Orbital stability of the high-current betatron

Abstract

Orbital stability of the high-current betatron is analyzed. In this modified betatron a toroidal magnetic field is added to the conventional betatron magnetic field. This increases substantially the space charge limit during injection. It gives rise, however, to new problems during acceleration, such as ring stability, Fermi drift, and orbital resonances. A detailed analysis is presented showing that two serious problems may arise: (i) The beam becomes highly unstable when the net focusing force on it becomes zero. The dominant instability in this region is the Fermi drift. This may, however, be utilized in extracting the beam. (ii) Errors in the vertical (betatron) magnetic field result in driven resonances that must be crossed during acceleration. The amplitude growth of the transverse betatron oscillations due to these resonances is negligible up to very high γ (low n resonances). In practice, it may become very difficult to cross the n=1 resonance. Thus, extracting the beam again making use of the Fermi drift while n>1 is preferable.

Drifts or drift surfaces

“…where -e and m are the charge and rest mass of an electron, respectively. The transverse equations of motion (BARAK and ROSTOKER: 1983) are where a and R are the minor and major radii of the torus, respectively, B,,o is the toroidal field on the minor axis, and Be,, is the poloidal field at r = a. A uniform current density is assumed so that 3,(r) = ( T / U ) B ~, ~.…”

“…EQUATIONS of motion have recently been developed which describe the orbits of electrons in a high current betatron having toroidal and poloidal magnetic fields and an accelerating toroidal electric field (BARAK and ROSTOKER, 1983). In this paper, we apply these equations to the description of the orbits of collisionless particles in a Tokamak.…”