A square electrostatic rainbow lens: Catastrophic ion beam focusing

Focusing properties of a square electrostatic rainbow lens

“…As we have said above, in our previous study [1], we approximated the electrodes of the lens with the uniformly charged infinite wires and assumed that the components of the electric field before and after the lens were equal to zero. Inside the lens, the transverse components of the electric field depended only on x and y and its longitudinal component was equal to zero.…”

“…This study is a continuation of our previous study [1]. The initial proton kinetic energy will also be E 0 ¼10 kV.…”

“…As in our previous study [1], we are going to apply to the problem in question the theory of crystal rainbows [4][5][6][7][8]. It is assumed that the proton propagation angle inside the lens and in the drift space after it remains small.…”

“…Such an ion beam optical element was recently studied for the first time by Nešković et al [1]. They analyzed the transmission of protons of the initial kinetic energy of 10 kV through the lens.…”

“…In our previous study [1], we explored the spatial distributions of transmitted protons inside the lens and in the drift space after it. It was demonstrated that the evolution of the spatial distribution was determined by the evolution of the corresponding rainbow pattern.…”