Particle trajectory in a constant magnetic field with radiation reaction. Panel a: trajectory of the simulated particle (in blue) compared to theoretical positions (in orange) for τ₀ ω_B = 10⁻⁵, γ₀ = 10⁴, initial speed along y. Panel b: relative error as a function of the proper time step dτ for the simulations in blue points, compared to the first order error expectations in red solid line.