  It has been recently reported that ultraviolet harmonic vortices can be
produced when a high-power circular-polarized laser pulse travels through a
micro-scale waveguide. However, the harmonic generation quenches typically
after a few tens of microns of propagation, due to the build-up of
electrostatic potential that suppresses the amplitude of the surface wave. Here
we propose to utilize a hollow-cone channel to overcome this obstacle. When
traveling in a cone target, the laser intensity gradually increases, allowing
the surface wave to maintain a high amplitude for a much longer distance. The
harmonic vortices can be produced with very high efficiency. According to
three-dimensional particle-in-cell simulations, the overall efficiency are
boosted by almost one order of magnitude, reaching $>20\%$. It is also found
that using the cone targets can mitigate efficiency decline due to pre-heating
of plasma by laser prepulse. The proposed scheme paves the way to the
development of powerful optical vortices sources in the extreme ultraviolet
regime - an area of significant fundamental and applied physics potential.
