0

i

a o

Z

a R

R

+

=

+ +

=

Basic Tokamak Variables

11

• Separation of plasma from wall by a limiter and a divertor

• Advantage of the divertor configuration

- First contact with material surface at a distance from plasma boundary - Reducing the influx of ionized impurities into the interior of the plasma

by diverting them into an outer „SOL“

Strike point

If no limiter and divertor?

Plasma diffusing into

the whole vessel along the magnetic

field → if touching the

wall, impurities coming out

Basic Tokamak Variables

Major Radius, R₀ Minor Radius, a Plasma Current, I_P Elongation, κ_x Triangularity, δ_x Toroidal Field, B₀ Pulse Length

Fuel

Parameters

1.8 m 0.5 m 2.0 MA 2.0 0.8 3.5 T 300 s H, D

KSTAR

6.2 m 2.0 m 15 MA 1.85 0.5 5.3 T 500 s D, T

ITER • Plasma shape

•

Plasma equilibrium parameters

13

Basic Tokamak Variables

2 0

/ 2 μ p B β =

z The ratio of the plasma pressure to the magnetic field pressure

z A measure of the degree to which the magnetic field is holding a non-uniform plasma in equilibrium.

magnetic pressure

plasma pressure

•

Beta

Basic Tokamak Variables

2 0

/ 2 μ p B β =

•

Beta

magnetic pressure plasma

pressure

Instability

(bad curvature region)

www.waterrocket.com/goachaik-28.htm the43sunsets.tistory.com/tag/코카콜라

15

Basic Tokamak Variables

2 0

/ 2 μ p B β =

z The power output for a given magnetic field and plasma assembly is proportional to the square of beta.

z In a reactor it should exceed 0.1 – economic constraint

•

Beta

r B NI

π μ

= 2

Basic Tokamak Variables

•

Beta

∫ ∫

∫

= ^a p r rdr

dS a pdS

p

0

2 ( )

/ 2

π π

Assuming that the magnetic surfaces have concentric, circular CXs and that conditions are independent of ϕ.

0 0

0 0 0

0

/ 2

2

) (

, )

1 (

μ π

π

μ μ μ

θ ϕ

ϕ θ

ϕ θ

a a

p

r

aB rdr

j I

r d r r r j

B j

r rB r

j B

∫

∫

=

=

′

′

= ′

∂ =

∂

=

×

∇G G G

Ampère’s law

Basic Tokamak Variables

•

Normalized beta – stability limit

17

• Fundamental elements for the β_N-limit

1. Current profile 2. Pressure profile 3. Plasma shape 4. Stabilising wall

5. Resistive instability

p t t

N

I

β aB

β =

Basic Tokamak Variables

•

Normalized beta – stability limit

• High β_N in KSTAR

1. Strong plasma shaping 2. Passive stabilizers

3. PF/CS system capability 4. High heating power

5. RWM control coils