1 - Nuclear Sciences and Applications - IAEA

IAEA-CN-50/E-I-2 529
2. ELECTRON CYCLOTRON HEATING
The results of experiments on rf heating are best described by placing
them in the context of the theory of wave propagation and absorption. In
the electron cyclotron frequency range, wave propagation is limited by
cutoffs or resonances which place upper limits on the density. For the
ordinary mode, the propagation limit is simply the condition wp < u>,
where w is the applied frequency and u>p is the plasma frequency. For
the extraordinary mode at the fundamental frequency, the propagation is
limited by the left-hand cutoff to the condition Wp < u>(o; + fle)(l — njj)
when the power is launched from the high field side, but to nearly zero
density by the right-hand cutoff when the power is launched from the
low field side. Here, fie is the electron cyclotron frequency and n\\ is the
parallel index of refraction. At the second harmonic, the launch can be
either high or low field side, and the density is limited by the right-hand
cutoff to the limit wp < u>(w — ne)(l — n 2 ).
Wave absorption has been summarized by Bornatici [6]. Ordinary
mode (O-mode) absorption is proportional to the density ne for quasiperpendicular
propagation, and second harmonic O-mode damping is
weaker than at the fundamental by the small factor Te/mec 2 . Extraordinary
mode (X-mode) absorption at the fundamental is proportional
to n?,/ne. In order to calculate the expected wave absorption in an experimental
situation, a ray tracing code like TORAY [7] can be used to
integrate the absorption along a ray started at the edge of the plasma,
using measured profiles of electron temperature and density and a measured
magnetic equilibrium. Figure l(a) shows the calculated absorption
for the DIII-D experiments, using 30 rays per antenna to simulate
the radiation pattern. The curves are calculated for a model density
profile ne(r) = n.o[l — (r/a) 2 ] 0-e and an electron temperature profile
Te(r) = Teo[l - {r/a) 2 } 1 - 5 typical of DIII-D experiments.
Comparison of experimental heating efficiency with theory is complicated
by the effect of the heating on global confinement, since it is
difficult to discern between a reduction in absorption and a deterioration
in confinement due to the auxiliary power. An additional factor is
that in divertor discharges in DIII-D, density is constrained to a narrow
range, the limits of which scale in proportion to plasma current. Therefore,
a scan in density over a wide range requires operation at different
currents, which by the Kaye-Goldston L—mode scaling [8] changes the confinement
time. Nevertheless, when the efficiency 77 of the heating process
neATe(0)V r //fecH is plotted, as in Fig. l(b), the nature of the dependence
on density can be seen and compared qualitatively with Fig. l(a). Here,
V is the plasma volume and PECK is the total ECH power incident on the
plasma.
As expected, the measurements shown in Fig. l(b) indicate that the
central heating extends to highest density, above 4 x 10 1B m~ 3 , by use of
the inside launch of the X-mode. For outside launch of the O-mode, the
peak in central heating is at slightly lower density than expected, about