Figure 2

The distributions of electric potential ϕ induced in a thin film due to (a) the adiabatic field (9) and (b) the non-adiabatic field (10), calculated by solving the Poisson equation (11) numerically, where the steady motion of eight identical bubbles along the x direction is assumed.

The profile of each bubble is given by Eqs. (1) and (2), with R = 50 nm, Δ = 2 nm, Q = 1, S = 1 and ψ₀ = π/2. The other parameters assumed here are γ = 1.76 × 10¹¹ T⁻¹ s⁻¹, α = 0.02, , P = 0.5 and the side lengths are 900 nm. The field gradient makes an angle 75.9° to the x axis with its strength |R∇H_z| = 10 Oe.