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DOE OSTI2022

Magnetic turnstiles in nonresonant stellarator divertor

Nonresonant stellarator divertors have magnetic flux tubes, called magnetic turnstiles, that cross cantori, which are fractal remnants of destroyed invariant tori with holes, that lie outside the outermost confining surface. The exiting and entering flux tubes can be adjacent as is generally expected but can also have the unexpected feature of entering or exiting at separate locations of the cantori. Not only can there be two types of turnstiles but pseudo-turnstiles can also exist. A pseudo-turnstile is formed when a cantorus has a sufficiently large, although limited, radial excursion to strike a surrounding chamber wall. The existence of non-adjacent and adjacent turnstiles and pseudo-turnstiles resolves issues that arose in earlier simulations of nonresonant stellarator divertors [A. Punjabi and A. H. Boozer, Phys. Plasmas 27, 012503 (2020)].

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1987

Solutions of some problems in applied mathematics using MACSYMA

Various Symbolic Manipulation Programs (SMP) were tested to check the functioning of their commands and suitability under various operating systems. Support systems for SMP were found to be relatively better than the one for MACSYMA. The graphics facilities for MACSYMA do not work as expected under the UNIX operating system. Not all commands for MACSYMA function as described in the manuals. Shape representation is a central issue in computer graphics and computer-aided design. Aside from appearance, there are other application dependent, desirable properties like continuity to certain order, symmetry, axis-independence, and variation-diminishing properties. Several shape representations are studied, which include the Osculatory Method, a Piecewise Cubic Polynomial Method using two different slope estimates, Piecewise Cubic Hermite Form, a method by Harry McLaughlin, and a Piecewise Bezier Method. They are applied to collected physical and chemical data. Relative merits and demerits of these methods are examined. Kinematics of a single link, non-dissipative robot arm is studied using MACSYMA. Lagranian is set-up and Lagrange's equations are derived. From there, Hamiltonian equations of motion are obtained. Equations suggest that bifurcation of solutions can occur, depending upon the value of a single parameter. Using the characteristic function W, the Hamilton-Jacobi equation is derived. It is shown that the H-J equation can be solved in closed form. Analytical solutions to the H-J equation are obtained.

Punjabi, Alkesh↗