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

Abstract

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 influence of rotational effects on stability behavior. It is found that the rotational motion also plays an important role in determining the stability properties of intense ion beams.