Gyrotropic guiding-center fluid theory for the turbulent heating of magnetospheric ions in downward Birkeland current regions. II

A new fluid theory in the guiding-center and gyrotropic approximation derivable from the ensemble-averaged Vlasov-Maxwell equations that included the effect of wave-particle interactions for weakly turbulent, weakly inhomogeneous, nonuniformly magnetized plasma was recently given by Jasperse, Basu, Lund, and Bouhram [Phys. Plasmas 13, 072903 (2006)]. In that theory, the particles are transported in one spatial dimension (the distance s along the magnetic field) but the turbulence is two-dimensional. In this paper, which is intended as a sequel, the above theory is used for quasisteady conditions to find: (1) a new formula for the perpendicular ion-heating rate per unit volume Ẇi⊥(s), where Ẇi⊥(s) decreases for large s by what we call the “finite ion gyroradius effect”; and (2) a new formula for the perpendicular ion temperature at low altitudes, Ti⊥(s). Parametrized calculations for Ti⊥(s) are also given.