Theoretical model of current propagation in a helical coil with varying geometry and screen tube

An analytical model of current propagation in a helical coil with varying geometry is developed. It can be used for post-acceleration and post-focusing of ions produced via laser-driven target normal sheath acceleration and generation of electromagnetic pulses. We calculate the current that propagates in a helical coil and suggest a method for improving its dispersion properties using a screening tube and with pitch and radius variation. The electromagnetic fields calculated with the analytical model are in agreement with particle-in-cell simulations. The model provides insights into the physics of current propagation in helical coils with varying geometries and enables a numerical implementation for rapid proton spectrum computations, which facilitate the design of such coils for future experiments.