  We present a model of magnetohydrodynamic (MHD) turbulence in the extended
solar corona that contains the effects of collisionless dissipation and
anisotropic particle heating. Measurements made by UVCS/SOHO have revived
interest in the idea that ions are energized by the dissipation of ion
cyclotron resonant waves, but such high-frequency (i.e., small wavelength)
fluctuations have not been observed. A turbulent cascade is one possible way of
generating small-scale fluctuations from a pre-existing population of
low-frequency MHD waves. We model this cascade as a combination of advection
and diffusion in wavenumber space. The dominant spectral transfer occurs in the
direction perpendicular to the background magnetic field. As expected from
earlier models, this leads to a highly anisotropic fluctuation spectrum with a
rapidly decaying tail in parallel wavenumber. The wave power that decays to
high enough frequencies to become ion cyclotron resonant depends on the
relative strengths of advection and diffusion in the cascade. For the most
realistic values of these parameters, though, there is insufficient power to
heat protons and heavy ions. The dominant oblique fluctuations (with dispersion
properties of kinetic Alfven waves) undergo Landau damping, which implies
strong parallel electron heating. We discuss the probable nonlinear evolution
of the electron velocity distributions into parallel beams and discrete
phase-space holes (similar to those seen in the terrestrial magnetosphere)
which can possibly heat protons via stochastic interactions.
