The Radio-Frequency Confinement and Acceleration of Plasmas

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

“…matches the known ponderomotive potential in a dc magnetic field [10,11]. Thus, m eff = m + (µB + Φ B )/c 2 , and…”

“…Let us apply the effective mass formalism to derive ponderomotive forces, starting with those in the nonrelativistic regime [7,10,11,12,94]. Consider a particle oscillating in a high-frequency wave E = −∇ϕ, where…”

“…is known as the ponderomotive potential [7,10,11,12,94], E 0 being the field amplitude; thus m eff = m + Φ/c 2 .…”

“…is the new adiabatic invariant proportional to the action of the particle Larmor rotation at frequency Ω 0 = eB/mc, v osc is the induced oscillatory velocity proportional to E [11,93,95,96], and L osc is proportional to E 2 . Suppose B ≈ẑB(z) [Eq.…”

“…Often, the average forces on a guiding center are then written in terms of effective potentials Ψ, such as ponderomotive [7,10,11,12], diamagnetic [13], or others [8,12]. Yet the applicability of the potential approximation is limited to, at most, nonrelativistic interactions, another drawback being the unphysical difference in fictitious fields −∇Ψ seen by different species.…”