An upper limit on the net current of a charged particle beam is derived by requiring the energy per unit length in the magnetic field to be less than that in the particles. The limit is calculated for five different current profiles. It is shown that an arbitrarily large net current can propagate in a large diameter ring. The results are found to be closely related to the Alfvén limit. A limit on the forward current in a conductor is calculated, which defines a magnetic inhibition time.

• Received 20 March 2003

DOI:https://doi.org/10.1103/PhysRevE.68.037501