Self-consistent space charge tracking method based on lie transform
In this paper we propose to describe the self-force of a particles beam, known as space charge, as a Hamiltonian term dependent on the distribution of the particles' coordinates: Hsc ≡ Hsc(ρ(x, y, z)). This Hamiltonian is then used, together with the kinetic component Hk in a Lie transform to generate a transport map by e-L:Hk+Hsc: where the Lie operator: Hk + Hsc : is defined according to the Dra
