A Colloquium at PosTechSep. 10, 2004

Tokamak PhysicsC.S. Chang

Department of Physics, KAIST

Contents• Why fusion?• Principles of Tokamak Confinement• Classical and neoclassical transport • Large scale MHD instabilities and disruption• Self-organization of turbulence

- Zonal Flow generation- Nonlinear break-up of streamers by zonalflows and self-reduction of Diffusion

• Self-organized High-mode and Edge Pedestal

Classical Charged Particle Physics

• Weak Coulomb Interaction, qaqb/rab≪ kT핵융합, 천체 (태양 및 별, 이온층)

가속기, 공정용, 무기용 (별들의 전쟁), 등등

• Strong Coulomb Interaction, qaqb/rab ≥ kT나노 scale plasma (DNA dynamics, 나노공정)

• λInter Particle >> λQM

Close packing ofstrongly negativecharged DNAs.

Why?Uniform counterions horizontally,but condensed to DNA surfacesvertically.

Why?Inter-counter iondistance is muchshorter than d &DNA diameter→ planarapproximationin 0th order

DNA-intercalation in positively charged multi-lamellar membranes

DNA: negativecharge

Red : positive counter charge

White : neutral

d~20 ÅL ~ 200,000 ÅBjerrum length = 7.1 Å

[1] Radler et al., Science 275, 810-814 (1997)“Structure of DNA-Cationic Liposome Complexes : DNA Intercalation in Multilamellar Membranes in Distinct Inter-helical Packing Regimes”

Facilities for the Future of ScienceA Twenty-Year Outlook

다른 에너지자원들은 지구환경 파괴, 곧 고갈

• 석유: 약60년

• 천연가스: 약100년

• 석탄: > 200년

• 우랴늄: > 200년?

• 태양, 풍력, 조력 등은 보조에너지일 뿐

• 플라즈마 핵융합:

Clean, Safe, 영구적

D-T > 100만년

D-D > 100억년

Global Warming is a more urgent problem than energy shortage

New York Times, 3/9/99

Martin I.Hoffert, et al., “Energy implications of future stabilization of atmospheric CO2,” Nature 409 (1998)

“The best hope for sustainable carbon-emission-free power may not be fission, but fusion.”

Fusion reactor

14 MeV NeutronsHeat the Li blanket

Well-Known TechnologyNot well-known(both Physicsand Engineering)

ITER(International Thermonuclear Experimental Reactor)

Fusion Requires niτETi > 5x1021 m-3keV sec

<Ti>∼ 10 keV (<ni> ∼ 1020 m-3)⇒ τE > 5 s

D+ + T+ → α+2 (3.5 MeV) + n (14 MeV)

niτΕTi ∝ H3.2B3.5/q3

Heat

Grand Challenge• Hot plasma: <Ti>∼ 10 keV and <ni>∼ 1014 cm-3

• In a star, hot plasma is gravitationally confined by enormous mass (and size).

• In a in fusion reactor, hot plasma must be confined in d 1,000 m3 for ∼ >10 s⇒ Huge free energy ⇒ Instabilities

• Large Ip (Low q) ⇒ disruption• Density limit• Manipulation Ø Defiance Ø Understanding Ø

Reconciliation ⇒ Advanced Tokamak

Numerical Tokamak• 전산장비의 급속한 발달

• Massively parallel computing (6,656개의 IBM RS6000/SP CPU at NERSC: 10 teraflop/s)

• 초고가, 초복합의 대형 실험에 만의 의존 탈피

• Construction of virtual tokamaks• Numerical Fokker-Planck particles• 원하는 실험과 측정을 자유로히

• 현재, 수백만개의 입자가능

• 토카막 플라즈마 현상의 획기적인 이해가 속출

-Magnetic Confinement-

Charged particles get tied to strong B

loss

Simplest confinement: Magnetic Mirrortoo much loss along open B lines

Best Confinement is in a Torus

Ion Grad-B Drift is Downward

|B| ∂ 1/R

If Ip=0 (Bp =0) in a tokamak

Bp gives toroidal confinement.Grad-B drift merely yields orbit shift.

Grad-B Drift

Βpol

Passing Orbit

Closed field lines in a finite volume ⇒Torus (Poincare’s Theorem)

Avoid fast loss from ∇B-Drift⇒ Add Bp by Ip

Ohmic Ip Transformer

Tokamak confinement concept

Tokamaks and StellatorsITER JT60-UJETDIII-DASDEXC-ModKSTARetc

NSTXSTART

LHDNCSXWendelsteinetc

Bp generation by Ip in a tokamak,coil in a stellerator

Classical Diffusion in BRandom walk argumentD≈f γ∆2

f : Participation fractionγ : Random walk frequency∆: Step size

f=1, γ=νc, ∆=ρ⇒ Dc= νc ρ2 ∝ B-2

ρX

Gyroradius

Mirror force yields banana orbit

Force on a Magnetic Dipole

Banana orbit at Low V∥

⇒ rp becomes basic physical size for

micro plasma activities

∇ B ⇒ Neoclassical Diffusion

Random walk argumentD≈f γ ∆2

f: Participation fractionγ : Random walk frequency∆: Step size

f=(r/R)1/2, γ =(R/r)νc, ∆=ρ q(R/r)1/2

⇒ DNC= (R/r)1/2 q2 νcρ2 ∝ B-2

DNC>> DC

∆

vperp

v//

banana(R/r)

1/2

Chaotic Ripple Transport of Hot Ions

• The steady banana orbits exist thanks to axisymmetry.

• In reality, number N of toroidal field coils is finite.There is a small ripple field.

• N should be large enough for a suitable confinement of neutral beam and rf ions. In KSTAR, N = 16 yields ripple <0.2% <0.3%

100 keV Beam Ion with EnhanedRipple in KSTAR

기본적인 이해없는 디자인은파멸적, 낭비적

예) JT-60리플이나 다이버트 현상의 이해없이 디자인

새 디자인 예상못한 현실완전 실패

Rayleigh Taylor Instability in a cup with heavy fluid on top of light fluid

A kink balooning MHD (NIMROD)

Currents induced in the passive plate and wallhelp stabilize global MHD (VALLEN)

Large Scale MHD Instability

NIMROD simulation of disruption

Nature’s Defiance - Turbulent Transport

EXB Drift is along Equipotential surface

Greater gyroradius

Smaller gyroradius

Decel.

Accel.

=V M/qB

Higher Potential surface

Lower Potential surface

D≈f γ ∆2

f: Participation fractionγ : Random walk frequency∆: Step size

Diffusion and random walk argument

Particle diffusion in E-turbulence(Hasegawa-Mima turbulence, GY Park)

Saturation of Electrostatic Turbulence• Turbulence gets energy from

∇ n/n (Drift Waves) Østreamersω≈ω∗ =k⊥vthρ/ L≈k⊥T/(eBL)

• n1/n= eΦ1/T• Nonlinear saturation of Φ1:

Chaotic particle motion at krVEXB = ω∗

VEXB= E/B = k⊥ Φ1 /B ⇒ n1/n= eΦ1/T = λturb/ L⇒ reduced Φ1 at reduced λ

λ n1

Ln

n

λ turb

EXB Flow Shearing of Streamers by Zonal Flow

ShearedE field

Ion Turbulence Simulation

Understanding the current driven instability and reconciliation with

radial current distribution• Current in the core Ø current driven instability

(eg, fire hose)• Current near the wall Ø Wall stabilization

⇒ Reversed shear mode

Reversed Shear Mode (j∝ 1/q)

1

2

3

4

5

r

q

Normal operation modedq/dr > 0

Particle Diffusivity is reduced to Neoclassical level (Reversed Shear)

D (m2/s)

Importance of sheared ExB Drift• Uniform ExB does not do anything.

- Lorentz Invariance of Physics• Sheared dE/drxB flow changes physics

- recognized not too long ago• Responsible for Internal transport barriers• H-mode transition• dE/dr is from classical or turbulence self-

organization

Oribt squeezing by Er-shear >0in NSTX

Orbit expansion by Er-shear <0 in NSTX

Neoclassical Polarization Drift by dEr/dt <0 in NSTX

Zonal Flow = Poloidal Shear Flow by Wave-Modulation

Radial

G. Tynant, TTF

2 side-band waves

H-mode Transition• High-Mode enhances confinement by ¥2(Fusion yield ∂ ntETi∂H3.2)

• Edge pedestal formation⇒ H-factor

• Reduction of Dα emission• Reduction (disappearance)of edge turbulence

Edge Pedestals and Er

D-Alpha, Ohmic L- Mode

H-Mode

Success of ITER may depend on the pedestal height. But, we do not understand it.

ProfileStiffness

New Theoretical Understanding of Pedestal Physics (장충석, 구승회)

• A massive Hamiltonian guiding center code has been developed to model the edge.

• Massively Parallel computing.• Conserving Monte Carlo collisions• Neutral collisions• Turbulence diffusion model

“World’s first self-consistent pedestal simulation”: in TTF2003 Conference summary

Pedestal buildup by neutral ionization in a quiecent edge plasma (APS 2003 Invited Talk)

There is a density limit, Why?

• Empirically, Greenwald found a denstiy limit nGW (1020m-3) =I(MA)/πa2

• Fusion reaction ∝ n2

Ø Huge impact on electrical cost• Another defiance by tokamak plasma

Replacing Divertor Module in ITER

도전과 융화⇒꿈의 에너지

• 극고온 쿨롱 통계 시스템에의 도전

• 막대한 Free energy에 의한 통계 시스템의 반항

• 반항의 이해에 의한 적합한 환경 조성으로 자체감금을 유도 ⇒ Advanced Tokamak

• 현재 KSTAR가 가장 Advanced Tokamak.• 언저리 플라즈마의 중요성이 점점 더 부각됨.• Numerical Tokamaks + Real Experiments ⇒

Enormous Advances are expected.• Caution: Inertial Fusion is for Atomic Bomb

Research