Positive and negative effective mass of relativistic particles in oscillatory and static fields

A relativistic particle oscillating in high-frequency and/or static fields can be treated as a quasiparticle with an effective mass $m_{\rm eff}$, which depends on the local parameters of the fields. Both ponderomotive and $\mu\nabla\kern -1pt B$ forces, as well as magnetic drifts, are derived from $m_{\rm eff}=m_{\rm eff} (\mathbf{r}, \dot{\mathbf{r}})$, $\mathbf{r}$ being the coordinate of the oscillation center. The effective mass is not necessarily positive; thus, if a (weak) external force is applied, acceleration in the direction opposite to this force is possible. As an example, adiabatic average dynamics with $m_{\rm eff}>0$ and $m_{\rm eff}<0$ is demonstrated for a wave-driven particle in a dc magnetic field. Different energy states are realized in this case, yielding up to three branches of $m_{\rm eff}$ for a given magnetic moment and parallel velocity.