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  ![](media/image1.jpeg){width="1.4791666666666667in"   ***Advanced Scientific\                 ![](media/image2.png){width="0.6666666666666666in"
  height="0.4791666666666667in"}                        Computing Research***                   height="0.4930555555555556in"}

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> **Simulations Predict Favorable Confinement Trend\
> for Reactor-Scale Plasmas (2001)**

## W. W. Lee, Z. Lin, W. M. Tang, J. L. V. Lewandowski, W. Wang, T. S. Hahm, and S. Ethier, Princeton Plasma Physics Laboratory

***Fusion research reached a milestone in 2001 with the first simulation
of turbulent transport in a full-sized reactor plasma by researchers at
the Princeton Plasma Physics Laboratory. This breakthrough full-torus
simulation was made feasible by a new generation of software and
hardware---better physics models and efficient numerical algorithms,
along with NERSC's 10 teraflop/s IBM SP. The new simulation produced a
result that was as welcome as it was surprising---as the size of the
plasma increased, the turbulent transport reached a plateau and leveled
off. This "rollover" from one scaling mode to another is an important
topic of current research.***

Most people do not think about turbulence very often, except when they
are flying and the captain turns on the "Fasten Seat Belts" sign. The
kind of turbulence that may cause problems for airplane passengers
involves swirls and eddies that are a great deal larger than the
aircraft. But in fusion plasmas, much smaller-scale turbulence, called
microturbulence, can cause serious problems---specifically,
instabilities and heat loss that could stop the fusion reaction.

In fusion research, all of the conditions necessary to keep a plasma
dense and hot long enough to undergo fusion are referred to as
confinement. The retention of heat, called energy confinement, can be
threatened by microturbulence, which can make particles drift across,
rather than along with, the plasma flow. At the core of a fusion reactor
such as a tokamak, the temperatures and densities are higher than at the
outside edges. As with weather, when there are two regions with
different temperatures and densities, the area between is subject to
turbulence. In a tokamak, turbulence can allow charged particles in the
plasma to move toward the outer edges of the reactor rather than fusing
with other particles in the core. If enough particles drift away, the
plasma loses temperature and the fusion reaction cannot be sustained.

One troublesome result of tokamak experiments to date is that as the
size of the plasma increases, the relative level of heat loss from
turbulent transport also increases. Because the size (and therefore
cost) of a fusion experiment is determined largely by the balance
between fusion self-heating and turbulent transport losses,
understanding this process is of utmost importance for the design and
operation of fusion devices such as the multi-billion-dollar ITER
project. ITER (Latin for "the way"), a multinational tokamak experiment
to be built at Cadarache in southern France, is one of the highest
strategic priorities of the DOE Office of Science.

ITER is expected to produce 500 million thermal watts of fusion
power---10 times more power than is needed to heat the plasma---when it
reaches full operation around the year 2016. As the world's first
production-scale fusion reactor, ITER will help answer questions about
the most efficient ways to configure and operate future commercial
reactors.

The growth of the microinstabilities that lead to turbulent transport
has been extensively studied over the years, not only because
understanding this process is an important practical problem, but also

![](media/image3.jpeg){width="3.0340277777777778in"
height="2.1277777777777778in"}

*Figure 1. Turbulence reduction via sheared plasma flow compared to case
with flow suppressed.*

because it is a true scientific grand challenge which is particularly
well suited to be addressed by modern terascale computational resources.
And the latest news, confirmed by multiple simulations using different
codes, is good: in reactors the size of ITER, heat losses caused by
plasma turbulence no longer follow the empirical trend of increasing
with the size of the plasma. Instead, the rate of heat loss levels off
and stabilizes.

Progress in understanding plasma ion dynamics has been impressive. For
example, studies show that electrostatic ion temperature gradient (ITG)
driven turbulence can be suppressed by self-generated zonal flows within
the plasma. The suppression of turbulence is caused by a shearing action
that destroys the finger-like density contours which promote thermal
transport (Figure 1).

This simulation is a good example of the effective use of powerful
supercomputers (in this case, the 10 teraflop/s Seaborg IBM SP at
NERSC). Typical global particle-in-cell simulations of this type have
used one billion particles with 125 million grid points over 7000 time
steps to produce significant physics results. Simulations of this size
would not be feasible on smaller computers.

Large-scale simulations have also explored key consequences of scaling
up from present-day experimental fusion devices (around 3 meters radius
for the largest existing machines) to ITER-sized reactors (about 6
meters). For the reactor-scale plasmas of the future, these simulations
suggest that the relative level of heat loss driven by electrostatic

ITG turbulence does not increase with plasma size (Figure 2). This
transition from "Bohm" (linear) scaling to "gyro-Bohm" (quadratic)
scaling is a positive trend, because simple empirical extrapolation of
the smaller system findings would produce much more pessimistic
predictions for energy confinement. Since neither experiments nor theory
and simulations have previously been able to explore such trends in an
ITER-sized plasma, these results represent a significant scientific
discovery enabled by the SciDAC program.

Exploration of the underlying causes for the transition in the rate of
heat loss that simulations show around the 400 gyroradii range has
inspired the development of new nonlinear theoretical models based on
the spreading of turbulence. Although this predicted trend is a very
favorable one, the fidelity of the analysis needs to be further examined
by investigating additional physics effects, such as kinetic
electromagnetic dynamics, which might alter the present predictions.

**Publications:**

Z. Lin, S. Ethier, T. S. Hahm, and W. M. Tang, "Size scaling of
turbulent transport in magnetically confined plasmas," Phys. Rev. Lett.
**88**, 195004 (2002).

**Funding:**

DOE Office of Fusion Energy Sciences, SciDAC.

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*Figure 2*. Full torus particle-in-cell gyrokinetic simulations (GTC) of
turbulent transport scaling. (a) The granular structures represent the
scales of the turbulence in a typical plasma which need to be included
in realistic plasma simulations. (b) The horizontal axis expresses the
plasma size, and the point at 1000 represents ITER's size. The vertical
axis represents the thermal diffusion, or heat loss.