Upper plot (a): x−z cut (the front plane) and the isosurface (behind the plane) of the electron energy at t = 1500 Ω⁻¹ in the 3D simulation. Upper right plots: (b) corresponding picture on the y−z plane at x = 0, (c): contour on the x−y plane at z = 960. The parameters are B_y/B₀ = 0.1, B_x/B₀ = 0.02, B₀ = 10⁻³ T, and E₀ = 250 V m⁻¹. Bottom panel (d): isosurface of the proton energy in the whole simulation domain including the x−z cut at y = 0 (Parameters and more details are explained in the next Sect. 3.2.1).