Gyrosymmetry: Global Considerations

In the guiding center theory, smooth unit vectors perpendicular to the magnetic field are required to define the gyrophase. The question of global existence of these vectors is addressed using a general result from the theory of characteristic classes. It is found that there is, in certain cases, an obstruction to global existence. In these cases, the gyrophase cannot be defined globally. The implications of this fact on the basic structure of the guiding center theory are discussed. In particular it is demonstrated that the guiding center asymptotic expansion of the equations of motion can still be performed in a globally consistent manner when a single global convention for measuring gyrophase is unavailable. The latter fact is demonstrated directly by deriving a new expression for the guiding-center Poincar\'e-Cartan form exhibiting no dependence on the choice of perpendicular unit vectors.Comment: 22 page

Guiding center dynamics as motion on a formal slow manifold in loop space

Since the late 1950's, the dynamics of a charged particle's ``guiding center" in a strong, inhomogeneous magnetic field have been understood in terms of near-identity coordinate transformations. The basic idea has been to approximately transform away the coupling between the fast gyration around magnetic fields lines and the remaining slow dynamics. This basic understanding now serves as a foundation for describing the kinetic theory of strongly magnetized plasmas. I present a new way to understand guiding center dynamics that does not involve complicated coordinate transformations. Starting from a dynamical systems formulation of the motion of parameterized loops in a charged particle's phase space, I identify a formal slow manifold in loop space. Dynamics on this formal slow manifold are equivalent to guiding center dynamics to all orders in perturbation theory. After demonstrating that loop space dynamics comprises an infinite-dimensional noncanonical Hamiltonian system, I recover the well-known Hamiltonian formulation of guiding center motion by restricting the (pre-) symplectic structure on loop space to the finite-dimensional guiding center formal slow manifold.Comment: 39 pages, preprint, v1.

Cargo Logistics Airlift Systems Study (CLASS). Volume 2: Case study approach and results

Models of transportation mode decision making were developed. The user's view of the present and future air cargo systems is discussed. Issues summarized include: (1) organization of the distribution function; (2) mode choice decision making; (3) air freight system; and (4) the future of air freight

Cargo Logistics Airlift Systems Study (CLASS). Volume 5: Summary

Findings and conclusions derived during the study of freighter aircraft requirements to the year 2008 are summarized. These results represent the stepping off point for the much needed coordinated planning efforts by government agencies, the airlines, the users, and the aircraft manufacturers. The methodology utilized in the investigations is shown. The analysis of the current system encompassed evaluations of the past and current cargo markets and on sight surveys of airport and cargo terminals. The findings that resulted provided the basis for formulating the case study procedures, developing the future scenario, and developing the future cargo market demand