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

Non-linear Plasma Activity

- Occurring under certain conditions when a high energy neutral beam is injected to heat the plasma.

- Driven by ∂f/∂r, the radial gradient in the fast particle distribution function: kinetic excitation of the internal helical mode by fast ions - Due to an interaction between the injected particle and

an m = 1, n =1 MHD perturbation.

Interaction of the resonance type characterized by Landau damping, but here causing growth

Resonance between the toroidal wave velocity of the instability and the toroidal drift experienced by trapped energetic particles from the injected beam Cf. Fishbones would not occur for injection parallel to B.

- Oscillations dropping when the energy of resonant particles is exhausted until the next spike of fishbone activity.

•

Fishbone Instability

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Non-linear Plasma Activity

- Leading to intensive loss of fast ions trapped in plasma

→ worsens the efficiency of additional heating - Dangerous in fusion reactors:

helical-mode destabilization may be excited by α-particle produced in the D-T reaction.

•

Fishbone Instability

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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)

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-modes: 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)

R. Carrera et al, Physics of Fluids 29 899 (1986) - One of the earliest theoretical paper

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Neoclassical Tearing Mode (NTM)

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neutron rate

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ASDEX Upgrade

φ

β φ

β aB

I

N t(%)=

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11

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

p

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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 12 cm inboard 2/1 island

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

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Neoclassical Tearing Mode (NTM)

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0.4 0.8 1.2

Pressure(kPa)

#662 0

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 12 cm inboard 2/1 island

Pressure flattening due to island

MAST (300 point Thomson scattering) #3730 3/2 matches

cyl. approx.

~4cm

2/1 is 25%

smaller than cyl. approx.

~10cm

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R. Buttery et al, Plasma Physics and Controlled Fusion (2000) sawtooth collapse

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Neoclassical Tearing Mode (NTM)

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JET

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- Increased sawtooth period due to

stabilisation by fast ions produced by ICRH leads to the triggering of n = 2 NTM

activity which causes a termination of the discharge.

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17

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• Loss of BS current inside magnetic islands (helical hole) acts as helical perturbation current driving the islands – so once seeded, island is sustained by lack of bootstrap current

• Inside islands ∇p and thus j_BS vanish

• At high β_p, pressure gradient drives plasma current by thermo-electric effects (Bootstrap current):

j

_BS

∝ ∇p

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Neoclassical Tearing Mode (NTM)

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4^th: Stabilization from small island & polarization threshold:

3^rd: Destabilization from perturbed bootstrap current:

5^th: Stabilization from replacing bootstrap current by ECCD:

1^st : Conventional tearing mode stability: assumed as for m/nΔ_{0 s}′ ≈ −r m NTM

2 1 2^/

marg i

w ≈ ε ρ_θ (= twice ion banana width)

2^nd: Tearing mode stab. enhancement by ECCD: Westerhof’s model with no-island assumption

3 2 2

5

32 ( )

/

q ec

s

ec

L j

r a F e

j

δΔ π τ

′ ≈ − δ

∥

2 3

1 2 43 1 40 0 23

( ) . . .

F e = − e+ e − e , where the misalignment function

calculated from improved Perkins’ current drive model K1

⎥ ⎥

⎦

⎤

⎢ ⎢

⎣

⎡ − −

+ Δ′

=

bs m ec

bs q s

s s

R

j K j L

j a j r

dt r d

r

² ¹

2 arg

||

2

0

1 3

ω ω δ ω

ω τ

R. J. La Haye et al, Nuclear Fusion 46 451 (2006) fitted by inferred size of saturated NTM island (e.g. ISLAND)

a2

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The Modified Rutherford Equation (MRE)

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• Complete stabilisation by searching the position of

the magnetic island by scanning magnetic field in quantitative agreement with theory!

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• Missing bootstrap current inside island can be

replaced by localised external current drive.

1^st Paper: G. Gantenbein et al, PRL 85 1242 (2000)

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Demonstration of individual elements as well as integrated feedback 21

Feedback controlled Deposition in DIII-D

NTM stabilisation with ITER relevant broad deposition in ASDEX Upgrade

NTM Stabilisation by ECCD

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NTM Stabilisation by ECCD

• JT-60U

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NTM Stabilisation by ECCD

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Courtesy from R. J. La Haye, APS (2005)

Fusion Reactor Technology I