Overview of Magnetic Fusion

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Overview of Magnetic Fusion Science Program The
Quest, The Questions, The Achievements
Presented by Herbert L. Berk Department 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
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An Optimistic Energy Projection New Non-Fossil
Energy Sources Needed
Optimistic Projection
New Sources
Phase-out of Conventional fission
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Practical Sources of Fusion Energy
D-T Lawson Criterion for Sustained
Confinement ? tE 10 atm sec (kT 10 to 20
keV) tE energy confinement time, p plasma
pressure
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Generic Magnetic Fusion Power Plant
Superconducting Magnet
PF
Magnetic pressure B2/2m0 confines particle
pressure (if done right) ????? ? ????
(kinetic/magnetic pressure) ? 4m0kT/B2 0.03 to
0.1 ?n ?? Normalized beta 1 To achieve
this, energy confinement time, ?E , must be large
enough!
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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

Todays Typical Magnetic Fusion Experiments
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Challenge for Physical Insight in Plasmas

• Non-equilibrium
• Different ion and electron temperatures.
• Anisotropic pressure
• Intrinsically kinetic problem
• Fluid closure fails parallel to B
• Anisotropic dispersion
• Long to short mean free paths
• Edge dynamics must handle
• plasma to neutral transition,
• myriad atomic and chemical processes,
• Strong coupling with core plasma

The Physics Isolate key issues and develop
methods to handle them
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Disparate Scales in a Fusion Experiment
Space (104 to 10-6 meters) Frequency
(102 to 1012 sec-1)
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Particle Orbits in Magnetic Fields
Particle Trajectory
Charged Particles gyrate around and nearly follow
field lines.
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Equilibrium Leads to Population Inversion
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 tE
Challenge understand and control Q of plasma
cavity to prevent self-excitation of such waves.
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Obtaining Stable Plasma Confinement
Field Line Bending
Magnetic Compression
Fluid Compression
Parallel Current Drive With 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
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Curvature Acts Like Gravity
g
Vdrift
Vdrift
n
n
n D?n
n D?n
g
n
n
VE ?E x b/B
VE ?E x b/B
g
B
- E
E -
E -
- E
g
n D?n
n D?n
Stable (Concave)
Unstable (Convex)
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Tokamak Has Produced Best Plasma Confinement
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Particle Orbits in Tokamak Bananas
Displaced bananas produce Unbalanced downward
drift Ware Pinch!
Balanced orbits radially confined
Ion Vgravity
Bpoloidal
Bpoloidal
Ion Vgravity
Etoroidal
Btoroidal
Btoroidal
Neo-classical diffusion collisions cause
random radial motion and loss
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Banana Trick Bootstrap Current
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-current
Bpoloidal
Btoroidal
Bootstrap Current and Ware Pinch Are both
related to Onsager Symmetry
Toroidal Electric Field gt Toroidal plasma
current
Pinch inward particle and heat flux
Off- diagonal
Generalized Thermo Force
Toroidal Current flow
Pressure gradient gt Radial heat flux
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High-quality Tokamak Plasmas Sustained with
Large Bootstrap Current Fraction
0.5 Non-inductive current fraction 0.75
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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 (driftcurvature driven) is principal
  driver.
• Detailed comparisons of theory with experiments
• over large range of plasma parameters.

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Tokamak Confinement
Empirical Scaling
Theory Prediction (J. Kinsey)
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Tokamak Issues
External shaping optimizes stability (elongation
triangularity)
Sawtooth region in core
(RF and neutral beam sources)
Pedestal (Core to edge transition)
In magnetic divertor region
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• Instability near plasma center
• Field line pitch too large (q lt 1) near plasma
  center
• Still elusive complete explanation for
  relaxation
• Usually not dangerous, only internal
  rearrangement.
• More worrisome at MHD beta limits
• a) Undo bootstrap current Carrera,Hazeltine,Kotsc
  henreuther
• b) Lock to wall error fields causing disruption
  (rapid plasma loss)
• Successful experimental cures
• Restore bootstrap with external current drive
• Keep plasma flowing

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Importance of Plasma Flows -I

• Prevent locking of internal modes to external
  error fields
• with 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
• Pedestal width banana width
• Strong drop in edge turbulence tE increases by
  2
• Shear flows are critical
• Interplay of drift wave turbulence and
  sophisticated neoclassical processes.
• Experimentally robust but theory still incomplete.

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Importance of Plasma Flows -II

• 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

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Mode Insulation at Zero Magnetic Shear Surface
q(r)
Rational Surfaces
?? r/R
Zero shear region does not support ITG eigenmode
excitations
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Zero Magnetic Shear Transport Barriers and
Nontwist Map
Surface of zero twist (shear) provides final
barrier to chaos
Critical surface has fractal properties
x (103)2
Nontwist map evolved from the use of maps in
generalized studies of chaos theory
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Role of Computation

• Many basic issues remain unresolved.
• 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
• Gyro-kinetic simulation shows turbulence lt-gt
  flow shear generation interplay
• Method applied to astrophysical accretion (Talk
  tomorrow by W. Dorland).

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Out-flowing Heat Must Be Removed

• Danger
• Wall sputtering and erosion causes wall
  deterioration
• Impurities fill plasma
• Solution
• Cool plasma outflow with neutral gas using
  recombination and radiation to spread heat load.
• Detach plasma from wall - already achieved.

• Challenges Compatibility with edge and core
  physics.
• Will steep pedestal survive?
• ELMS Edge-localized Modes, energy bursts.

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Detached Divertors Enable Nondestructive Power
Handling
Conduction Zone Te 30 - 50 eV
Carbon Radiation Zone Te 10 - 15 eV
Ionization Zone Te 5 - 10 eV
Ion-Neutral Interaction Zone Te 2 - 5
eV Deuterium Radiation
Recombination Zone Te 1 eV
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Emerging Frontiers

• Energetic Alpha Particles (new physics issues)
• Is it like a stabilizing passive internal coil?
• (Rosenbluth, Van Dam, Berk, Wong, early 1980s)
• May induce a giant sawtooth, (violent
  relaxation)
• Universal drift wave mechanism (Ea 100 Ti)
  allows
• new resonant particle instabilities
• Shear Alfven interaction gt radial alpha
  diffusion
• (Led to compact, general, non-linear theory
  to predict saturation, Berk Breizman)
• New Drift instabilities gt operating space
  limits on burning plasmas

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Theoretical Fit of Pitchfork Splitting in JET
Experiment
Time Evolution of the Bifurcating Mode
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Burning Plasma Experiment

• Can we produce fusion energy?
• Near energy break-even in JET (Europe).
• Copious energy production in TFTR (Princeton).
• Proposed Experiments
• ITER-FEAT (International) Moderate B 5.5
  Tesla.
• FIRE (US) High B 10 Tesla.
• Ignitor (MIT-Italy) Very High B 13 Tesla.
• New interesting diagnostics with nuclear reactions

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Gamma ray Spectroscopy in Fusion Plasmas
Excitation functions of the 4.44 MeV 7.65 MeV
levels of C12 in Be9(a,n ????C.
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Promising Alternate Approaches

• Compact aspect ratio, highly elongated tokamaks.
• MAST (Culham), NSTX (Princeton).
• Stable to ITG mode gt high beta achieved.
• Large elongation plus liquid metal walls
  (Lithium).
• M. Kotschenreuther proposal for power handling.
• Stellarators Confinement with in vacuum fields.
• Avoids sawteeth and disruptions.
• Quasi-symmetry to improve orbit losses.
• Use large plasma flows to achieve relaxed high
  beta states.
• Mahajan-Yoshida Double Beltrami states
• (experiment initiated by P. Valanju R.
  Bengtson)

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Importance of Fusion Research
Quote from V. L. Ginzburg who discussed remaining
interesting physics 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 Person
al View We need to determine rather quickly
whether controlled fusion is a viable energy
option, as only relatively wealthy economies with
an inexpensive energy supply have the resources
to answer the needed intellectually challenging
science and technology issues needed to achieve
controlled fusion.