Difference between the 2F and the 1F wave numbers relative to the 2F wave number. Left column: Calculations for the real part of k_z; right column: same calculations, but for the imaginary part of k_z. Only the upwards fast mode solution is represented. Solid black line: differences computed asumming the 1F model described in Section 2.2; dashed red line: differences computed extending the 1F for accounting the contributions of q_w and G; dashed-dotted red line: differences computed extending the 1F for accounting the contributions of q_w alone and G alone. The vertical dashed line indicates the equipartition layer β_plasma = 1.