Linear and nonlinear development of the negative mass instability in a modified betatron accelerator

In the modified betatron concept, an intense ring of electrons is confined within a torus by a combination of a vertical mirror field Bz and a strong toroidal magnetic field Bθ. Above a transition energy YT ≈ (4vr²0/a²)^1/3, where v is Budker´s parameter and ro, a are the major and minor radii of the torus, respectively, the effective mass of the particles becomes negative. In this regime, the ring is unstable to a kinking and bunching instability, the negative mass instability. Numerical calculations of the linear growth rates and nonlinear development of this instability are presented. The scaling of growth rate with beam energy y, toroidal mode number ℓ, and the toroidal field Bθ is obtained. The effect of varying the beam emittance and energy spread is also studied. All the simulations were performed with the 3-D electromagnetic PIC code IVORY.