Top: Surface plots for the period of longitudinal oscillations under model M₁ (left, given by Equation (4)) and model M₂ (right, given by Equation (8)) as a function of particle density and magnetic field strength. Bottom: Cuts along a given value of magnetic field strength (left, B = 50 G) and particle density (right, n = 10¹⁰ cm⁻³). The solutions have been computed on a uniform 2D grid with N_n = N_B = 800 points.