Electromagnetic Jekyll and Hyde: Understanding Waves
that Suddenly Change Their Nature

D.B. Batchelor, L.A. Berry, M.D. Carter, E. F. Jaeger, E. D’Azevedo – ORNL
C.K. Phillips, A. Pletzer – PPPL, P.T. Bonoli, J. C. Wright – MIT
D.N. Smithe –Mission Research Corporation, R.W. Harvey – CompX
D.A. D’Ippolito, J.R. Myra Lodestar Research Corporation

Summary

In a magnetized plasma, such as in fusion devices or the Earth’s magnetosphere, several different kinds of waves can exist simultaneously, having very different physical properties. Under the right conditions one wave can quite suddenly convert to another type. Depending on the case, this can be either a great benefit or a problem for the use of waves to heat and control fusion plasmas. Understanding and accurately modeling such behavior is a major computational challenge.

A fascinating property of magnetized plasmas is that at a given frequency, several different kinds of plasma waves can exist with very different wavelength and polarization. If the wave frequency is near the frequency at which plasma ions gyrate around the magnetic field, called the ion cyclotron frequency, there are two very different electromagnetic waves, similar to light waves, the fast magnetosonic wave and the slow ion cyclotron wave. In addition, there is an electrostatic wave, similar to a sound wave, called the ion Bernstein wave. These different types of waves or modes interact very differently with the plasma. We are developing techniques to use the different kinds of interaction to exert control on the hot magnetized plasmas in fusion devices – heating plasma electrons separately from ions, producing highly energetic populations of ions, driving electric currents in the plasma, and forcing plasma flows which in turn affect stability. This is done by injecting high power waves into the plasma, typically in the frequency range of short wave, or FM radio.

A wave launched into a non-uniform plasma can in a short distance completely change its character to another type of wave, a process called mode conversion. In order to study these effects the computer model must have very high resolution to see the small-scale structures that develop, which means that very large computers are needed to solve for the very large number of unknowns in the equations, Also, the computers must be extremely fast in order to obtain the solutions in a reasonable time. We have been studying mode conversion processes in tokamaks using two 2D computer codes – TORIC and AORSA2D. Within our SciDAC project the TORIC code, originally developed at IPP in Germany, was accelerated by orders of magnitude allowing us to increase the spatial resolution sufficiently to solve for the ion Bernstein waves. The All-Orders code AORSA2D, which allows for arbitrarily short wavelength and includes a model for driven plasma flow was developed under the SciDAC project.

The figure shows an example of application of the AORSA2D code to understand the mode conversion process in a fusion experiment at MIT called the Alcator C-mod tokamak. An antenna (not shown) at right launches a long wavelength wave, the fast magnetosonic mode. The figure shows conversion to one type of short wavelength mode propagating to the left near the horizontal mid-line, an ion Bernstein wave. However, we also see conversion to a completely different type of short wavelength mode, the slow ion cyclotron wave, above the mid-line propagating to the left and below the mid-line propagating back to the right. This result is a surprise. The previous expectation was that the conversion would dominantly be to the ion Bernstein wave. An early approximate calculation in one dimension suggested that both types of conversion could, in principle, occur. Although the 1D model gave a qualitative paradigm for understanding the process, itcould not predict how important each mode conversion process would be. The 2D code results give a complete, quantitative picture. Such short-length waves propagating back to the right have recently been seen experimentally on Alcator Cmod. These results are likely to have significant practical consequences because Bernstein waves are absorbed primarily by electrons and are effective at driving current, whereas the slow ion cyclotron wave is absorbed by ions and is much more effective at driving plasma flow and improving the ability of the magnetic field to hold the hot plasma.

We will be working in the future as a collaboration among plasma physicists, applied mathematicians, and computer scientists to develop advanced algorithms that increase the resolution and computational efficiency still further. This will be necessary to study these processes in reactor scale devices such as the International Thermonuclear Experimental Reactor (ITER) project.

These specific studies are directed to fusion applications. However, the process of mode conversion can occur when waves propagate in any non-uniform medium. It is seen in magnetized plasmas in astrophysics, such as in radio wave emission from Jupiter, in the Earth’s magnetosphere and possibly in the solar corona. Mode conversion is important in non-plasma fields such as seismology, and in the theory of Hawking particle flux due to the extremely non-uniform gravitational field near a black hole. We anticipate that physics understanding and numerical techniques developed within our project will have benefits far outside the fusion program.

For further information on this subject contact:
Dr. Donald B. Batchelor, Principal Investigator
Oak Ridge National Laboratory
Phone: (865) 574-1288
batchelordb@ornl.gov

We find that fast, long- wavelength electromagnetic waves launched from the right can be converted to slow electromagnetic ion-cyclotron waves, as well as the previously expected electrostatic ion Bernstein waves

back to project page