Imprint reduction in rotating heavy ions beam energy deposition

The compression of a cylindrical target by a rotating heavy ions beam is contemplated in certain inertial fusion schemes or in heavy density matter experiments. Because the beam has its proper temporal profile, the energy deposition is asymmetric and leaves an imprint which can have important consequences for the rest of the process. In this paper, the Fourier components of the deposited ion density are computed exactly in terms of the beam temporal profile and its rotation frequency Ω. We show that for any beam profile of duration T, there exist an infinite number of values of ΩT canceling exactly any given harmonic. For the particular case of a parabolic profile, we find possible to cancel exactly the first harmonic and nearly cancel every other odd harmonics. In such case, the imprint amplitude is divided by 4 without any increase of Ω