  We investigate the possibility of stochastic acceleration of background
low-energy electrons by turbulent plasma waves. We consider the resonant
interaction of the charged particles with all branches of the transverse plasma
waves propagating parallel to a uniform magnetic field. Numerical results and
asymptotic analytic solutions valid at non-relativistic and ultra-relativistic
energies are obtained for the acceleration and scattering times of electrons.
These times have a strong dependence on plasma parameter alpha = Omega_pe /
Omega_e (the ratio of electron plasma frequency to electron gyrofrequency) and
on the spectral index of plasma turbulence. It is shown that particles with
energies above certain critical value may interact with higher frequency
electromagnetic plasma waves and this interaction is allowed only in plasmas
with alpha < 1. We show that for non-relativistic and semi-relativistic
electrons in low-alpha plasmas the ratio of the acceleration time to the
scattering time can be less than unity for a wide range of energies. From this
we conclude that the transport equation derived for cosmic rays which requires
this ratio to be much larger than one is not applicable at these energies. An
approximate "critical" value of particle energy above which the dynamics of
charged particles may be described by this transport equation is determined as
a function of plasma parameters. We propose new transport equation for the
opposite limit (energies less than this critical value) when the acceleration
rate is much faster than the pitch angle scattering rate. This equation is
needed to describe the electron dynamics in plasmas with alpha <= 0.1.
