In
news items about controlled fusion research (see, for example, PHYSICS TODAY, August 2005, page 26), it has become commonplace to dwell on the political and financial aspects but to act as if the
important scientific questions have been answered and only engineering details remain. However,
there are scientific gaps in the conceptual foundations of ITER, the proposed international prototype
fusion energy reactor—or any other magnetic confinement device—that are worth further
consideration from the whole physics community.
The most awkward gap is the lack of a manageable mathematical
framework for calculating the state of the plasma in a confinement device in a way that relates the
calculation globally and convincingly to what actually happens in the machine. This becomes apparent
when theoretical claims are set alongside the experiments being contemplated. For half a century,
the textbook theoretical starting point for such a global calculation has been the use of ideal
magnetohydrodynamics to provide a zeroth-order description of the state of the confined plasma.
"Ideal" MHD here means a fluid-mechanical formulation from which the dissipative terms (viscous
and resistive) have been dropped. Much more elaborate and less restrictive descriptions are often
used to identify instabilities that might make the confined plasma less tractable than the initial
ideal MHD equilibria would suggest. In such perturbative instability or "turbulent transport"
calculations, which sometimes claim to include microscopic turbulence, dissipative terms are
often reintroduced, despite their omission from the calculated ideal MHD con_1figuration that
is being "perturbed."
This perspective, which slides freely back and forth between
ideal and non-ideal descriptions, is not supportable in fluid mechanics, nor is there reason to
expect it to be in plasma physics.1 In both cases the introduction of the dissipative
terms changes the mathematical character of the steady states that can be sustained and made to
satisfy boundary conditions. One cannot generally get close to a non-ideal steady state with an
ideal one, nor can one treat the stability of a non-ideal steady state with anything like the systematic
mathematics that the ideal case permits. This awkwardness is not the subject of debate; rather,
it is simply ignored. So is the fact that the extent of MHD turbulence is often best predicted by dimensionless
numbers, such as Reynolds or Hartmann numbers, that have dissipation coefficients in their denominators
and diverge as these coefficients approach zero.
It follows that in any project as ambitious as ITER (or for
that matter, the Joint European Tokamak or the Tokamak Fusion Test Reactor, or other similar devices),
what one is doing is carrying out experiments—mostly just trying things—with theory
largely having a decorative role, or at best providing suggestions for something to try next. Such
a secondary role for theory is not necessarily fatal. Many important discoveries have been made
in the absence of a proper theoretical framework to predict them. But two points should be noted
here. First, the conceptual gap between the theory and device building does not need to be as great
as it becomes when discussions of it are essentially not taking place. And second, all the consensus,
all the money, publicity, and sophisticated organization in the world will not necessarily satisfy
the "aim to get 10 times more power out than goes in," as the August PHYSICS TODAY item reports. That
is still just wishful thinking.
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