  To reveal the mysterious and still controversial mechanism of high ionization
efficiency during helicon discharges, this work focuses particularly on the
role of second-order derivative in radial density profile, both analytical and
numerically. It is found that: (i) the radially localized potential well that
plays a critical role in resonance power absorption from antenna to plasma is
localized where the second-order derivative vanishes, (ii) the power absorption
increases for positive second-order derivative, decreases for negative
second-order derivative, and maximizes where second-order derivative becomes
zero, (iii) the power absorption decreases near plasma core and increases near
plasma edge when the radial location of vanishing second-order derivative moves
outwards, which is also a process of Trivelpiece-Gould mode overwhelming
helicon mode. These findings can be very interesting for helicon plasma
applications that require certain power distribution or heat flux
configuration, e. g. material processing, which can be controlled by adjusting
the profile and zero-crossing location of second-order radial density gradient.
