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

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.

Axiomatic geometrical optics, Abraham-Minkowski controversy, and photon properties derived classically

“…(77) in terms of Lorentz-invariant proper parameters of the medium [141]. Since Φ that enters here depends on the wave intensity, it must be gauge-invariant; thus, being (minus) the interaction Lagrangian of a single element, it transforms as Φ = Φ ′ /γ [142], with primes in this section (Sec. V) denoting the medium rest frame, and γ = (1 − v 2 /c 2 ) −1/2 .…”

Supra-bubble regime for laser acceleration of cold electron beams in tenuous plasma

“…Also, Q = P ⊥ /(mc) is the normalized canonical momentum transverse to the direction of the pulse propagation; a = eA/(mc 2 ) is the laser parameter (the term proportional to a 2 is due to the laser ponderomotive potential [20,[29][30][31][32][33][34]); Π is a constant, which is determined by initial conditions and, for a particle outside the pulse, equals…”

Axiomatic Geometrical Optics, Abraham-Minkowski Controversy, and Photon Properties Derived Classically

“…(77) in terms of Lorentz-invariant proper parameters of the medium [138]. Since Φ that enters here depends on the wave intensity, it must be gauge-invariant; thus, being (minus) the interaction Lagrangian of a single element, it transforms as Φ = Φ /γ [139], with primes in this section (Sec. V) denoting the medium rest frame, and γ = (1 − v 2 /c 2 ) −1/2 .…”