  Electron cyclotron harmonic (ECH) waves play a significant role in driving
the diffuse aurora, which constitutes more than 75% of the particle energy
input into the ionosphere. ECH waves in magnetospheric plasmas have long been
thought to be excited predominantly by the loss cone anisotropy (velocity-space
gradients) that arises naturally in a planetary dipole field. Recent THEMIS
observations, however, indicate that an electron beam can also excite such
waves in Earth's magnetotail. The ambient and beam plasma conditions under
which electron beam excitation can take place are unknown. Knowledge of such
conditions would allow us to further explore the relative contribution of this
excitation mechanism to ECH wave scattering of magnetospheric electrons at
Earth and the outer planets. Using the hot plasma dispersion relation, we
address the nature of beam-driven ECH waves and conduct a comprehensive
parametric survey of this instability. We find that growth is provided by beam
electron cyclotron resonances of both first and higher orders. We also find
that these waves are unstable under a wide range of plasma conditions. The
growth rate increases with beam density, beam velocity, and hot electron
temperature; it decreases with increasing beam temperature and beam temperature
anisotropy, hot electron density, and cold electron density and temperature.
Such conditions abound in Earth's magnetotail, where magnetospheric electrons
heated by earthward convection and magnetic reconnection coexist with colder
ionospheric electrons.
