Relative error in the magnetic moment with analytically given fields (left-hand panel) and interpolated fields (right-hand panel) for one cycle in 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. In the left-hand panel, for analytic fields (see the dashed blue line), the error already slightly differs after one cycle, eventually growing unboundedly until the particle escapes after a few cycles. The errors with interpolated fields (right-hand panel) are nearly identical for all methods, and much worse than those for analytical fields.