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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
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