Fusion Reactor Technology I

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F usion Reactor Technology I

(459.760, 3 Credits)

Prof. Dr. Yong-Su Na

(32-206, Tel. 880-7204)

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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

Tokamak Operation Scenario

JT-60U

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H-mode

• 1982 IAEA F. Wagner et al. (ASDEX, Germany)

- Transition to H-mode: state with reduced turbulence at the plasma edge - Formation of an edge transport barrier: steep pressure gradient at the edge

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H-mode

τ

_E

≈ a χ

²

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H-mode

8

• Established in stellarators as well

Wendelstein 7-AS

V. Erckmann et al, Physical Review Letters 70 2086 (1993)

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H-mode

Hoover dam

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Time Temperature

Basic Tokamak Variables

• Energy confinement time

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τ

_E

• 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.

1/e

Time Temperature

• Energy confinement time

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H-mode

Hoover dam

• 1982 IAEA F. Wagner et al. (ASDEX, Germany)

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H-mode: How to?

13

• 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

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Tokamak

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H-mode: How to?

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H-mode: How to?

• Role of wall condition

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P

_th

= 2.84M

^-1

B

_t^0.82

n

₂₀^0.58

R

^1.0

a

^0.81

H-mode: How to?

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H-mode: Why?

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H-mode: Why?

Theoretical physics

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H-mode: Why?

Theoretical physics

Experimental physics

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• Safety factor q = number of toroidal orbits per poloidal orbit

Magnetic field lines Magnetic flux surfaces

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B

p

B

B G G K +

=

_φ

R B

r B

π π θ φ ι

φ θ

2 2 Δ =

= Δ

Rotational transform

number of toroidal windings number of poloidal windings

= q

θ φ

ι π

B B R

= r

= 2

Δθ ? when ΔΦ=2π

- The effect of the twisted magnetic field lines–each of which completely traces out a magnetic flux surface by its revolutions around the toroidal and poloidal axes–is to create a system of nested toroidal flux surfaces which guide ion motion.

θ φ

B rd B

Rd =

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q-profiles

0 1 2 3 4 5

0 0.5 1

r/a

H-mode ELMy

Tokamak Operation Modes

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Conventional Operation Mode – H-mode

• Naturally peaked current profile

• Mild pressure gradient with steep edge pedestal

• Monotonic q-profile

• Positive magnetic shear

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q

₀

< 1: Sawtooth instability, periodic flattening of the pressure in the core Stability of H-mode plasmas related safety factor profile: q(r)

H-mode: Limitations

0 1 2 3 4 5

0.5 1

r/a

H-mode, q-profile

q = 1

0

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Sawtooth

time (s)

0 2 4 6 8

8 6 1 10 1

I_p(MA)

P_NBI(MW) P_RF(MW)

W_MHD(MJ)

Nel x1.10¹⁹

T_i(keV) T_e (keV)

pulse 20438

- nonlinear low-n internal mode - internal (minor) disruption - enhanced energy transport

in the plasma centre

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q

₀

q = 3/2 and q = 2:

Neoclassical Tearing Modes (NTMs):

• limit the achievable β ≡ 2µ

₀

p/B

²

• degrade confinement (+ disruptions)

• often triggered by sawteeth.

H-mode: Limitations

0 1 2 3 4 5

0.5 1

r/a

H-mode, q-profile

q = 1

0

q = 3/2

q = 2

• ITER work point is chosen

conservatively: β

_N

≤1.8 !

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Neoclassical Tearing Mode (NTM)

ASDEX Upgrade

φ

β φ

β aB

I

N t(%)=

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• Pressure flattening across magnetic islands due to large transport coefficients along magnetic field lines

p

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Neoclassical Tearing Mode (NTM)

0.4 0.8 1.2

Pressure(kPa)

6620

Temperature(keV)

Radius (m) 0.7

0.6 0.5 0.4 0.3 0.2 0.1 0.8 0.6 0.4 0.2

0 EFIT q=2 surface

magnetic estimate

12cm inboard 2/1 island

• Pressure flattening across magnetic islands due to large transport

coefficients along magnetic field lines

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q

₀

q = 3/2 and q = 2:

₀

p/B

²

H-mode: Limitations

0 1 2 3 4 5

0.5 1

r/a

H-mode, q-profile

q = 1

0

q = 3/2

q = 2

• ITER work point is chosen conservatively: β

_N

≤1.8 !

K. Miyamoto, “Controlled Fusion and Plasma Physics” Taylor & Francis (2007)

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q

₀

q = 3/2 and q = 2:

₀

p/B

²

H-mode: Limitations

0 1 2 3 4 5

0.5 1

r/a

H-mode, q-profile

q = 1

0

q = 3/2

q = 2

• ITER work point is chosen conservatively: β

_N

≤1.8 !

q

₉₅

(∝ 1/I

_p

) = 3: Safe operation at max. I

_P

Periodic collapses of

the ETB (ELMs)

q

₉₅

=3

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Edge Localised Mode (ELM)

• Example of sawteeth and ELMs JET, Pulse 52022

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Edge Localised Mode

Disruption

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t(s)

Power Supply Limit

Inherent drawback of Tokamak!

Faraday‘s law

ds dt B

v d

S

⋅

−

= ∫

H-mode: Limitation

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Plasma Current

PF Coil Flux [Wb]

[MA]

Fusion Reactor Technology I