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Low‐frequency flute instabilities in intense nonneutral electron and ion beams

The stability properties for low‐frequency flute perturbations in a relativistic nonneutral electron beam are investigated within the framework of the Vlasov–Maxwell equations. It is assumed that ν/γb<<1, where ν is Budker’s parameter and γbmc2 is the characteristic electron energy. The analysis is carried out for the rigid‐rotor equilibrium distribution function in which all electrons have the same value of energy in a frame rotating with angular velocity ωb and the same value of axial canonical momentum. Strong instability is found for aximuthally symmetric perturbations (∂/∂ϑ=0) with radial mode numer n=2 and rotational frequency ωb=0.5 ωcb, where ωcb is the electron cyclotron frequency. However, the instability can easily be stabilized by slightly detuning the rotational frequency from the value ωb=0.5 ωcb. The transverse stability properties of an intense ion beam in a quadrupole magnetic field are also investigated by analogy with the electron beam stability analysis, including the important influen...