The dynamics of ion with electrostatic waves in a sheared magnetic field

The interaction between an ion and multiple electrostatic waves propagating perpendicularly to an ambient magnetic field with shear is investigated. Based on the Lie transformation method, with the wave amplitude and the magnetic shear both as the perturbation parameters, the analytical formulas for the reduced Hamiltonian is derived and results are compared with numerical calculations of the complete equations of motion for the case of two on-resonance waves and the case of two off-resonance waves, respectively. It is found that the effect of magnetic shear drastically prevents the acceleration of an ion in both cases. This result will help us to understand the behaviors of ions in a magnetic sheared device, such as tokamak.