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Cylindrical implosions driven by intense heavy ions beams should beinstrumental in a near future to study High Energy Density Matter. By rotatingthe beam by means of a high frequency wobbler, it should be possible to depositenergy in the outer layers of a cylinder, compressing the material deposited inits core. The beam temporal profile should however generate an inevitableirradiation asymmetry likely to feed the Rayleigh-Taylor instability (RTI)during the implosion phase. In this paper, we compute the Fourier components ofthe target irradiation in order to make the junction with previous works on RTIperformed in this setting. Implementing a 1D and 2D beam models, we find thesecomponents can be expressed exactly in terms of the Fourier transform of thetemporal beam profile. If $T$ is the beam duration and $\Omega$ its rotationfrequency, "magic products" $\Omega T$ can be identified which cancel the firstharmonic of the deposited density, resulting in an improved irradiationsymmetry.

Harmonic analysis of irradiation asymmetry for cylindrical implosions driven by high-frequency rotating ion beams