5.3 Resonant wave-particle interactions

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Figure 12: Left: The proton cyclotron dissipation wave number for parallel Alfvén-cyclotron waves as a function of βp. The solid line represents kdlp, and the dashed line represents kdrp, where the thermal proton gyroradius, r = v ∕ Ω p p p, and the proton inertial length, l = c∕ω = V ∕Ω p p A p, are used for normalization, and kd is the dissipation wave vector. Right: The damping rate divided by the real frequency, γ∕ω, of the oblique Alfvén-cyclotron waves as a function of the perpendicular wave number for three values of the electron βe as labelled. Here k∥ = kd∕3 and − 0.01 ≤ γ∕Ωp ≤ 0. Note the increasing damping, leading to oblique wave dissipation, with growing electron temperature, i.e. with increasing β e (after Gary and Borovsky, 2004Jump To The Next Citation Point).

For the solar wind, the dispersion relations like (43View Equation) or (41View Equation) can be evaluated by using VDFs obtained from either measurements or models. The involved dielectric constants are functionals of f(w ), which might, for example when being non-Maxwellian, contain free energy for wave excitation. If the growth rate γ(k) > 0, then a micro-instability occurs. Differently shaped VDFs can thus lead to wave emission and absorption, and as a result to a depletion or growth of the electromagnetic field.

In this process the fluctuations will be excited or damped through resonant particles, which may be either in Landau resonance, ω (k ) − k ⋅ v = 0, or in cyclotron resonance, with ω (k) − k ⋅ v = ± Ωj, in which the Doppler-shifted frequency matches the particle’s gyrofrequency. For general considerations see the books of Stix (1992Jump To The Next Citation Point) and Gary (1993Jump To The Next Citation Point). A plasma composed of non-drifting Maxwellian VDFs will always lead to wave damping and absorption. Free energy for wave excitation requires thermal anisotropies, beams, differential motions, or skewed VDFs. Most of the stability analyses which were carried out for the solar wind were based on idealised model distributions, such as drifting bi-Maxwellians or Lorentzians with high-energy tails. However, sometimes also the measured VDFs were implemented, e.g., by Dum et al. (1980Jump To The Next Citation Point) or Leubner and Viñas (1986Jump To The Next Citation Point), in the numerical dispersion codes to diagnose the stability of the measured VDFs and predict the possible wave activity caused by the non-thermal features.

Resonant wave-particle processes in the inhomogeneous corona, as compared to the locally uniform solar wind, are complicated by the non-uniformity of the coronal magnetic field and radial variation of other plasma parameters. In a series of papers Hollweg (1999a,b,c) looked into these complications and did some detailed kinetic studies of ion resonances with cyclotron waves in coronal holes. In addition, Hollweg and Markovskii (2002) discussed the behaviour of cyclotron resonances when the waves propagate obliquely to the magnetic field.

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