Chaos, Magnetic Fields, and the Cosmic Ray Anisotropy

Recent experimental results on the arrival direction of high-energy cosmic rays have motivated studies that call for a deeper understanding of their propagating environment. Interstellar and local magnetic fields shape this observed anisotropy. In coherent magnetic structures, such as the heliosphere, or due to magnetohydrodynamic turbulence, magnetic mirroring can temporarily trap particles, leading to chaotic behavior. In this work, we develop a new method for characterizing the chaotic behavior of cosmic rays in magnetic systems using finite-time Lyapunov exponents. This quantity determines the degree of chaos and adapts to transient behavior. We study particle trajectories in an axisymmetric magnetic bottle to highlight mirroring effects. By introducing time-dependent magnetic perturbations, we study how temporal variations affect chaotic behavior. We tailor our model to the heliosphere; however, it can also represent diverse magnetic configurations that exhibit mirroring phenomena. Our results have three key implications: 1. Theoretical: We find a correlation between the finite-time Lyapunov exponent, i.e., the level of chaos, and the particle escape time from the system, revealing a power law that persists even under additional perturbations. This power law may reveal intrinsic system characteristics, providing insight into propagation dynamics that go beyond simple diffusion. 2. Simulation: Chaotic effects play a role in cosmic ray simulations and can influence the resulting anisotropy maps. 3. Observational: Arrival maps display areas where chaotic properties vary significantly; these changes can be the basis for time variability in the anisotropy maps. This work lays the foundation for studying the effects of magnetic mirroring of cosmic rays within the heliosphere and the role of temporal variability in the observed anisotropy.