Chaotic Behavior of Trapped Cosmic Rays

Abstract

Recent experimental results on the arrival direction of high-energy cosmic rays have motivated studies to understand their propagating environment. The observed anisotropy is shaped by interstellar and local magnetic fields. 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 to characterize cosmic rays' chaotic behavior in magnetic systems using finite-time Lyapunov exponents. This quantity determines the degree of chaos and adapts to transitory behavior. We study particle trajectories in an axial-symmetric 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 represent diverse magnetic configurations exhibiting mirroring phenomena. Our results have three key implications. (1)Theoretical: We find a correlation between the finite-time Lyapunov exponent and the particle escape time from the system, which follows a power law that persists even under additional perturbations. This power law may reveal intrinsic system characteristics, offering insight into propagation dynamics 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 the chaotic properties vary significantly; these changes can be the basis for time variability in the anisotropy maps. This work lays the framework for studying the effects of magnetic mirroring of cosmic rays within the heliosphere and the role of temporal variability in the observed anisotropy.

arXiv comment20 pages, 11 figures; submitted to ApJ

References in corpus (37)

• HEALPix -- a Framework for High Resolution Discretization, and Fast Analysis of Data Distributed on the Sphere
• The Galactic Magnetic Field
• The origin of Galactic cosmic rays: challenges to the standard paradigm
• Diffusive propagation of cosmic rays from supernova remnants in the Galaxy. II: anisotropy
• Observation of Cosmic Ray Anisotropy with the IceTop Air Shower Array
• Anisotropy in Cosmic-Ray Arrival Directions in the Southern Hemisphere with Six Years of Data from the IceCube Detector
• The Anisotropy of Galactic Cosmic Rays as a Product of Stochastic Supernova Explosions
• Local Magnetic Turbulence and TeV-PeV Cosmic Ray Anisotropies
• Testing Physical Models for Cosmic Ray Transport Coefficients on Galactic Scales: Self-Confinement and Extrinsic Turbulence at GeV Energies
• Northern sky Galactic Cosmic Ray anisotropy between 10-1000 TeV with the Tibet Air Shower Array
• Deciphering the Dipole Anisotropy of Galactic Cosmic Rays
• Origin of Small-Scale Anisotropies in Galactic Cosmic Rays
• Spectrum and Anisotropy of Cosmic Rays at TeV-PeV-energies and Contribution of Nearby Sources
• Anisotropy of TeV Cosmic Rays and the Outer Heliospheric Boundaries
• Anomalous Anisotropies of Cosmic Rays from Turbulent Magnetic Fields
• Solution to the cosmic ray anisotropy problem
• Understanding TeV-band cosmic-ray anisotropy
• Anisotropic diffusion of galactic cosmic ray protons and their steady-state azimuthal distribution
• Cosmic Rays in Intermittent Magnetic Fields
• All-Sky Measurement of the Anisotropy of Cosmic Rays at 10 TeV and Mapping of the Local Interstellar Magnetic Field
• Small-Scale Anisotropies of Cosmic Rays from Relative Diffusion
• Observation of Anisotropy of TeV Cosmic Rays with Two Years of HAWC
• Deflections of UHECRs in the Galactic magnetic field
• Trapping of cosmic rays in MHD turbulence
• Galactic Cosmic-Ray Anisotropy in the Northern hemisphere from the ARGO-YBJ Experiment during 2008-2012
• Cosmic Ray Small Scale Anisotropies and Local Turbulent Magnetic Fields
• The Transport of Cosmic Rays Across Magnetic Fieldlines
• Strangelets and the TeV-PeV cosmic-ray anisotropies
• TeV Cosmic-Ray Anisotropy from the Magnetic Field at the Heliospheric Boundary
• Magnetic fields and cosmic ray anisotropies at TeV energies
• Explaining TeV Cosmic-Ray Anisotropies with Non-Diffusive Cosmic-Ray Propagation
• Turbulent Reacceleration of Streaming Cosmic Rays
• The Local Bubble, Local Fluff, and Heliosphere
• Measurements and implications of cosmic ray anisotropies from TeV to trans-EeV energies
• No longer ballistic, not yet diffusive--the formation of cosmic ray small-scale anisotropies
• Cosmic rays and random magnetic traps
• Time variability of TeV cosmic ray sky map