Energetic Particle Effects Can Explain the Low Frequency of Alfvin Modes in the DIII-D Tokamak Page: 4 of 18
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in Ref. [5] and an energetic-particle mode (EPM) in Refs. [6], [7], [8]. An extensive database
of frequency measurements from DIII-D was compared with simplified frequency scalings
based on these four theories, but none of the simple models adequately explained all of the
observations [9]. On balance, the data appeared most consistent with the hypothesis that
the instability was an RTAE/EPM, but more detailed comparisons were clearly required.
This work reports the first of such comparisons. A non-perturbative fully kinetic code
HINST [10], which stands for high-n stability code, is used to compute the expected fre-
quency and stability of the RTAE in a typical DIII-D plasma with slightly negative shear
and with unstable "BAE" activity. As we will show, the code successfully finds an unstable
mode with a frequency that is consistent with the measured frequency. The toroidal mode
numbers n of the unstable modes are also close to the experimental observations.
II. EXPERIMENT: DESCRIPTION OF THE INSTABILITY
The case selected for the comparison is a double-null divertor, deuterium plasma that
is heated by 9.5 MW of 76 keV deuterium neutral beams. At the time of interest, the
safety factor profile is weakly reversed (Fig. 1d) and the plasma has entered an ELM-free
H-mode, so the stored energy, neutron rate, and density are rapidly increasing. As shown
in Fig. 1, the central ion temperature is approximately 10 keV and there is an edge pedestal
in the density and temperature profiles. Because the density is still relatively low and the
confinement is high, the classically-expected beam pressure (Fig. ic) is a significant fraction
of the total plasma pressure. Phenomenologically, "BAEs" are often observed in plasmas
with large beam-ion pressure. [9]
Instabilities are observed by a Mirnov coil that is situated about 450 degrees below the
outer midplane (Fig. 3a). Three types of coherent magnetic activity are observed (Fig. 2).
Low frequency (< 20 kHz), low n (n =1-2) modes appear intermittently. A fairly steady
n = 5 mode with a frequency of 90-100 kHz is also seen. Bursts of activity appear between
150-250 kHz (Fig. 3c). Virtually all of the bursts have a dominant n = 4 or n = 5 mode2
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Gorelenkov, N. N. & Heidbrink, W. W. Energetic Particle Effects Can Explain the Low Frequency of Alfvin Modes in the DIII-D Tokamak, report, January 31, 2001; Princeton, New Jersey. (https://digital.library.unt.edu/ark:/67531/metadc722559/m1/4/: accessed April 18, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.