  Runaway electron distributions are strongly anisotropic in velocity space.
This anisotropy is a source of free energy that may destabilize electromagnetic
waves through a resonant interaction between the waves and the energetic
electrons. In this work we investigate the high-frequency electromagnetic waves
that are destabilized by runaway electron beams when the electric field is
close to the critical field for runaway acceleration. Using a runaway electron
distribution appropriate for the near-critical case we calculate the linear
instability growth rate of these waves and conclude that the obliquely
propagating whistler waves are most unstable. We show that the frequencies,
wave numbers and propagation angles of the most unstable waves depend strongly
on the magnetic field. Taking into account collisional and convective damping
of the waves, we determine the number density of runaways that is required to
destabilize the waves and show its parametric dependences.
