A Brief Introduction to Fusion Energy Simulations
This is a set of information that I've found useful in collaborating with plasma
physicists. The work is
but there are other fusion reactors of promise like
This material is definitely slanted
and not an even-handed presentation of the field, since it's based on my
personal collaborations and experiences. This just provides a start point for
computer scientists and applied mathematicians wanting to look into the area of
fusion energy simulations.
For those who don't want to wade through my rambling, skip down to the
publications/papers section below and get the first 2-3.
This is all one big web page to make it easy to download, and because my web
design talents are nill.
A gas of light nuclides (hydrogen variants) is ionized by having the
electrons stripped away by heating. That leaves the ions with an
electrical charge, so they can be herded with magnetic fields. It takes high
heat and/or pressure to start a fusion reaction. The sun achieves it at
relatively moderate temperatures (~ 10M kelvin) by extremely high pressures
in the core. Fusion reactors try to confine the plasma by magnetic fields,
at a relatively low pressure of a few bars, and then achieve fusion by adding
heat. Once fusion begins, it should start generating its own heat and not require
further energy inputs to sustain it.
Hydrogen is used because with just one electron it is easily fully ionized, and
overcoming the electrical repulsion between two like-charged ions is
achievable with less energy input. The nuclides used are generally deuterium
(one proton + one neutron) and tritium (one proton + two neutrons)
since adding neutrons increases the cross-section of the ion, making it
easier to have collisions. But as a neutral particle, a neutron doesn't add to the
electrical repulsion that has to be overcome.
Wikipedia has a
good article on nuclear fusion that provides more details.
A tokamak is a torus, where the
plasma is contained and controlled by magnetic fields. Radio frequency (RF)
waves from antennae heat the plasma, and can help in controlling it in some cases. A
phenemenon called tearing modes can lead to sawtoothing during a
burn (a single run of the
reactor). In sawtoothing plasma state quantities like temperature and pressure oscillate
wildly, and it can sometimes damp out spontaneously or through RF injection.
But they often end in a disruption event, where containment of the plasma is lost and
it can touch the containment vessel, leading to abrupt and catastrophic cooling
terminating the run. A run is often called a shot, apparently because of
the sound made when a reactor loses containment.
ELMs are edge localized modes, and appear like a sawtooth event. The
difference seems to primarily be in the location: ELMs are on the outboard
side of the torus, while sawtoothing is a core event. A third major feature that
modern simulations try to deal with are neo-classical tearing modes,
which I won't attempt to define here.
The goodies in the plasma are ions: hydrogen nuclei
with one, two, or three particles in the nucleus.
The electrons stripped away from the hydrogen
forms another set of ions. Deuterium (one proton + one neutron) is the majority
A single ion circles around the torus following a magnetic field line,
and at the same time orbits the field line in a gyrokinetic orbit.
Gyrokinetics occur on much faster time scales than a trip around the torus.
A magnetic flux surface is a two-dimensional manifold that is drawn out
by following a single ion around the tokamak for an infinite number
of times. Ions on the same flux surface tend to have the same properties
(energy, momentum, ...).
The plasma state is in equilibrium when the equations for energy,
material, etc. are balanced. Note that an equilibrium can extend in time, and is
not a single point in time like it is for other application areas. And there
are both stable and unstable equilibria, sort of counter-intuitive based just
on the English language sense of the terms. The
magnetic field lines are closed in the core region, and beyond a
separatrix (the edge region) they are open and can intersect the
containment vessel. Pedestal effects are a form of edge phenomena.
Islands form sometimes, which are a secondary core region unconnected
with the central core. They can dissipate eventually, or end up becoming the
central core while the original one dissipates. Islands rob energy from the
main confinement area. A magnetical reconnection event is what it sounds
like: field lines get connected and two magnetic flux surfaces rejoin.
Some categories of codes include
- Transport. Examples include TRANSP (PPPL), TSC (PPPL), BALDUR, ONETWO
(General Atomics), CORSICA (LLNL).
- Gyrokinetics (the orbit of ions around the toroidal direction magnetic
field lines). Examples include GTC and GYRO.
- Magnetohydrodynamics (MHD) in three flavors: equilibria (with no time
dependency), linear, and nonlinear. The equations include terms not in
the standard MHD equations, so it's called extended MHD.
Examples include M3D (PPPL), and NIMROD(NTCC).
- RF for radio frequency heating and control . AORSA, TORIC, TORAY, and
METS are examples.
- Sources for the injection of fuel as a gas or pellets. NUBEAM is part
of TRANSP that handles "neutral beam injection". Fuel must be electrically
neutral to penetrate the containment magnetic field, and then is ionized
into the plasma.
- Edge codes include their own MHD modeling, neutrals, etc. I know far
less about this area, the reason it's getting short shrift here. It's an
important area and a driving need in integrating fusion codes, I just
have not dealt with it in detail.
The tokamak is discretized generally in the poloidal direction (a slice
taken through the torus perpendicular to the inner and outer circle. The
toroidal direction goes around the torus. Structures like flux surfaces
are stretched out around the torus while being small in the poloidal field, leading
to high anisotropy both physically and computationally.
The codes use the full range of space and operator
discretization methods: finite differences,
finite elements, spectral elements, FFT, Monte Carlo, ray tracing.
Also, codes within a single category like RF differ greatly in just what
quantities they model so it's not always possible to do a head-to-head
comparison. The majority of code is in Fortran95 and the physicists use the
modern features, so don't count on g77 to compile them. The physics involved is
highly nonlinear and sensitive to parameter settings and currently it does take
an expert to run them and get meaningful results. Some of these codes require
HPC parallel machines to run since the amount of data involved won't live on a
single processor without thrashing, or the amount of computation is too high to
wait several months for.
Publications/papers that I've found useful:
Simulation of Fusion Plasmas (unfortunately, link removed by AIP) by Don Batchelor
is a short six-page overview. It is
in Physics Today, February 2005, pages 35-40,
(Copyright 2005 American Institute of Physics).
- The Science of JET
by Wesson. Although this
concentrates on results from the Joint European Tokamak, it gives a good
overview of issues like sawtoothing, ELMs, and other buzzwords you'll
commonly see in more detailed works. JET
also has a web site on fusion basics.
- Bill Tang's Overview paper
is a good state of the field
review, with more of the mathematics issues
- The ISOFS
report (PDF), otherwise known as the Dahlburg
report, is what kickstarted the whole code integration effort. It also has
an extensive appendix (also PDF)
with technical details.
- John Wesson's book
Tokamaks is an outstanding reference
for those who have a bit more time. It provides the relevant math at the
level a mathematically inclined scientific computing researcher would be
able to follow and use. Unfortunately you get what you pay for: it costs
$340 for the third edition. Even an earlier edition can provide much of
what a collaborating computer scientist or applied mathematician needs.
Other Web Sites
Web sites of use include
Of course, web sites abound in the fusion energy simulation field and you can
find them readily with Google; these two are just general overviews.
- The Fire Place at Princeton Plasma Physics Lab (PPPL)
provides up-to-date news about the field, and has some introductory
material. More generally rummaging around the pppl.gov web site can provide
many useful links and information
- A glossary of terms has proven
useful for when I get my q-numbers mixed up.
Projects and sites heavily involved in fusion energy simulations include but are
not limited to
Indiana University Computer Science Department
Thu Feb 23 05:57:52 EST 2006
Modified: Sun Feb 26 15:07:00 EST 2006
Modified: Tue Mar 7 09:00:59 EST 2006
Modified: Tue Mar 7 09:00:59 EST 2006 to add initial three paragraphs.
Modified: Thu May 4 15:46:53 EDT 2006 to add fusioncoalition.org