Electron distribution functions able to amplify radio waves. (a) In a shell-type distribution, the ∇υ_⊥ positive gradient of the distribution function is located along the inner edge of the distribution (red arrows). The ECM resonance circle leading to amplification is tangent to it and centred at υ_‖0 = 0. (b) In a loss-cone distribution, the loss-cone is a region depleted in electrons, lost by collision with the atmosphere. This region is located below the dashed line, defined by the pitch angle α. The largest positive gradient ∇υ_⊥ of the distribution function (red arrow) is along the edge of the loss-cone, at some resonance velocity υ_r. The ECM resonance circle leading to maximum amplification is tangent to this gradient, and is centred on υ_‖0 = υ_r / cosα. The figure is reproduced from Hess et al. (2008).