Hamiltonian and dissipative structures for reduced plasma kinetic models

This Project Grant from the National Science Foundation, under the Mathematical and Physical Sciences program (CFDA 47.049), provides $134,481 to Saint Michael's College for theoretical development of reduced plasma kinetic models that allow simultaneous treatment of charged particles and electromagnetic fields. The award supports derivation of new theoretical structures for reduced plasma models, including gyrokinetic plasma models, that preserve exact conservation properties and enable particle-field treatment. This will facilitate development of structure-preserving computational algorithms for studying complex magnetized plasma dynamics over longer timescales under realistic conditions. Key outcomes include Hamiltonian and dissipative bracket structures for gyrokinetic plasma equations, addressing unique challenges in theoretical physics. Formulating gyrokinetic models in terms of fields rather than potentials will open new areas of space and astrophysical plasma research. The dissipative bracket structure of the gyrokinetic Landau collision operator will ensure exact conservation properties crucial for investigating synergies between collisionless and collisional plasma evolutions over long periods. This work provides powerful theoretical and computational tools advancing non-linear turbulent modeling of laboratory, space and astrophysical magnetized plasmas.

Abstract

This award supports theoretical development of reduced plasma models that allow for accurate and simultaneous treatment of charged particles and electromagnetic fields. The description of plasma physics phenomena, whether observed in a laboratory or in space, must consider the complex interactions between the orbits of charged plasma particles and the electromagnetic fields that control their dynamics. In realistic plasma conditions, however, the underlying plasma equations are often too complex to be solved, even with the help of the most powerful computers available. The complexity of the plasma physics description can be simplified by the adoption of reduced plasma models, which are faithful to the exact plasma dynamics only if their exact conservation properties are preserved from the original plasma equations. A major outcome of this project is the derivation of new theoretical structures for a variety of reduced plasma models with exact conservation properties that allow for the simultaneous treatment of particles and fields under general plasma conditions. The simultaneous treatment of particles and fields within a reduced plasma model can yield significant increases in the power and speed of new numerical algorithms developed for these reduced plasma models. These new numerical algorithms, in turn, will enable the study of the complex dynamics of laboratory and space magnetized plasmas over longer time scales and under more realistic conditions. The existence of hamiltonian and dissipative bracket structures for plasma kinetic models have led to the emergence of novel structure-preserving computational algorithms in the past ten years. An important new application of these structure-preserving algorithms carried out in this project is concerned with the development of hamiltonian and dissipative bracket structures for reduced plasma gyrokinetic models. The derivation of a hamiltonian bracket structure for a given set of gyrokinetic plasma equations, which presents unique challenges in theoretical physics, is a major outcome of this project. The formulation of gyrokinetic plasma models in terms of fields, instead of potentials, will open new frontiers of research in space and astrophysical plasma physics. The gyrokinetic hamiltonian bracket structure will also allow for the derivation of the dissipative bracket structure of the gyrokinetic landau collision operator under general magnetic geometries. By construction, the dissipative gyrokinetic bracket structure will have exact conservation properties, which is a crucial requirement to investigate the synergy between collisionless (hamiltonian) and collisional (dissipative) plasma evolutions over long time scales. The development of advanced hamiltonian and dissipative structure-preserving algorithms associated with reduced plasma gyrokinetic models will thus provide a set of powerful theoretical and computational tools for investigations of a wider range of research problems associated with the nonlinear turbulent evolution of laboratory, space, and astrophysical magnetized plasmas. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the foundation's intellectual merit and broader impacts review criteria.