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A simple nonlinear equation is derived to describe the pseudo-three-dimensional dynamics of a nonuniform magnetized plasma with Te≫Ti by taking into account the three-dimensional electron, but two-dimensional ion dynamics in the direction perpendicular to B0. The equation bears a close resemblance to the two-dimensional Navier–Stokes equation. A stationary spectrum in the frequency range of drift waves is obtained using this equation by assuming a coexisting large amplitude long wavelength mode. The ω-integrated k spectrum is given by k1.8(1+k2)−2.2, while the width of the frequency spectrum is proportional to k3(1+k2)−1, where k is normalized by cs/ωci. The result compares well with the recently observed spectrum in the ATC tokamak.
Hasegawa et al. (Sun,) studied this question.
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