Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 1112.3487

Trajectories of charged particles trapped in Earth's magnetic field

M. Kaan Öztürk
View original source ↗Read source document ↗Export metadata ↓

Abstract

I outline the theory of relativistic charged-particle motion in the magnetosphere in a way suitable for undergraduate courses. I discuss particle and guiding center motion, derive the three adiabatic invariants associated with them, and present particle trajectories in a dipolar field. I provide twelve computational exercises that can be used as classroom assignments or for self-study. Two of the exercises, drift-shell bifurcation and Speiser orbits, are adapted from active magnetospheric research. The Python code provided in the supplement can be used to replicate the trajectories and can be easily extended for different field geometries.

Explore related subjects

physics.space-phphysics.ed-ph

Keep this discovery

BibTeXRIS

M. Kaan Öztürk. 2011-12-15. Trajectories of charged particles trapped in Earth's magnetic field. https://doi.org/10.1119/1.3684537

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Cascade models of anisotropic turbulence in magnetized plasma of solar wind

We present a physical framework for Alfv\'enic solar wind turbulence in which the plasma is modeled as discrete domains with local rotational symmetry about the domain-mean magnetic field. Using this symmetry, we construct minimalist cascade models governed by two characteristic time scales, nonlinear and Alfv\'enic, associated, respectively, with the perpendicular and parallel directions relative to the domain-mean magnetic field. Within this partial symmetry, we also characterize the anisotropy of each domain by a single additional geometrical parameter, the alignment angle between the domain-mean velocity and magnetic fields. We introduce a stochastic renewal process with a bimodal waiting-time distribution based on these two time scales, yielding a two-branch renormalization solution for the total energy cascade: a statistically robust branch with an Iroshnikov-Kraichnan-like $k^{-3/2}$ spectrum, and a statistically marginal branch with a Kolmogorov-like $k^{-5/3}$ spectrum. Utilizing principles of causality and cascade stability, we show that the system selects the faster cascade rate between the two available whenever energy-flux fluctuations become supercritical, preventing intermittent flux accumulation. Consequently, during solar wind expansion, balanced domains (with low cross-helicity) undergo a first-order phase transition from the slow $k^{-3/2}$ cascade to the fast $k^{-5/3}$ cascade. The transition is accelerated by heterogeneous nucleation at switchbacks. Incorporating a forward magnetic helicity cascade slaved to the energy cascade, we show that the large-scale spectra decouple into a flat $k^{-3/4}$ magnetic spectrum and a $k^{-3/2}$ kinetic spectrum. Data from Voyager, Ulysses, Helios, Wind, and PSP confirm these spectral signatures across diverse heliospheric regions.

physics.space-ph↗
arXiv2026

AETHER-P3 Nowcast v1.0: Model Description, Training-Data Construction, and Validation Technical report prepared in support of CCMC onboarding

AETHER-P\textsuperscript{3} Nowcast v1.0 is a machine-learning-based global thermospheric neutral-density model developed for low-Earth-orbit applications and prepared for onboarding to NASA's Community Coordinated Modeling Center (CCMC). The model provides pointwise neutral-density estimates together with predictive uncertainty using a deep evidential regression framework driven by causal solar, solar-wind, geomagnetic, spatial, temporal, and empirical-model inputs. This report documents the released model configuration, training-data construction, software traceability, output products, validation strategy, benchmark performance, and known limitations. The training archive combines accelerometer- and mission-derived density observations from CHAMP, GRACE-A, GOCE, Swarm-C, and GRACE-FO spanning 2000--2023. More than 40 million eligible 30-s observations are available, but the archive is strongly dominated by consecutive quiet-time measurements. To preserve coverage of physically important regimes, the final 1.67-million-sample training set is constructed using deterministic regime-aware sampling that progressively subsamples quiet conditions while retaining all available extreme-condition observations. Validation uses temporally disjoint chronological blocks with exclusion guards to reduce information leakage. Evaluation across quiet, moderate, and extreme conditions shows competitive performance relative to HASDM, JB2008, NRLMSISE-00, and available WAM-IPE cases, while also identifying limitations associated with sparse training coverage, mission-dependent density products, and condition-dependent uncertainty calibration. The report provides a reproducible technical description of the AETHER-P\textsuperscript{3} Nowcast v1.0 research release and its current CCMC onboarding configuration.

physics.space-ph↗
arXiv2026

Direct Four-Spacecraft Measurement of Reconnection Exhaust Thickness in the Solar Wind

The thickness of a reconnecting solar wind current sheet is normally inferred from a single spacecraft as the product of the boundary-normal speed and the crossing duration. Multipoint measurements have tested this method for generic solar wind current sheets and constrained the geometry of reconnection exhausts, but a direct comparison with single-spacecraft thickness estimates for the same reconnection-associated crossings is still lacking. We analyze four current-sheet crossings observed by Magnetospheric Multiscale in the pristine solar wind on 2017 November 10 the two boundaries of a confirmed reconnection exhaust and two nearby current sheets. The tetrahedron separation was $\approx 16$ km. Cross-correlation of the magnetic-field ramps gives millisecond-level lag uncertainties, boundary normals to $4^\circ-8^\circ$ and speeds to $5\%-8\%$, while single-threshold timing at these separations is noise dominated. The exhaust edges are 29-31 ion inertial lengths ($d_i$) thick. The two edge normals differ by $22^\circ$ (68% interval [$19^\circ,26^\circ$]), resolving a nonparallel exhaust geometry. At the exhaust edges, the measured boundary speeds agree with three standard single-spacecraft estimates to 4%-15% and remain within about one Alfv\'en speed of the plasma motion. Estimating the normal from one spacecraft is the larger source of error, though the thickness is still recovered to within tens of percent when a degenerate minimum-variance solution is rejected. At the actively reconnecting sheet, the boundary speed exceeds the local plasma speed along the normal by $29\% \pm 10\%$.

physics.space-ph↗