  Magnetization loss on a twisted superconducting (SC) tape in a ramped
magnetic field is theoretically investigated through the use of a power law for
the electric field--current density characteristics and a sheet current
approximation. First, the Maxwell equation in a helicoidal coordinate system is
derived to model a twisted SC tape, taking account of the response to the
perpendicular field component in the steady state. We show that a loosely
twisted tape can be viewed as the sum of a portion of tilted flat tapes of
infinite length by examining the perpendicular field distribution on a twisted
tape. The analytic formulae for both magnetization and loss power in the tilted
flat tape approximation are verified based on the analytic solution of the
reduced Maxwell equation in the loosely twisted tape limit of $L_{\rm
p}\rightarrow \infty$ with the twist pitch length $L_{\rm p}$. These analytic
formulae show that both magnetization and loss power decrease by a factor of
$B(1+1/2n,1/2)/\pi$ (where $B$ is the beta function) for an arbitrary power of
SC nonlinear resistivity $n$, compared with those in a flat tape of infinite
length. Finally, the effect of the field-angle dependence of the critical
current density $J_{\rm c}$ on the loss power is investigated, and we
demonstrate that it is possible to obtain an approximate estimate of the loss
power value via $J_{\rm c}$ in an applied magnetic field perpendicular to the
tape surface (i.e., parallel to the $c$ axis).
