Theoretical investigations of ion differential streaming in the solar wind have been done for a long time. McKenzie et al. (1979), McKenzie and Marsch (1982), and Isenberg and Hollweg (1983) described a mechanism for ion acceleration by waves, and Marsch et al. (1982a) developed the first semi-kinetic models to explain these phenomena. Isenberg (1984a,b) first studied the thermal effects on the cyclotron-wave dispersion relation in a proton-alpha-particle plasma. McKenzie (1994) investigated the interaction between Alfvén waves and a multi-component plasma, including ion differential streaming. More recently, Gomberoff et al. (1996a,b,c) investigated in detail the subtleties of the dispersion relations of ion-cyclotron waves in a multi-component solar wind containing minor ions.
The preferential heating and acceleration of minor ions in the solar wind is an issue of ongoing research, in particular through theory and simulation. Ion resonant acceleration and heating by dispersive ion cyclotron waves was studied by Hu and Habbal (1999). Gary et al. (2000c) and Li and Habbal (2000) investigated the alpha/proton magnetosonic instability in the fast solar wind. Helium ion acceleration and heating by Alfvén/cyclotron fluctuations in the solar wind was studied by Gary et al. (2001a). Facing new SOHO observations, the resonant heating and acceleration of heavy ions in coronal holes driven by cyclotron resonant spectra was addressed and simulated by Ofman et al. (2002). Gary et al. (2003) looked into the consequences of proton and alpha anisotropies in the solar wind by means of numerical hybrid simulations, following earlier work by Winske and Omidi (1992) on the electromagnetic ion/ion cyclotron instability. Dubinin et al. (2005) showed that the ion differential speed can be understood as the result of a non-linear ion-wave equilibrium.
Electromagnetic heavy-ion/proton instabilities driven by the relative velocity of two distinct ion components were generally studied by means of linear theory and non-linear numerical hybrid simulation by Wang et al. (1999). Linear dispersion theory (see again the discussion in the previous Subsection 6.5) predicts that the fastest growing mode is the right hand polarised proton beam instability. The simulations provided scaling relations for the magnetic field fluctuation level at saturation and the maximum growth rate, results which are also relevant for the solar corona and solar wind. Alpha/proton streaming instabilities in the solar wind were further studied by Gary et al. (2000d) by help of bydrid simulations, which allowed them to derive wave-particle scattering rates of the two components. This scattering reduces and limits the differential speed and heats the alpha particles more strongly than the protons perpendicular to the field.
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