A 2 keV, 10 m electron beam creates its own helium plasma (ne approximately=109 cm-3, Te approximately=4 eV) in a cylindrical interaction chamber (L=75 cm, phi =8 cm, pHe approximately=1.3*10-3 torr) in a multiple magnetic mirror (Bav approximately=B0=112 G, periodicity of 22 cm). The frequency spectrum reveals the excitation of the electron cyclotron instability with a central frequency which depends almost exclusively on the average magnetic field and with an amplitude varying with the mirror ratio as well as with the average plasma density. These experimental results are interpreted in terms of the analysis of the instability theoretical spectrum, constructed from the space-time evolution, in the WKB approximation of waves with frequencies belonging to the unstable band.