  It is shown that in low-beta, weakly collisional plasmas, such as the solar
corona, some instances of the solar wind, the aurora, inner regions of
accretion discs, their coronae, and some laboratory plasmas, Alfv\'enic
fluctuations produce no ion heating within the gyrokinetic approximation, i.e.,
as long as their amplitudes (at the Larmor scale) are small and their
frequencies stay below the ion Larmor frequency (even as their spatial scales
can be above or below the ion Larmor scale). Thus, all low-frequency ion
heating in such plasmas is due to compressive fluctuations ("slow modes").
Because these fluctuations energetically decouple from the Alfv\'enic ones
already in the inertial range, the above conclusion means that the energy
partition between ions and electrons in low-beta plasmas is decided at the
outer scale, where turbulence is launched, and can be determined from
magnetohydrodynamic (MHD) models of the relevant astrophysical systems. Any
additional ion heating must come from non-gyrokinetic mechanisms such as
cyclotron heating or the stochastic heating owing to distortions of ions'
Larmor orbits. An exception to these conclusions occurs in the Hall limit,
i.e., when the ratio of the ion to electron temperatures is as low as the ion
beta (equivalently, the electron beta is order unity). In this regime, slow
modes couple to Alfv\'enic ones well above the Larmor scale (viz., at the ion
inertial or ion sound scale), so the Alfv\'enic and compressive cascades join
and then separate again into two cascades of fluctuations that linearly
resemble kinetic Alfv\'en and ion cyclotron waves, with the former heating
electrons and the latter ions. The two cascades are shown to decouple, scalings
for them are derived, and it is argued physically that the two species will be
heated by them at approximately equal rates.
