1. All numbered equations are expressed in rationalized mks units unless otherwise noted. When numerical values of common physical quantities are given which involve magnetic field, length, or mass they are quoted in the somewhat more familiar units of kilogauss, centimeter, and gram.
2. The velocity of a nonrelativistic particle with chargeqand massmlocated in an azimuthally symmetric radial electric fieldEand a uniform orthogonal magnetic fieldBmay be decomposed into three velocities v = vD+vL+vz (where vD is the drift velocity of the guiding center located at a radiusrand is given by vD = E×B∕B2; vL is a circular rotation with an angular frequency ω = qB∕m at a radius rL about the guiding center, and Vz is a constant drift velocity in the direction of the magnetic field) to a degree of accuracy dependent upon the smallness of the quantities vD∕ωr and rL∕r compared to unity. In instances where charge densities are present and collisions are negligible, the additional restriction must be imposed that the fractional change of the radial component of the electric field over the distance of the Larmor radius rL is small, i.e., the particle must not pass through a thin voltage sheath. Under typical Ixion operating conditions, vD≈8×106 cm∕sec, ω≈4×107 sec−1 and rL≈0.1 cm for deuterium. The rotating plasma is located at r>4.5 cm so that vD∕ωr≲0.04 and rL∕r≲0.02.
3. R. F. Post, inProceedings of the Second United Nations International Conference on the Peaceful Uses of Atomic Energy(United Nations, Geneva, 1958), Vol. 32, p. 245.
4. Ion Confinement by Rotation in Magnetic Mirror Geometry