Allen Boozer has developed many of the concepts that underlie modern stellarator theory.  For this he was elected to scientific membership in the German Max Planck Society (Auswärtiges Wissenschafliches Mitglied der Max-Planck-Gesellschaft) in 1989 and awarded the Alfvén Prize by the Division of Plasma Physics of the European Physical Society in 2010.

Four contributions are related to these honors.  (1) Demonstrated, Physics of Fluids 23, 904 (1980), that the standard equations for the guiding center motion of particles are inconsistent with Hamiltonian mechanics and derived a form that is consistent.  This form depends on the magnetic field strength, not the vector, and naturally leads to the concept of quasisymmetry, Physics of Fluids 26, 496 (1983).  (2)  Developed with G. Kuo-Petravik the techniques of Monte Carlo calculations of transport in stellarators, Physics of Fluids 24, 851 (1981).  (3)  Gave the proof of the existence of coordinates in which the magnetic field has simple covariant and contravariant forms, Physics of Fluids 24, 1999 (1981).  This paper showed that singularities in the equilibrium current density where magnetic field lines close on themselves, made famous by H. Grad, are removed for equilibria consistent with Ohm's law.  (4) Was an author on the paper that showed a great improvement in particle confinement in stellarators when all minima of the field strength on a magnetic surface have the same value, Physical Review Letters 48, 322 (1982).

Recent contributions by Allen Boozer to stellarator design are given in Journal of Plasma Physics 81, 515810606 (2015): (1) Simplification of stellarator coils, gave a simple method to order the magnetic field distributions produced by coils by their difficulty of production.  (2) Control of magnetic field errors and the design of stellarators for physics flexibility, showed that both issues are addressed using circuit equations, where the circuit parameters are defined by a perturbation analysis.  (3) Distinguished the two types of stellarator divertors, and defined the investigations of edge magnetic topology that are needed.  The techniques for carrying out these divertor investigations together with examples are given in a paper submitted by A. Boozer and A. Punjabi to the Physics of Plasmas.