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

TL;DR

This paper explores how classical particles in high-frequency or static fields exhibit an effective mass that can be positive or negative, influencing their dynamics and leading to multiple energy states.

Contribution

It introduces the concept of effective mass derived from the averaged Lagrangian for particles in oscillatory and static fields, including cases with negative effective mass.

Findings

Effective mass can be negative, causing backward acceleration.

Multiple energy states and branches of effective mass are possible.

Relativistic forces are derived from the effective mass dependence.

Abstract

A classical particle oscillating in an arbitrary high-frequency or static field effectively exhibits a modified rest mass m_eff derived from the particle averaged Lagrangian. Relativistic ponderomotive and diamagnetic forces, as well as magnetic drifts, are obtained from the m_eff dependence on the guiding center location and velocity. The effective mass is not necessarily positive and can result in backward acceleration when an additional perturbation force is applied. As an example, adiabatic dynamics with m_|| > 0 and m_|| < 0 is demonstrated for a wave-driven particle along a dc magnetic field, m_|| being the effective longitudinal mass derived from m_eff. Multiple energy states are realized in this case, yielding up to three branches of m_|| for a given magnetic moment and parallel velocity.