  Kinetic Alfv\'en Waves (KAWs) are generated in magnetized space and
laboratory plasmas due to a continuous shear Alfv\'en wave (SAW) spectrum and,
unlike SAWs, are characterized by microscale perpendicular structures of the
order of the thermal ion Larmor radius. This has important consequences on
heating, acceleration and transport processes connected with KAWs.
Historically, KAWs generation by mode conversion of SAWs in laboratory plasmas
and their strong damping/absorption right after SAW mode conversion have been
investigated for plasma heating. Here, we focus on the opposite limit: a mode
converted KAW weakly absorbed in a periodic magnetized plasma cylinder. We show
that a KAW may be excited as resonant cavity mode in the region between the
magnetic axis and the SAW resonant layer generated externally by an antenna
launcher; this process is qualitatively similar to mode converted electron
Bernstein waves. In this way, large amplitude KAWs may be generated time
asymptotically with relatively small coupled antenna power. This case has
little or no relevance for plasma heating but interesting nonlinear
implications for plasma equilibrium. In particular, we demonstrate that KAWs
may generate convective cells (CCs) by modulational instability, that a
consequence of plasma nonuniformity is the azimuthal symmetry breaking due to
plasma diamagnetic effects, that the modulational instability growth rate is
enhanced over the corresponding uniform plasma limit, that the unstable
parameter space is extended, and that the cylindrical geometry causes a complex
interplay between nonlinearity and nonuniformity. As a result, we show that it
is possible to control the CC radial structures and the corresponding parallel
electric field generation not only by means of the antenna frequency but also
by fine tuning of its amplitude.
