Self-Consistent Field of Single-Type Electrons in a Uniform Magnetic Field

A problem which has been brought to the fore by Christofilos' proposed thermonuclear machine, "Astron," is that of electrons rotating in a uniform impressed magnetic field in such a way as to form a cylinder in space—a disembodied current-carrying helix. In the present paper the self-consistent magnetic field for such a "helix," infinitely long and made up of relativistic electrons of identical mass, axial velocity and canonical angular momentum, has been calculated for the interesting range of the two pertinent parameters. The first is the ratio, denoted by $g_2$, of apogee radius to the radius of gyration in the impressed field. The second is the quotient of the number of electrons per classical-electron diameter along the axis and the ratio of relativistic to rest mass. It is denoted by $\left(\frac{2r_e}{\gamma }\right)N$ and is called the "strength" of the layer.