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
An Optimistic Energy Projection
New Non-Fossil Energy Sources Needed
Optimistic Projection:
New Sources
Phase-out of
Conventional fission
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
Generic Magnetic Fusion Power Plant
Superconducting Magnet
PFF
(1-R)
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, tE , must be large enough!
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
Today’s Typical Magnetic Fusion Experiments
B  2 to 10 Tesla, n  1020 m3 , kT  10 keV to 1 eV at edge
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
Disparate Scales in a Fusion Experiment
B = 3 T, kT  5 keV to 1 eV, n  5 10 m , Device size 1m
19
Space (104 to 10-6 meters)
Mean Free Path =
kT / m
c
Frequency (102 to 1012 sec-1)
Collision :  c  n /T 3 / 2
e  e : 10 4  4  109
 3 10 3 to 10 -4
Debye Length   D 
3
i  i : 2  102  8  107
 0 kT
ne 2
 7  105 to 1 106
 c 
Collisionless skin depth    7  10 -4
 pe 
mkT

eB
electrons: 5  10-5 to 8  10 -7 ,
Larmor Radius =
ions: 3  10-3 to 5  10-5
e  i : 10  3 10 6
ne 2 -1
Plasma :  p 
s ,
 0m
 pe  4 1011,  pi  7  109 ,
Hybrid :  pH   pe pi  5  1010
eB
m
electron : 5  1011, ion : 1.4  108
Cyclotron :  c 
Particle Orbits in Magnetic Fields
Particle Trajectory
Charged Particles gyrate
around and nearly
follow field lines.
B

V  V  V|| bˆ  VF , VF  eE  mgeff
bˆ

 VE  Vgravity
eB

 2 V 2 
"gravity" geff  V|| 
,  = bˆ   bˆ  Field line curvature

2 

 
Curvature drift may separate electron and ion flows
2
=> Electic fields.
mV
Adiabatic Invariant m 
leads to " mirror trapping" of some
2B
particles as they move along field lines towards increasing B.
Equilibrium Leads to Population Inversion
Equilibrium: j  B  p   n eTe  niTi 
Diamagnetic Current (relative flow between e and i)
b   n iTi
b  ne Te 
Vi  VDi 
, and Ve  VDe 
n iZieB
n e ZeeB
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.
Obtaining Stable Plasma Confinement
Field Line
Bending
Magnetic
Compression
Fluid
Compression
2
2


B
1
B
2
2
3
W   dr 

     2     p  
2
2m0
 m0
J||   b B  2   p   
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
Curvature Acts Like Gravity
n
g
+
VE  E x b/B
- E +
E -
n+Dn
Stable (Concave)
Vdrift
n
n+Dn
n+Dn
n
g
g
Vdrift
B
g
n
-
VE  E x b/B
+ E E +
n+Dn
Unstable (Convex)
Tokamak Has Produced Best Plasma Confinement
B toroidal field from coils that link plasma torus,
increases inward
I toroidal current driven inductively by central solenoid
[or by non - inductive sources (rf, ion beams," bootstrap current" )]
B poloidal field produced from I  in plasma and external coils
Winding net magnetic field generates nested flux surfaces,
q
Magnetic shear: s 


Particle Orbits in Tokamak: Bananas
Balanced orbits radially confined
Bpoloidal
Ion Vgravity
Btoroidal
Neo-classical diffusion:
collisions cause random
radial motion and loss
Displaced bananas produce
Unbalanced downward drift;
Ware Pinch!
Bpoloidal
Ion Vgravity
Etoroidal
Btoroidal
V pinch 
E toroidal
B poloidal
E  b E toroidalB poloidal


2
B
Btoroidal
Banana Trick: Bootstrap Current
Feeds counter-current passing
Feeds co-current passing
particles inside base flux tube
particles outside base flux tube
Gradient drives net co-current
Bpoloidal
Gradient drives net co-current
Btoroidal
Bootstrap Current and Ware Pinch
Are both related to Onsager Symmetry
Toroidal Electric Field
=> Toroidal plasma current
Generalized Thermo Force
Pressure gradient
=> Radial heat flux
Offdiagonal
“Pinch”: inward
particle and heat flux
Toroidal
Current flow
High-quality Tokamak Plasmas Sustained with
Large Bootstrap Current Fraction ≈ 0.5
Non-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)
Sawtooth region in core
(RF and neutral beam sources)
Pedestal (Core to edge transition)
In magnetic divertor region
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 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
1. Pedestal width ~ banana width
2. Strong drop in edge turbulence; tE increases by ~ 2
3. Shear flows are critical
4. Interplay of drift wave turbulence and sophisticated
neoclassical processes.
5. Experimentally robust but theory still incomplete.
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
Mode “Insulation” at Zero Magnetic Shear Surface
q(r)
Rational Surfaces
= r/R
Zero shear region does not support ITG eigenmode excitations
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
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.
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
Recombination
Zone Te ~ 1 eV
Ion-Neutral
Interaction Zone
Te ~ 2 - 5 eV
Deuterium
Radiation
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 (Ea ~ 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
Theoretical Fit of Pitchfork Splitting in JET Experiment
Frequency
Time Evolution of the Bifurcating Mode
dA

 A  L
dt
2
t/2
t
0
2
dt
t 2 t

dt 1 exp[ 3eff t 2 (2t / 3  t1 )]
0

A(t  t )A(t  t  t 1 )A (t  2t  t 1 )
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
Gamma ray Spectroscopy in Fusion Plasmas
Excitation functions of the 4.44
MeV & 7.65 MeV levels of C12
in Be9(a,n C.
Promising Alternate Approaches
• 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)
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”
Personal 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.