Negative-mass instability in a cylindrical layer of relativistic electrons

The purpose of this work is to examine the stability of a cylindrical layer of relativistic particles in a geometrical configuration that approximates the Astron machine. The model is that of a long thin cylindrical shell of relativistic electrons that gyrate in an axial magnetic field and are enclosed in cylindrical conducting walls. It is shown that a number of the lower azimuthal (`negative-mass') modes can be rendered stable even in the absence of any energy spread by the proximity of a highly conductive outer wall. This stabilization is a property of the cylindrical geometry, and is in marked contrast to the results for a toroidal tank geometry such as those used in particle accelerators. A calculation of the instability growth rates in the presence of the Astron resistor structure is also presented.