Among the largest and most expensive of all scientific instruments, particle accelerators have impacts in many fields of science and society. The theory behind their operation, developments of their technical design, and the understanding of their performance require a host of tools and methods ranging from applied physics and engineering to pure mathematics. For more information on this rapidly growing discipline, please visit:
Our program has been primarily theoretical and has entailed the development of cross-disciplinary techniques of nonlinear dynamics and their application to charged-particle beams. These techniques are related (but not limited) to the validity of the continuum limit in N-body simulations of beams, the existence of chaotic orbits in both time-independent and time-dependent N-body systems, chaotic mixing in these systems, the validity of the continuum limit (Vlasov-Poisson formalism), and noise-enhanced halos.
Our initial work included laboratory experiments involving novel beam diagnostics that were performed at the Fermilab/NICADD Photoinjector Laboratory (FNPL). Collaborations with the University of Maryland in planning experiments on the fundamental dynamics of space charge in beams were performed at the University of Maryland Electron Ring (UMER). We are also building an in-house Beam Diagnostic Laboratory, one that will include an electron gun for testing and commissioning new instrumentation.
Our research has revealed that the hierarchies of temporal and spatial scales are critically important drivers of the evolution of beams with space charge; we have found that details do matter. Consequently, we have embarked on an intensive effort to develop a new space-charge algorithm that faithfully preserves these hierarchies while still enabling efficient computations. The underlying methodology is multiresolution analysis, e.g., application of wavelets.
The study of Hamiltonian systems in general led to the development of seemingly two different branches of mathematics: the theory of dynamical systems and symplectic geometry. Both fields have undergone dramatic recent development and it is becoming clear that there is a common core which could lead to a new field called "symplectic dynamics". We (especially Prof. Bela Erdelyi) are investigating this connection. One of the best test beds of this new field is the accelerator (or particle beams in general).