Electromagnetic instability in an electron beam-ion channel system

The transverse electromagnetic instability in the electron beam-ion channel system is investigated using kinetic theory. The equilibrium distribution function of a relativistic electron beam, which takes into account a strong ion channel effect, is obtained. The linearized Vlasov equation is solved and the dispersion relation of the system is derived by perturbing the equilibrium with a high frequency electromagnetic wave (EMW). Analysis of the dispersion relation shows that the coupling of the electron beam with the transverse high frequency EMW is achieved through the deflection of the beam electrons due to the synergistic effects of the transverse high frequency EMW and transverse betatron oscillation. The numerical calculation finds that a branch of slow wave instability (SWI) with a wide frequency band is excited. The attenuation index of the SWI increases and its frequency band broadens as the normalized beam radii increases. Besides, the SWI will be suppressed as the longitudinal velocity of the electron beam increases to a certain value; meanwhile, a bunch of fast wave instability (FWI) is excited, which is equal to the increase of the relativistic factor. Also both the SWI and the FWI reach maximum when the EMW frequency meets a resonance condition.