Left column: Failing perpendicular (a) and fulfilled parallel (c) energy conservation for the test particle evolving in the Alfvén-wave test case. Right column: (b) Fixed perpendicular energy after the new GCA implementation and (d) effect of the new equation on the magnetic moment evolution in time. μ_const is the constant value of the magnetic moment in the standard GCA evolution, while μ is the varying value in the current new energy-conserving GCA implementation.