Overview of Magnetic Fusion Overview of Magnetic Fusion Science ProgramScience Program
The Quest, The Questions, The AchievementsThe Quest, The Questions, The Achievements
Presented by Herbert L. BerkDepartment of Physics and Institute for Fusion Studies
Assisted by Prashant Valanju
Physics Department Colloquium Feb. 20, 2002
Support of DIII-D team of General Atomics gratefully acknowledged
An Optimistic Energy ProjectionNew Non-Fossil Energy Sources Needed
New Sources
Phase-out ofConventional fission
Optimistic Projection:
Practical Sources of Fusion Energy
D-T “Lawson” Criterion forSustained Confinement:E = 10 atm sec (kT ~ 10 to 20 keV);
E = energy confinement time,
p = plasma pressure
Generic Magnetic Fusion Power Plant
Magnetic pressure B2/20 confines particle pressure (if done right) (kinetic/magnetic pressure) 40kT/B2 ≈ 0.03 to 0.1
n Normalized beta ≈ 1; To achieve this, energy confinement time, E , must be large enough!
PF(1-R)PF
Superconducting Magnet
Plasma: The “fourth” State of Matter
•Ubiquitous:
Astrophysics, Fusion, Chip manufacture
•Dominated by collective behavior
Inherently complex system
•Large ranges of space and time scales
All scales affect plasma evolution
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B=2 to 10 Tesla, n≈1020
m−3
, kT=10 keV to 1 eV at edge
Today’s Typical Magnetic Fusion Experiments
Challenge for Physical Insight in Plasmas
•Non-equilibrium:Different ion and electron
temperatures.•Anisotropic pressure•Intrinsically kinetic problemFluid closure fails parallel to B•Anisotropic dispersion•Long to short mean free paths•Edge dynamics: must handleplasma to neutral transition, myriad atomic and chemical
processes,Strong coupling with core plasma
The Physics: Isolate key issues and develop methods to handle them
Disparate Scales in a Fusion Experiment
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Mean Free Path =kT / mν c
≈ 3×103 to 10-4
Debye Length = λ D =ε 0kTne2
≈ 7 ×10−5 to 1×10−6
Collisionless skin depth c
ωpe
⎛
⎝ ⎜ ⎞
⎠ ⎟ ≈ 7 ×10 -4
Larmor Radius = mkT
eB≈
electrons: 5 ×10-5 to 8 ×10 -7,
ions: 3 ×10-3 to 5 ×10-5
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Collision: ν c ∝ n/T3/2
e−e: 104 −4×109
i −i : 2×102 −8×107
e−i : 10−3×106
Plasma: ωp =ne2
ε0m s-1,
ωpe ≈4×1011, ωpi ≈7×109,
Hybrid: ωpH = ωpeωpi ≈5×1010
Cyclotron: ωc =eBm
electron: 5×1011, ion: 1.4×108
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B =3 T, kT ≈5 keV to 1 eV, n≈5×1019m3, Device size≈1m
Space (104 to 10-6 meters) Frequency (102 to 1012 sec-1)
Particle Orbits in Magnetic Fields
Charged Particles gyrate
around and nearly
follow field lines.
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rV =
r V ⊥ +V||
ˆ b +r
V F , r V F = e
r E + m
r g eff( ) ×
ˆ b
eB≡
r V E +
r V gravity
"gravity" r g eff =
r κ V||
2 +V⊥
2
2
⎛
⎝ ⎜
⎞
⎠ ⎟,
r κ = ˆ b • ∇( ) ˆ b = Field line curvature
Curvature drift may separate electron and ion flows => Electic fields.
Adiabatic Invariant μ ≡mV⊥
2
2B leads to "mirror trapping" of some
particles as they move along field lines towards increasing B.
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r B
Particle Trajectory
Equilibrium Leads to Population Inversion
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Equilibrium: r j ×
r B = ∇p =∇ n eTe + niTi( )⇒
Diamagnetic Current (relative flow between e and i)
r V i ≡
r V Di =
r b ×∇ n iTi( )
n iZieB, and
r V e ≡
r V De =
−r b ×∇ neTe( )
n eZeeB
In ion frame: electron distribution is inverted
In electron frame: ion distribution is inverted
Can amplify waves with speeds between ions and electrons.Basic source of “drift wave turbulence” that degrades E
Challenge: understand and control “Q” of plasma cavity to prevent self-excitation of such waves.
Obtaining Stable Plasma Confinement
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δW =12
dr3∫ δB2
μ0
+B2
2μ0
∇ •ξ⊥ +2ξ⊥•κ2+γp∇ •ξ
2⎧ ⎨ ⎩
−J || ξ⊥ ×b( )•δB−2ξ⊥•∇p( ) κ •ξ⊥( )}
Field LineBending
MagneticCompression
FluidCompression
Parallel Current DriveWith resistivity, changes magnetic topology(tearing modes)
Curvature -pressure gradient(related to geff)
Hybrid Culprit Ion Temperature Gradient Mode (ITG):Combined “Drift Wave-Curvature Driven” Mode
Curvature Acts Like Gravity
Stable (Concave) Unstable (Convex)
B
n
n + n
nVdrift Vdrift
n + n
g
g
g
gn
n + n
n
n + n
+ E - - E +- E + + E -
VE E x b/B VE E x b/B
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Bφ toroidal field from coils that link plasma torus, increases inward
Iφ toroidal current driven inductively by central solenoid
[or by non- inductive sources (rf, ion beams,"bootstrap current")]
Bθ poloidal field produced from Iφ in plasma and external coils
Winding net magnetic field generates nested flux surfaces, Ψ
Magnetic shear: s∝ ∂q
∂Ψ
Tokamak Has Produced Best Plasma Confinement
Particle Orbits in Tokamak: Bananas
Ion Vgravity
Btoroidal
Bpoloidal
Neo-classical diffusion: collisions cause random radial motion and loss
Balanced orbits radially confined
Bpoloidal
Displaced bananas produce
Unbalanced downward drift;
Ware Pinch!
Btoroidal
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r
V pinch =E toroidal
Bpoloidal
>>E × b
B≈
E toroidal Bpoloidal
Btoroidal2
Etoroidal
Ion Vgravity
Banana Trick: Bootstrap Current
Bootstrap Current and Ware Pinch Are both related to Onsager Symmetry
Toroidal Electric Field => Toroidal plasma current
Pressure gradient=> Radial heat flux
“Pinch”: inwardparticle and heat flux
ToroidalCurrent flow
Btoroidal
Feeds co-current passing
particles outside base flux tube
Gradient drives net co-current
Feeds counter-current passing
particles inside base flux tube
Gradient drives net co-currentBpoloidal
Off-diagonalGeneralized Thermo Force
High-quality Tokamak Plasmas Sustained with Large Bootstrap Current Fraction ≈ 0.5Non-inductive current fraction ≈0.75
Scientific Progress in Plasma Confinement
•Empirical scaling: traditional experimental guidelines
•Emergence of theory-based scaling
Breakthrough with IFS (UT) - Princeton (PPPL) model
(Dorland, Kotschenreuther, Hammett)
Accurate stability criteria with simulations showing
“stiffness” of plasma response.
“ITG” mode (drift+curvature driven) is principal driver.
•Detailed comparisons of theory with experiments
over large range of plasma parameters.
Tokamak Confinement
Empirical Scaling Theory Prediction (J. Kinsey)
Tokamak Issues
External shaping optimizes stability (elongation & triangularity)
Pedestal (Core to edge transition)
(RF and neutral beam sources)
In magnetic divertor region
Sawtooth region in core
Sawtooth Oscillations
•Instability near plasma center:
a) Field line pitch too large (q < 1) near plasma center
b) Still elusive: complete explanation for relaxation
•Usually not dangerous, only internal rearrangement.
•More worrisome at MHD beta limits:
a) Undo bootstrap current; Carrera,Hazeltine,Kotschenreuther
b) Lock to wall error fields causing disruption (rapid plasma loss)
•Successful experimental cures:
a) Restore bootstrap with external current drive
b) Keep plasma flowing
Importance of Plasma Flows -I
•Prevent locking of internal modes to external error fieldswith plasma flow and magnetic feedback(Seminal work: R. Fitzpatrick)•Shear flow enhances MHD stability, quenches drift waves(F. Waelbroeck; W. Horton; M. Kotschenreuther)•H (high-confinement) -mode: Self-organized spontaneous steep barrier formation
1. Pedestal width ~ banana width2. Strong drop in edge turbulence; E increases by ~ 2
3. Shear flows are critical4. Interplay of drift wave turbulence and sophisticated
neoclassical processes.5. Experimentally robust but theory still incomplete.
•Internal barrier formation:
• Concentrate heating to create strong flow shear,
• Easiest to make around zero magnetic shear region
[reduce transport to intrinsic collisional (neo-classical) loss]
• Critical Experimental Issue: Reversed shear needs hollow
currents that diffuse within “skin-time” unless non-ohmic
current drives maintain hollow current profiles.
• Horton: difficult to find “nucleation centers”
• Modeled by P. Morrison in non-twist maps
Importance of Plasma Flows -II
Mode “Insulation” at Zero Magnetic Shear Surface
Zero shear region does not support ITG eigenmode excitations
= r/R
Rational Surfaces
q(r)
Zero Magnetic Shear Transport Barriers and Nontwist Map
Surface of zero twist (shear)provides final barrier to chaos
Critical surface has fractal properties
Nontwist map evolved from the use of maps in
generalized studies of chaos theory
x (103)2
Role of Computation
a) Many basic issues remain unresolved.
b) Modern computers allow calculation on multiple scales:
• Gyro-kinetic: Global to ion Larmor radius
• Resolution of collisionless electron skin scale for sawteeth (A. Aydemir)
• Resulting predictions being tested in experiment
c) Gyro-kinetic simulation shows turbulence <-> flow shear generation
interplay
d) Method applied to astrophysical accretion (Talk tomorrow by W. Dorland).
Out-flowing Heat Must Be Removed
•Danger:
a) Wall sputtering and erosion causes wall deterioration
b) Impurities fill plasma
•Solution:
a) Cool plasma outflow with neutral gas using
recombination and radiation to spread heat load.
b) Detach plasma from wall - already achieved.
Challenges: Compatibility with edge and core physics.• Will steep pedestal survive?• ELMS: Edge-localized Modes, energy bursts.
Conduction ZoneTe ~ 30 - 50 eV
Detached Divertors Enable Nondestructive Power Handling
Ionization Zone
Te ~ 5 - 10 eVIon-Neutral Interaction
ZoneTe ~ 2 - 5 eVDeuterium Radiation
Recombination Zone Te ~ 1 eV
Carbon Radiation Zone Te ~ 10 - 15 eV
Emerging Frontiers
•Energetic Alpha Particles (new physics issues):
a) Is it like a stabilizing passive internal coil?
(Rosenbluth, Van Dam, Berk, Wong, early 1980s)
b) May induce a giant sawtooth, (violent relaxation)
•Universal drift wave mechanism (E ~ 100 Ti) allows
new resonant particle instabilities
a) Shear Alfven interaction => radial alpha diffusion
(Led to compact, general, non-linear theory to predict
saturation, Berk & Breizman)
b) New “Drift” instabilities => operating space limits on
burning plasmas
Frequency
Intensity
γ/ νeff
=0.47
γ/ νeff
=0.52 γ/ νeff
=0.59
340 345 350 355Frequency (kHz)
t=52.62 s
Intensity
330 335 340
t=52.70 s
310 315 320 325
t=52.85 s
52.56 52.6 52.64 52.68 52.720
1 10-7
2 10-7
3 10-7
4 10-7
5 10-7
6 10-7
7 10-7
Amplitude (a.u.)
t (sec)
Experiment
52.56 52.6 52.64 52.68 52.72
Central lineUpshifted sidebandDownshifted sideband
0
1 10-7
2 10-7
3 10-7
4 10-7
5 10-7
6 10-7
7 10-7
t (sec)
Simulation
dA
dt
= γ A −
γ
L
2
2
d
0
t / 2
∫ d
1
0
t − 2
∫[exp − ν
eff
3
2
( 2 / 3 +
1
)]
× A ( t − ) A ( t − −
1
) A
∗
( t − 2 −
1
)
Theoretical Fit of Pitchfork Splitting in JET Experiment
Time Evolution of the Bifurcating Mode
Burning Plasma Experiment
•Can we produce fusion energy?
a) Near energy break-even in JET (Europe).
b) Copious energy production in TFTR (Princeton).
•Proposed Experiments:
a) ITER-FEAT (International): Moderate B ~ 5.5 Tesla.
b) FIRE (US): High B ~ 10 Tesla.
c) Ignitor (MIT-Italy): Very High B ~ 13 Tesla.
•New interesting diagnostics with nuclear reactions
Excitation functions of the 4.44MeV & 7.65 MeV levels of C12
in Be9(,n γ12C.
Gamma ray Spectroscopy in Fusion Plasmas
•Compact aspect ratio, highly elongated tokamaks.
a) MAST (Culham), NSTX (Princeton).
b) Stable to ITG mode => high beta achieved.
•Large elongation plus liquid metal walls (Lithium).
a) M. Kotschenreuther proposal for power handling.
•Stellarators: Confinement with in vacuum fields.
a) Avoids sawteeth and disruptions.
b) Quasi-symmetry to improve orbit losses.
•Use large plasma flows to achieve relaxed high beta
states.
a) Mahajan-Yoshida “Double Beltrami” states
(experiment initiated by P. Valanju & R. Bengtson)
Promising Alternate Approaches
Quote from V. L. Ginzburg who discussed remaining interestingphysics problems at end of the twentieth century: Controlled Nuclear Fusion (first on his list):“This is however an exceedingly important and still unsolved problem, and therefore I would discard it from the list only after the first thermonuclear reactors start operating”
Personal ViewWe need to determine rather quickly whether controlled fusion is a viable energy option, as only relatively wealthy economies with aninexpensive energy supply have the resources to answer the needed intellectually challenging science and technology issues needed to achieve controlled fusion.
Importance of Fusion Research