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

€

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

€

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

€

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

€

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.

€

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.

€

r B

Particle Trajectory

Equilibrium Leads to Population Inversion

€

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

€

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

€

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

€

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