Electromagnetic ion beam instabilities: Growth at cyclotron harmonic wave numbers

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Abstract
The linear theory of electromagnetic ion beam instabilities for arbitrary angles of propagation is studied, with emphasis on the conditions necessary to generate unstable modes at low harmonics of the ion cyclotron resonance condition. The present results extend the analysis of Smith et al. (1985). That paper considered only the plasma parameters at a time during which harmonic wave modes were observed in the earth's foreshock. The parameters of that paper are used as the basis of parametric variations here to establish the range of beam properties which may give rise to observable harmonic spectra. We show that the growth rates of both left‐ and right‐hand cyclotron harmonic instabilities are enhanced by an increase in the beam temperature anisotropy and/or the beam speed. Decreases in the beam density and/or the core ion beta reduce the overall growth of the cyclotron harmonic instabilities but favor the growth of these modes over the growth of the nonresonant instability and thereby enhance the observability of the harmonics.