Lower-hybrid wave generation in an electron beam of finite transverse dimension

The generation of lower-hybrid waves in an inhomogeneous electron beam is examined. Wave amplitudes are invariably limited by the convective nature of the instability. The self-consistent shear of the magnetic-field geometry due to the beam current is limited to the role of dividing the general problem into separate cases according to the relative orientation of the wave vector and direction of inhomogeneity. Moreover, the limiting case of small shear is smoothly connected to the case where shear is altogether negligible. Estimates of the amplification of lower-hybrid waves propagating across the electron beam are made for the various cases.