We develop a series expansion for the calculation of the magnetic field near the center of Helmholtz coils and apply the result to a magnet of our design. Our analysis considers geometric details of the coils, the magnetic properties of the form and windings, conductor insulation effects, and several winding imperfections. We also consider the relaxation of coil symmetry which happens when the mean radius of each coil and the coil midplane separation distance are unequal. We compute the field uniformity near the coil's center for three cases, including one where axial symmetry remains but geometric imperfections of the order of 10(-3) of the coil "radius" exist.

We present the field-line modeling, design and construction of a prototype circular-coil tokamak-torsatron hybrid called Proto-CIRCUS. The device has a major radius R = 16 cm and minor radius a < 5 cm. The six "toroidal field" coils are planar as in a tokamak, but they are tilted. This, combined with induced or driven plasma current, is expected to generate rotational transform, as seen in field-line tracing and equilibrium calculations. The device is expected to operate at lower plasma current than a tokamak of comparable size and magnetic field, which might have interesting implications for disruptions and steady-state operation. Additionally, the toroidal magnetic ripple is less pronounced than in an equivalent tokamak in which the coils are not tilted. The tilted coils are interlocked, resulting in a relatively low aspect ratio, and can be moved, both radially and in tilt angle, between discharges. This capability will be exploited for detailed comparisons between calculations and field-line mapping measurements. Such comparisons will reveal whether this relatively simple concept can generate the expected rotational transform.

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