The study explores the dynamics of relativistic particles in an ion–cyclotron trap under ultrashort laser pulses with intensities around 1022 W/cm2. The focus is on the trajectory, speed, momentum, and energy of the particles in the ion trap, aiming to determine the optimal electric and magnetic field intensities for effective confinement. The effects of Gaussian laser pulses and the ion trap field are analyzed in the context of achieving cyclotron autoresonance. Numerical solutions of relativistic particle motion, including methods such as Boris, GIGI2, and Runge–Kutta, are compared. The results demonstrate the complementary nature of analytical solutions in Lobachevskian geometry and numerical solutions in Euclidean geometry.
Akintsov et al. (Fri,) studied this question.