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# Resonant Interactions Between Protons and Oblique Alfv\'en/Ion-Cyclotron Waves

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### Abstract

Resonant interactions between ions and Alfv\'en/ion-cyclotron (A/IC) waves may play an important role in the heating and acceleration of the fast solar wind. Although such interactions have been studied extensively for "parallel" waves, whose wave vectors $${\bf k}$$ are aligned with the background magnetic field $${\bf B}_0$$, much less is known about interactions between ions and oblique A/IC waves, for which the angle $$\theta$$ between $${\bf k}$$ and $${\bf B}_0$$ is nonzero. In this paper, we present new numerical results on resonant cyclotron interactions between protons and oblique A/IC waves in collisionless low-beta plasmas such as the solar corona. We find that if some mechanism generates oblique high-frequency A/IC waves, then these waves initially modify the proton distribution function in such a way that it becomes unstable to parallel waves. Parallel waves are then amplified to the point that they dominate the wave energy at the large parallel wave numbers at which the waves resonate with the particles. Pitch-angle scattering by these waves then causes the plasma to evolve towards a state in which the proton distribution is constant along a particular set of nested "scattering surfaces" in velocity space, whose shapes have been calculated previously. As the distribution function approaches this state, the imaginary part of the frequency of parallel A/IC waves drops continuously towards zero, but oblique waves continue to undergo cyclotron damping while simultaneously causing protons to diffuse across these kinetic shells to higher energies. We conclude that oblique A/IC waves can be more effective at heating protons than parallel A/IC waves, because for oblique waves the plasma does not relax towards a state in which proton damping of oblique A/IC waves ceases.

### Most cited references3

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### Limit on stably trapped particle fluxes

(1966)
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### Resonant particle instabilities in a uniform magnetic field

(1967)
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### Weak compressible magnetohydrodynamic turbulence in the solar corona

(2005)
This Letter presents a calculation of the power spectra of weakly turbulent Alfven waves and fast magnetosonic waves ("fast waves") in low-beta plasmas. It is shown that three-wave interactions transfer energy to high-frequency fast waves and, to a lesser extent, high-frequency Alfven waves. MHD turbulence is thus a promising mechanism for producing the high-frequency waves needed to explain the anisotropic heating of minor ions in the solar corona.
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### Author and article information

###### Journal
28 December 2009
10.1063/1.3395966
0912.5184