μ μ is a constant of the motion to all orders in an expansion in ω ω / ω ω c , where ω ω is the rate of any changes experienced by the particle, e.g., due to collisions or due to temporal or spatial variations in the magnetic field. Consequently, the magnetic moment remains nearly constant even for changes at rates approaching the gyrofrequency. When μ μ is constant, the perpendicular particle energy is proportional to B , so the particles can be heated by increasing B , but this is a "one-shot" deal because the field cannot be increased indefinitely. It finds applications in magnetic mirrors and magnetic bottles.