Levitated Toroidal Multipole Design Study and Optimization

Designing a useful plasma toroidal multipole requires optimization of many parameters. The selection and design of the Wisconsin levitated octupole involved study of over 200 multipole configurations with a computer program based on the stream function ψ=rA_θ. Plasma bridge thickness was maximized subject to having equal MHD‐stable flux inside and outside of the separatrices. To achieve sufficient outside flux in a quadrupole with reasonable stored energy and hoop weight requires hoops with a long and (radially) thin cross section. The field properties are then poor because of $\mathrm{E}{\displaystyle {lim}^{\to }}\times \mathrm{B}{\displaystyle {lim}^{\to }}$ drift into hoops. Octupoles do not have this problem, since (much lighter) hoops of circular cross section were essentially optimum. Sextupoles had disadvantages similar to quadrupoles. Octupole hoop levitation by the fields was achieved with two wall projections and no major sacrifice in outer flux. Perfect critical‐point degeneracy was traded for improved horizontal injection geometry, but flux between separatrices was held to 1% of plasma flux. These criteria were satisfied independently of effective skin depth (up to 1.5 rms resistive skin depths at 10 Hz) of field penetration. Construction of the octupole has been completed, and initial experiments have largely confirmed the design qualities sought.