STRAIGHT HELICAL HELIOTRON FIELD

The general expression of the l equals 2 straight helical heliotron field is obtained by integrating Biot-Savart's formula after expanding the integrand. Solving the differential equation of the line of force, a general expression for the magnetic surfaces, which is in good agreement with the results of a computer calculation up to the separatrix, is obtained. The rotational transform and the shear of this field are calculated as functions of the average radius of the magnetic surface. For a certain range of alpha *, the ratio of the longitudinal field produced by the B//z-coil to the longitudinal component of the field produced by the helical coil, the field cannot form a closed magnetic surface. The width of this range, the forbidden zone, is a function of gamma equals 2 pi a/p, where a is the radius of the helical winding and p is the pitch. For small gamma , the zone is wide and the closed magnetic surface has very small shear. For large gamma , the zone is narrow and the magnetic surface has very small rotational transform and shear. Only for intermediate gamma , the zone is narrow and rotational transform and shear are both large. These values of gamma could be considered to be optimum values for plasma confinement.