Relative error in the Lorentz factor with analytically given fields (left-hand panel) and interpolated fields (right-hand panel), for 10 cycles through the magnetic bottle. The error for the Vay scheme in interpolated fields and time step ﹩{\rm{\Delta }}t={10}^{-8}﹩ is not shown in the right-hand panel because the particle’s magnetic moment is not conserved due to numerical errors, and the particle escapes the magnetic bottle immediately.