  Turbulent dissipation is considered a main source of heating and acceleration
in cosmological plasmas. The alternating current Joule-like term,
$\langle\delta j \cdot \delta E\rangle$, is used to measure the energy transfer
between electromagnetic (EM) fields and particles. Because the electric field
depends on the reference frame, in which frame to calculate $\langle\delta
j\cdot \delta E\rangle$ is an important issue. We compute the scale-dependent
energy transfer rate spectrum in wavevector space, and investigate the
electric-field fluctuations in two reference frames: $\delta E$ in the mean
bulk flow frame and $\delta E'$ in the local bulk flow frame (non-inertial
reference frame). Considering Alfv\'enic waves, we find that $\langle\delta
j\cdot\delta E^\prime\rangle$, which neglects the contribution of work done by
the ion inertial force, is not consistent with the magnetic field energy
damping rate ($2\gamma \delta B^2$) according to linear Maxwell-Vlasov theory,
while $\langle\delta j\cdot \delta E\rangle$ is exactly the same as $2\gamma
\delta B^2$ in wavenumber space $(k_\parallel, k_\perp)$, where $\gamma$ is the
linear damping rate. Under typical conditions of solar wind at 1 au, we find in
our theoretical calculation that the field energy is mainly converted into
proton kinetic energy leaving the residual minor portion for electrons.
Although the electrons gain energy in the direction perpendicular to the mean
magnetic field, they return a significant fraction of their kinetic energy in
the parallel direction. Magnetic-field fluctuations can transfer particle
energy between the parallel and perpendicular degrees of freedom. Therefore,
$\langle\delta j_\parallel\cdot \delta E_\parallel\rangle$ and $\langle\delta
j_\perp\cdot \delta E_\perp\rangle$ cannot solely describe the energy transfer
in parallel direction and perpendicular direction, respectively.
