Toward a self‐consistent treatment of the cyclotron wave heating and acceleration of the solar wind plasma

Abstract

[1] We have developed a steady state two-fluid description of the radial solar wind expansion close to the coronal base. The model is formulated self-consistently with respect to the radial evolution of turbulence by supplementing the moment equations of the plasma with an equation describing the radial evolution of the Alfvén wave power as originally suggested by Tu et al. [1984]. We assume that there is sufficient wave power in the ion-cyclotron frequency range and determine the resulting acceleration and heating rates of the thermal plasma in the corona and interplanetary space. In improvement of earlier models of the nonlocal dynamics of the expanding corona, the dissipation frequency is determined self-consistently from the ion-cyclotron damping rate. After demonstrating that the time-independent modeling can correctly reproduce the solutions obtained with (in the above sense) non-self-consistent models, the significance of the selfconsistent treatment is pointed out. The new solutions are studied in detail, and their implications for the transport of solar energetic particles are discussed.

The Coupled Evolution of Electrons and Ions in Coronal Mass Ejection-Driven Shocks

“…There are more sophisticated one-dimensional treatments of the solar corona (e.g., Tu & Marsch 1997;Laitinen et al 2003;Vainio et al 2003;Suzuki 2006;Cranmer 2010) that include advanced treatment of Alfvén waves, heat conduction, and radiation. For our CME simulations, we make use of a coronal model that addresses the same physical processes in fully 3D geometry, the two-temperature coronal model developed by van der Holst et al (2010), which describes the coronal plasma as a magnetized proton-electron neutral fluid with a single velocity.…”

A simple analytical expression for the power spectrum of cascading Alfvén waves in the solar wind

“…A conventional way of choosing the dissipation frequency is to take it as a fixed fraction of the local ion cyclotron frequency. We, however, use a recent model (Vainio & Laitinen 2001;Laitinen et al 2003), which incorporates the thermal dependence of cyclotron resonance by calculating the dissipation frequency from the quasilinear damping rate, γ( f, r), of the Alfvén waves as V/2γ( f H , r) = r − r , i.e., equating the damping length with the distance traveled by the wave. The proton temperature, T p , is modeled using a fit to the results of Tu & Marsch (1997) …”

“…Out of the many proposed candidates few have survived and among those the most promising one is the damping of ion-cyclotron waves as is discussed, along with an extended review of related work, by Hollweg & Isenberg (2002). Laitinen et al (2003) have recently discussed various approaches employed for an explicit incorporation of the process of ion-cyclotron damping into kinetic (e.g. Isenberg 2001), semi-kinetic (e.g.…”

“…Laitinen et al (2003) classified the various corresponding modeling attempts by distinguishing between ad-hoc, phenomenological, and consistent heating functions. The ad-hoc heating functions, originally introduced by Hartle & Barnes (1970), are formulated without explicitly specifying a physical process and do not depend on the plasma parameters.…”

4π Models of CMEs and ICMEs (Invited Review)

“…This formalism has been successfully applied to purely radial models of the quiet-Sun solar wind (Laitinen, Fichtner, and Vainio, 2003), and appears to be a promising alternative to the phenomenological heating functions discussed in Section 2.5, although the extension to the generally more complicated magnetic field structures encountered in symmetry-free CME simulations is clearly non-trivial. First results obtained with a wave-heated solar wind model (albeit relying on the scalar wave energy densities ε ± parallel (+) and anti-parallel (−) to B rather than the full spectral information) have been presented by van der Holst et al (2010).…”