Ultrafast nonequilibrium dynamics and polarization dependent high-harmonic generation in crystalline solids excited by intense infrared ultrashort laser pulses
Abstract
The aim of this proposal is to approach very old and complex problems in celestial mechanics, such as the circular restricted three-body problem, from the modern perspective of symplectic geometry, and for the purposes of space mission design. The field of symplectic geometry, with origins in classical mechanics, has seen spectacular activity in the last 30 years, since Gromov introduced the notion of pseudoholomorphic curves in 1985, and Floer theory was developed soon afterwards. Much more recently, the author and collaborators have initiated a systematic approach that falls within the scope of a new field- symplectic dynamics. The running theme of the line of research we propose is to extract tools from general methods of very abstract nature, but which are amenable to practical applications, with the aim to disseminate our findings among the astrodynamics community. We outline a research program aimed at studying existence, stability and bifurcations of trajectories, with emphasis on the Earth-Moon system and cislunar space. The current interest in cislunar dynamics is motivated by the Artemis program and related missions. We will combine invariants extracted from Floer theory, global topological methods, index theory, and numerical implementations, in order to- (1) carry out bifurcation studies of families of periodic orbits in the Earth-Moon system, including the halo orbits; (2) Implement algorithms for the effective computation of the relevant indices attached to each family of orbits; (3) develop a three-dimensional refinement of the Broucke diagram for the purpose of studying stability of orbits in non-autonomous systems with three degrees of freedom. The methods we propose are completely novel and at the cutting-edge, and have already born fruits, as witnessed by the results obtained by the PI and collaborators. We expect not only to provide new insights and perspectives, but to provide groundwork which may later be employed as the theoretical backbone for actual mission proposals.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Feb 05, 2025
- Source ID
- FA86552417014
Entities
People
- Tzveta Apostolova
Organizations
- Air Force Office of Scientific Research
- New Bulgarian University
- United States Air Force