Streams consisting of a mixture of ions and electrons in which the average velocity of the electrons in the direction of the stream is different from the average stream velocity of the ions can be magnetically self-focusing. The random velocities of the electrons and ions about their respective average stream velocities do not need to be Maxwellian. The only condition which must be met is that the total electric current in stream must exceed a critical value which can be calculated in terms of the stream velocities and the average kinetic energies of the particles due to components of velocity transverse to the axis of the stream. Streams containing both slow and fast particles of like kind tend to eject the slow particles and keep the fast ones. Streams of particles of one kind only, entering an ionized or ionizable region can be self-focusing. Axial asymmetries grow in arcs but disappear in low-density self-focusing streams.

• Received 30 September 1953

DOI:https://doi.org/10.1103/PhysRev.98.1584