Showing papers by "John R. Cary published in 1997"

Omnigenity and quasihelicity in helical plasma confinement systems

Abstract: Omnigenous stellarators, those with bounce averaged drifts lying within the magnetic surfaces, form a much larger class than quasihelical stellarators (i.e., with magnetic-field strength depending on only a single linear combination of the toroidal flux angles) while nevertheless having very good transport properties. It is shown by construction that exactly omnigenous magnetic strengths can be very far from quasihelical, but that all such magnetic strengths are nonanalytic. However, by truncation of the Fourier representation one can obtain analytic magnetic strengths that are very close to being omnigenous while still very far from quasihelical. This indicates that the condition of quasihelicity can be significantly relaxed and yet retain good neoclassical transport. Finally, it is conjectured that reasonably good transport can be obtained by requiring omnigenity for only the deeply trapped and marginally trapped particles. Such fields will have no transition particles and, hence, no separatrix crossing chaos. These conditions reduce to the requirements that the field line maxima and minima of the magnetic field and the separatrix action be constant on a magnetic surface.

Helical plasma confinement devices with good confinement properties

Abstract: The criterion of approximate omnigeneity (i.e., having bounce-averaged drift lying within the magnetic surfaces) is much easier to satisfy than quasihelicity, the condition that $B$, the magnitude of the magnetic field, is a function of only a single linear combination of the toroidal angles. Simple criteria for omnigeneity are presented and used to construct exactly omnigenous forms for $B$ that are far from quasihelical. Though this construction gives a nonanalytic function $B$, close to the constructed systems there exist other systems with analytic $B$. These results indicate that finding helical plasma confinement systems with minimal neoclassical transport is much easier than previously believed.

Numerical observation of turbulence enhanced growth rates

Abstract: An enhancement of the velocity diffusion over the quasilinear value is observed in the regime where the autocorrelation time is much smaller than the linear growth time or resonance broadening time. The diffusion enhancement occurs when the resonance broadening time is small compared with the linear growth time. These simulations are self consistent and have enough modes to be in the continuous spectrum limit. That is, even at the initial amplitudes the intermode spacing is sufficiently small that the resonance overlap parameter is large. A possible mechanism for the enhanced diffusion (spontaneous spectrum discretization) is discussed.

Mapa-an object oriented code with a graphical user interface for accelerator design and analysis

Abstract: We developed a code for accelerator modeling which will allow users to create and analyze accelerators through a graphical user interface (GUI). The GUI can read an accelerator from files or create it by adding, removing and changing elements. It also creates 4D orbits and lifetime plots. The code includes a set of accelerator elements classes, C++ utility and GUI libraries. Due to the GUI, the code is easy to use and expand.

Expression templates for truncated power series

Abstract: The truncated power series technique (differential algebra or DA) is a powerful tool for non-linear map analysis of accelerators. The most natural language for numerical DA's is C++, since it is object oriented and has operator overloading. Traditional C++, though, can be inefficient for scientific programming due to creation of many temporaries and extra loops in overloaded operators. The recent expression templates technique allows a user to combine the elegance of the object oriented approach with the speed of procedural languages. The way it was created, it is not directly applicable for DA. We created a set of classes whose structure will be suitable for implementing DA vectors and maps. Classes realizing the expression templates technique are separated from the client classes, which allows their reuse for different mathematical concepts. Speed tests on the KCC compiler showed that new C++ classes for DA have the same speed as hand-coded C.

Expression Templates for Truncated Power Series

Abstract: The truncated power series technique (differential algebra or DA) is a powerful tool for non-linear map analysis of accelerators. The most natural language for numerical DA's is C++, since it is object oriented and has operator overloading. Traditional C++, though, can be inefficient for scientific programming due to creation of many temporaries and extra loops in overloaded operators. The recent expression templates technique allows a user to combine the elegance of the object oriented approach with the speed of procedural languages. The way it was created, it is not directly applicable for DA. We created a set of classes whose structure will be suitable for implementing DA vectors and maps. Classes realizing the expression templates technique are separated from the client classes, which allows their reuse for different mathematical concepts. Speed tests on the KCC compiler showed that new C++ classes for DA have the same speed as hand-coded C.