  We aim at studying the effect of radial motions on the spectrum emitted by
moving prominences in the helium resonance lines and at facilitating the
interpretation of observations, in order to improve our understanding of these
dynamic structures. We develop our non-local thermodynamic equilibrium
radiative transfer code formerly used for the study of quiescent prominences.
The new numerical code is now able to solve the statistical equilibrium and
radiative transfer equations in the non-static case by using velocity-dependent
boundary conditions for the solution of the radiative transfer problem. This
first study investigates the effects of different physical conditions
(temperature, pressure, geometrical thickness) on the emergent helium
radiation. The motion of the prominence plasma induces a Doppler dimming effect
on the resonance lines of He I and He II. The velocity effects are particularly
important for the He II 304 A line as it is mostly formed by resonant diffusion
of incident radiation under prominence conditions. The He I resonance lines at
584 and 537 A also show some sensitivity to the motion of the plasma, all the
more when thermal emission is not too important in these lines. We also show
that it is necessary to consider partial redistribution in frequency for the
scattering of the incident radiation. This set of helium lines offers strong
diagnostic possibilities that can be exploited with the SOHO spectrometers and
with the EIS spectrometer on board the Hinode satellite. The addition of other
helium lines and of lines from other elements (in particular hydrogen) in the
diagnostics will further enhance the strength of the method.
