Double-cross instability in nonuniform plasma

One fascinating characteristic associated with the presence of an energetic minority-ion population in a background magnetized plasma is that, if the population is inverted, it can support negative-energy waves (e.g., negative-energy energetic-minority-ion Bernstein waves supported by an inverted alpha-population in tokamak plasmas). In our continuing study of negative-energy waves in nonuniform magnetized plasmas, we investigate a new type of linear absolute instability associated with the resonant interaction between a negative-energy wave and a positive-energy wave in a nonuniform plasma. According to the standard scenario for a linear convective instability associated with the resonant interaction between a negative-energy wave and a positive-energy wave in a one-dimensional background plasma, a negative-energy ray crosses transversely the dispersion surface of a positive-energy wave and resonantly transfers some of its action to create a positive-energy ray. Because of background plasma nonuniformity, however, the two waves interact resonantly only during a finite time interval and, consequently, this linear instability is convective. In this work, we investigate a new scenario for a linear absolute instability in which the negative-energy ray crosses the dispersion surface of the positive-energy wave twice. The new ray topology allows repeated resonant interactions between the two waves if they experience constructive interference at each crossing. This double-cross absolute instability is shown to have a threshold which depends on the area enclosed between the two dispersion curves and the strength of the wave coupling. Numerical and analytical descriptions of this new absolute instability will be presented as well as a discussion of its possible significance in magnetic fusion research