the 1950s, Lawrence Livermore has been one of the worlds leading
centers of magnetic fusion energy research. Magnetic fusion uses
intense magnetic fields to confine an extremely hot gas of electrons
and positively charged ions called a plasma. Under the right conditions,
the plasma ions undergo fusion reactions, the energy source of the
Sun and other stars.
The long-standing goal of
fusion researchers has been to duplicate the cosmoss means
of producing energy to provide a virtually inexhaustible source
of reliable and environmentally benign energy on Earth. Despite
the immense technical challenges involved in making magnetic fusion
a source of commercial electrical power, important progress has
been made in the past decade as researchers nationwide have collaborated
on experiments and computer simulations.
Fusion Energy Program carries out magnetic fusion energy research
in two complementary thrusts. The first thrust is performing advanced
fusion experiments. Livermore researchers are collaborators at the
national DIII-D tokamak experiment at General Atomics in San Diego,
Laboratory scientists are
also pursuing novel designs for magnetic fusion reactors, such as
the spheromak experiment dedicated in 1998. (See S&TR,
Experiment Mimics Nature's
Way with Plasmas.)
Complementing the experimental
work is an effort to accurately simulate the extraordinarily complex
physics involved in magnetically confined plasmas. Lawrence Livermore
scientists have developed a number of codes for simulating different
aspects of magnetic fusion energy experiments. Its PG3EQ program,
developed by physicists Andris Dimits, Dan Shumaker, and Timothy
Williams, for example, is one of the most advanced programs available
for simulating plasma turbulence. Another Livermore code, called
CORSICA, goes a step further and links individual programs that
model different aspects of magnetic fusion energy physics. (See
Integrated Simulations for Magnetic Fusion Energy.)
Livermore simulation shows a magnetic field line (white) wrapping
around a torus, or doughnut-shaped configuration of plasma.
Magnetic field lines are embedded within the plasma, with individual
particles traveling along each field line. The color contours
indicate microturbulent fluctuations in the plasma density.
Regions with similar densitymicroturbulent eddies indicated
by regions of similar colorstretch along the field lines,
while varying rapidly across the field lines. These microturbulent
eddies transport heat from the plasmas superhot core to
the cold outer edge.
national team of researchers led by Laboratory physicist Bill Nevins
is developing advanced simulation codes running on supercomputers
to deepen scientific understanding of the plasma turbulence that
occurs inside a tokamak, a magnetic confinement device. Tokamaks
use powerful magnets to confine plasmas of fusion fuel on the toroidal,
or doughnut-shaped, magnetic surfaces defined by individual
magnetic field lines as they wind about within a vacuum chamber.
Plasma turbulence causes
thermal energy to leak across the magnetic surfaces faster than
it can be replaced by fusion reactions. This lost energy must be
replaced by external sources to prevent the plasma from cooling
below the 100-million-degree temperatures needed to optimize the
rate of fusion reactions. However, current tokamak experiments are
close to the major goal of breakeven, that is, the point at which
the energy produced by the fusion reactions equals the energy applied
from an external source to heat the fuel. A better understanding
of plasma turbulence may allow researchers to reduce the rate of
energy loss so that energy breakeven could be achieved in the current
generation of tokamaks.
The national collaboration
is called the Computational Center for the Study of Plasma Microturbulence.
It is funded by the Department of Energys Office of Fusion
Energy Sciences, a part of DOEs Office of Science. The work
is part of the Office of Sciences Scientific Discovery through
Advanced Computing (SciDAC) program, which was launched in late
2000. SciDACs goal is to develop the scientific computing
hardware and software needed for terascale (trillion-operations-per-second)
supercomputing. The effort is similar to the National Nuclear Security
Administrations Accelerated Strategic Computing Initiative,
which is making available terascale computers for the nations
Stockpile Stewardship Program.
The collaboration involves
researchers from Lawrence Livermore, the Princeton Plasma Physics
Laboratory, the University of California at Los Angeles, the University
of Colorado, the University of Maryland, and General Atomics. These
institutions were part of previous DOE magnetic fusion energy simulation
efforts, including the Numerical Tokamak Turbulence Project (1993
to 1999), led by Livermore physicist Bruce Cohen, and the Plasma
Microturbulence Project (2000 to 2001), led by Nevins.
The simulations are focused
on microturbulence, a long-time nemesis of achieving breakeven conditions
in magnetic fusion energy experiments. Microturbulence is one of
two forms of plasma turbulence observed in magnetic confinement
experiments. Macroturbulence, on the scale of centimeters to meters,
has been largely tamed in advanced tokamak designs. Microturbulence,
on the scale of tenths of millimeters to centimeters, has not.
simulation, done by Livermore collaborator General Atomics of
San Diego, California, with the GYRO code, shows a cross section
of a tokamak over time (t) in microseconds (ms). The color contours
indicate microturbulent fluctuations in the plasma density.
The center sections have been removed to facilitate comparison.
Microturbulence is an irregular
fluctuation in the plasma soup of electrons and ions.
The fluctuations are caused by gradients of density and temperature.
The fluctuations, a collective phenomenon, form unstable waves and
eddies that transport heat from the superhot core across numerous
magnetic field lines out to the much cooler plasma surface and,
ultimately, to the tokamaks walls. Energy researchers call
this phenomenon energy transport.
Nevins notes that a tokamaks
plasma will undergo fusion reactions only if it is hot enough, dense
enough, and kept away from the much colder reactor walls. By causing
heat to be lost from the plasma core, microturbulence helps to degrade
confinement and prevent breakeven conditions. We want plasma
at about 100,000,000°C in the center and below 1,000°C at
the walls, so they dont melt, says Nevins. We
obviously need good thermal insulation, and thats provided
by the confining magnetic field. If we can minimize microturbulence,
we can prevent heat leaking out faster than the fusion reactions
can generate heat.
will be immensely important in determining whether an advanced experiment,
currently in the early planning stages, will be a success. Nevins
says that the largest tokamaks cost several hundred million dollars
to build. Constructing an experimental device that would go beyond
breakeven for a net production of energy would cost about $2 billion.
If a way were found to control microturbulence, construction costs
could decrease significantly.
Says Cohen, If we had
better energy confinement, we could build the next generation device
at a much lower cost. To do that, we need to understand better the
nature of plasma microturbulence.
of the cross section of a tokamak plasma. The color contours
indicate microturbulent fluctuations in the plasma density.
Livermores PG3EQ code, which was used to produce this
simulation, models a tube of magnetic flux as it
wraps once around the tokamak poloidally, or the short way around.
Toroidal symmetry was then used to displace this flux tube and
fill the annulus.
current focus is on advanced codes, algorithms, and data analysis
and visualization tools. Nevins says that simulating microturbulence
has proved difficult because of the enormous range of time and space
scales that occur in magnetic fusion plasmas. Indeed, scientists
within the national magnetic fusion energy program have worked to
model microturbulence for more than two decades.
Fortunately, massively parallel
computers, which use thousands of microprocessors in tandem, are
well-suited to this simulation task. These machines are ideal because
the collective behavior of trillions of electrons and ions is complex,
but the underlying physicsand the equations that describe
itare relatively straightforward.
Most computing is done remotely
at the Department of Energys National Energy Research Scientific
Computing Center (NERSC) at Lawrence Berkeley National Laboratory.
In fact, the collaboration is the biggest user of NERSC facilities.
The current simulations typically require from 10 to 20 hours to
complete using NERSCs most powerful machines.
The simulations are run
on the ASCI Blue supercomputer using Lawrence Livermore software
adapted for multiprocessor machines. Despite the enormous computational
power of the computer, Lightstone can only simulate one trillionth
of a second per month. "As a result," says Lightstone, "we have
to be selective in what we simulate."
UCAN code, developed by Livermore collaborators at the University
of California at Los Angeles, produced these two images of tokamak
plasmas. (a) Early in the development of the microturbulence,
small-amplitude, radially elongated turbulent eddies form. (b)
Fully developed microturbulence exhibits smaller, disordered
The hardware advances have
been accompanied by the equally impressive development of efficient
algorithms with which to solve the equations that form the basis
of plasma simulation. The algorithms are of two kinds, particle-in-cell
(PIC) models and continuum models, depending on how they track simulated
electrons and ions in space and time. PIC models track individual
electrons and ions; continuum models solve equations that do not
involve individual particles.
The national effort is developing
both kinds of algorithms because they offer a valuable means of
verifying new codes. Together, the two kinds of algorithms
provide a balanced scientific approach to understanding microturbulence,
says Nevins. Each approach, however, pushes the limits of current
PIC and continuum algorithms
can be used in two geometric representations: global and flux tube.
Global simulations model the entire plasma core of a tokamak, whereas
flux tube simulations represent a more limited area. Here again,
says Nevins, the two geometric approaches serve as a useful cross-check
on the results obtained from each other.
With the increased speed
of microprocessors, additional memory, massively parallel supercomputers,
and advanced algorithms, important progress has been made in the
past few years in modeling microturbulence. Nevins points to significant
improvements in the comparisons of simulations to experiment results,
in the agreement of results from codes developed by collaborators
from different centers of magnetic fusion energy research, and in
the increasingly thorough and accurate physics content of the models.
An important aspect of the
code work is developing new tools to analyze and visualize the simulation
results. Data analysis and visualization provide the bridge between
the microturbulence simulation and experimental research. Nevins
has developed GKV, a program that allows the user to easily compute,
analyze, and display results (in presentation-quality form) easily
from microturbulence simulation data. The program is used by researchers
A strong numerical model
of microturbulence, combined with better data analysis and visualization
tools, is aiding the interpretation of experimental data and the
testing of theoretical ideas about microturbulence and how to control
it. The simulations are also helping scientists to plan future experiments.
In addition, continued progress in code development may stimulate
advances in the understanding of astrophysical plasmas and turbulence
for the Future
Fusion combines the nuclei of light elements to form a
heavier element. For example, two nuclei of hydrogen isotopes,
deuterium and tritium, will overcome the natural repulsive
forces that exist between such nuclei and combine under
enormous temperature and pressure. The fusion reaction
produces a single nucleus of helium, a neutron, and a
significant amount of energy.
A device that
creates electricity from fusion must heat the fuel to
a sufficiently high temperature and then confine it for
a long enough time so that more energy is released than
must be supplied to keep the reaction going. To release
energy at a level required for electricity production,
the fusion fuel must be heated to about 100,000,000°C,
more than 6 times hotter than the interior of the Sun.
At this temperature, the fuel becomes a plasma, an ionized
gas of negatively charged electrons and positively charged
ions. Although rare on Earth, plasmas constitute most
of the visible universe.
for scientists is how to confine the plasma under extreme
temperatures and pressures. One solution is to use powerful
magnetic forces. In the absence of a magnetic field, a
plasmas charged particles move in straight lines
and random directions. Because nothing restricts their
motion, the charged particles can strike the walls of
a containing vessel, thereby cooling the plasma and inhibiting
fusion reactions. In an appropriately designed magnetic
field, the particles are forced to follow spiral paths
about the magnetic field lines so they do not strike the
vessel walls. The plasma is thus confined to a particular
magnetic field line. The magnetic field line itself can
be confined within a vacuum chamber if its path is restricted
to a toroidal, or doughnut, shape.
A bundle of such
magnetic field lines forms a doughnut-shaped magnetic
bottle called a tokamak, an acronym derived
from the Russian words meaning toroidal chamber and magnetic
coil. In the tokamak, the stable magnetic bottle is generated
both by a series of external coils, which are wrapped
around the outside of the doughnut, and by a strong electrical
current, up to several million amperes, that is induced
in the plasma itself.
Century of Research
energy research has been under way for more than a half
century and was one of Lawrence Livermores original
programs. The idea was classified because the concept
uses the energy released by the same reaction that takes
place in a hydrogen or thermonuclear bomb. In the late
1950s, the research program, called Project Sherwood,
was partially declassified because it was viewed as a
long-term effort without immediate military application
and one that would benefit greatly from international
has been made in the last 20 years at Livermore and other
research centers in meeting the scientific challenges
of attaining the combination of temperature, density,
and confinement time necessary to promote fusion reactions.
At one point, several different types of devices, including
Livermores magnetic mirror design, were
pursued within the national program. Budget constraints,
however, led to the adoption of the tokamak as the principal
design for the U.S. program, with other approaches being
explored at lower levels of resources.
goal of magnetic fusion energy is to produce abundant,
environmentally acceptable electric energy from a fusion-powered
reactor. In fusion power plants, the heat from deuteriumtritium
fusion reactions would be used to produce steam for generating
electricity. Deuterium is abundant and easily extracted
from ordinary water (about one water molecule out of every
6,000 contains deuterium). Tritium can be made from lithium,
a plentiful element in Earths crust.
One kilogram of
deuteriumtritium fusion fuel would produce the same
energy as 30 million kilograms of coal. Other major advantages
include no chemical combustion products and therefore
no contribution to acid rain or global warming, radiological
hazards that are thousands of times less than those from
fission, and an estimated cost of electricity comparable
to that of other long-term energy options.
a tokamak, magnetic fields from surrounding magnets confine
a plasma fuel of hot, ionized gas within a hollow, doughnut-shaped
Now Getting Respect
Cohen recalls that five years
ago, experimentalists paid much less attention to theorists regarding
plasma turbulence. Today, however, simulations do such a good job
in predicting experimental results that experimentalists are
really paying attention to the codes. Simulations, he says,
have achieved such a level of fidelity to the underlying plasma
physics that they can often be used as a tool for experiments regarding
Nevins points out that the
cost of doing simulations is nearly negligible compared with the
cost of building and running a new fusion ignition experiment (around
$1 billion to $2 billion). Inexpensive but increasingly realistic
simulation capability will continue to have immense leverage on
relatively expensive experiments, he says.
He also points out that
numerical simulation has a distinct advantage over experimental
observations of microturbulence: The simulations give users access
to virtually any portion of the plasma in time or space. Simulations
use synthetic diagnostic tools, which mimic the signal
that an experiment would be expected to produce on an experimental
Says Nevins, We can
put in better diagnostics on a computer code than we can during
an experiment. Whats more, the physics underlying observed
microturbulence can often be ambiguous. With a simulation,
we can turn different physics on and off to isolate what is driving
the microturbulence observed in the experiment.
Not only have recent simulations
produced a clearer understanding of microturbulence, but they have
also provided a few surprises as well. For example, scientists have
long puzzled over large but transient bursts of heat that are transported
out of the core plasma by microturbulence eddies. We would
have expected the transfer of heat from the plasma core out to the
walls to be homogeneous because of the small eddies caused by microturbulence.
Instead, weve seen large, intermittent bursts 10 times the
size of the eddies, Nevins says.
simulation reveals the binding mechanism between a food mutagen
and cytochrome P450, the enzyme that catalyzes the initial activation
step for this mutagen.
and others have noticed that these intermittent spikes are characteristic
of self-organized criticality, a phenomenon that occurs
in a system when certain key parameters reach critical values. Self-organized
criticality is responsible, for example, for the occurrence of sudden
avalanches as grains of sand are slowly added to the top of a sandpile.
The Livermore simulation team is using the insights derived from
self-organized criticality to account for these unexpected bursts
of heat, which apparently are the combination of many turbulent
recent addition to the simulation codes is a phenomenon called flow
shear that works to dampen microturbulence and thereby improve plasma
confinement. The plasma rotates (flows) within each of the nested
magnetic surfaces defined by individual magnetic field lines. The
term flow shear describes spatially localized changes in the rate
of plasma rotation. The flow shear sharply reduces the rate at which
heat is transported out to the cold plasma edge by stretching and
tearing apart the microturbulence eddies.
experiments have detected puzzling bursts of heat produced by
microturbulence. Recent simulations show the same phenomenon,
where the heat pulses are indicated by bright regions. Researchers
have noticed the similarity between these heat pulses and other
instances of self-organized criticality, which resemble the
sudden occurrence of avalanches as grains of sand are slowly
added to the top of a sandpile. The simulation also shows the
spontaneous transition in time from a state of high heat transport,
with many heat pulses, to a state of low heat transport, in
which the heat pulses are largely absent. This transition was
caused by microturbulence-induced changes in the plasmas
explains that heat must travel to the outer plasma edge across many
nested magnetic surfaces. When the magnetic surfaces rotate relative
to each other, the eddies transporting the heat tend to dissipate.
He offers the analogy of a busy freeway, with each lane of cars
(magnetic surface) at a different speed. If a driver must hand a
rubber band (microturbulence eddy) to a driver in another lane passing
by at a much faster rate, the rubber band will soon break and not
be passed to the driver in the faster lane.
shear can appear spontaneously during a magnetic fusion energy experiment.
When that happens, says Cohen, We get it for free. Flow
shear can also be created experimentally by applying a twisting
force (torque) to the plasma using, for example, intense beams of
neutral hydrogen atoms. The force pushes on the center of the plasma
core to create barriers to heat transport.
want to understand much better how flow shear functions so we can
know how much to apply to effectively control microturbulence,
says Cohen. Precisely applying flow shear could increase plasma
confinement and significantly decrease the cost of new experimental
national collaboration is working to provide a suite of modular,
complementary computer programs, each with an identical user interface.
Together, the modules will constitute a comprehensive code for microturbulence
simulation, data analysis, and visualization. The modular architecture
will enable physics simulations on diverse computer architectures
with much less effort than current software approaches demand. Says
Nevins, We want to revolutionize the fusion communitys
ability to interpret experimental data and test theoretical ideas.
The result will be a much deeper understanding of microturbulence.
of a tokamak and two plasma cross sections. In the simulation
that produced the plasma cross section on the left, the flow
shear was suppressed, while the self-generated flow shear was
retained in the simulation that produced the cross section on
the right. These cross sections illustrate the role of flow
shear in suppressing plasma microturbulence and thereby forming
barriers to unwanted heat transport. This simulation was created
using the GTC code developed at the Princeton Plasma Physics
the codes themselves, the collaborators are working on consolidating
programs developed by individual research groups. Another area of
activity is improving the physics simulated by the codes, for example,
by refining the simulated diagnostic instruments and more accurately
modeling the role of electrons involved in microturbulence.
is hopeful that by making the simulations easier to run and analyze,
even more experimenters will choose to use them. It was a
heroic feat to make the codes work, but now we need to make them
available to the experimental community, he says. We
want these tools to be used more widely so that we expand the use
of microturbulence simulation well beyond the existing small group
of code developers. Our goal is to have experimentalists run the
codes and understand the results much faster.
simulation tools could bring dependable fusion energy much closer
to reality. That would be welcome news for a nation recently reminded
about the fragility of steady energy supplies and prices.
Key Words: fusion,
macroturbulence, magnetic fusion, microturbulence, National Energy
Research Scientific Computing Center (NERSC), plasma, Scientific
Discovery through Advanced Computing (SciDAC), tokamak, turbulence.
information contact Bill Nevins (925) 422-7032 (firstname.lastname@example.org).