Particle tracing in the magnetosphere: New algorithms and results

Sheldon, Robert B.; Gaffey, J. D.

doi:10.1029/93gl00835

Cited by 23 publications

(20 citation statements)

References 15 publications

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“…This allows one to either simulate many more particles [Hudson et al, 1997] or cast the problem analytically in a different parameter representation by explicitly invoking conservation of m [Sheldon and Gaffey, 1993]. However, even if we ignore the effects of collisions, waves, and other time variations of the magnetic field, m conservation cannot be invoked in all regions of the magnetosphere or for all particle energies.…”

Section: Introductionmentioning

confidence: 99%

Empirical model for μ scattering caused by field line curvature in a realistic magnetosphere

Young¹

2002

J. Geophys. Res.

101

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[1] The combination of magnetic field line curvature (FLC) and weak magnetic field strength affects charged particle motion in a magnetic field by causing changes of the particle's first adiabatic invariant, m. In this paper we refer to these changes as FLC induced m scattering or simply m scattering. Both large single scatterings and the cumulative effects of many small scatterings (Ám/m ( 1) influence particle populations in the Earth's magnetosphere. Because FLC-induced m scattering is strongly dependent on the magnetic field geometry and strength, realistic magnetospheric models must be employed in order to gain a quantitative understanding of how m scattering affects the evolution of these populations. This requires a m-scattering model that is accurate for many different magnetic field geometries. Though several m-scattering models have been developed previously, we demonstrate that their accuracy is limited to the simple field geometries for which they were derived. In realistic magnetic fields, there are regions where these m-scattering models depart from Lorentz integration results by a factor of 2 or greater. The source of these discrepancies is attributed to the fact that the only magnetic field information used is the field line curvature R C and magnetic field strength B both evaluated at a single point, the magnetic equator. To generalize the analytical representation of m scattering to a range of magnetic field geometries, we have developed a new m-scattering model that uses two additional parameters. These are proportional to the second derivatives of the field line curvature, @ 2 R C /@S 2 , and the field intensity, @ 2 B /@S 2 , where S is the distance along the field line and the derivatives are evaluated at the magnetic equator. We have defined an error parameter that measures the fit between the model and Lorentz integration results. Using this parameter, we show that the difference between our model Ám values and those based on Lorentz integration is, on average, only 4%; this is at least a factor of 5 less than the difference using previous analytical models. Our new model will greatly facilitate quantitative analysis of m scattering for realistic magnetospheric magnetic field geometries including active as well as quiet conditions.

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Section: Introductionmentioning

confidence: 99%

Empirical model for μ scattering caused by field line curvature in a realistic magnetosphere

Young¹

2002

J. Geophys. Res.

101

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“…To use this technique for particle tracing, the functional dependence of B m (K) on K needs to be known, which is determined by inverting K(B m ) calculated at each field line [Sheldon and Gaffey, 1993]. In this paper, we call this calculation of B m (K) the preparation step.…”

Section: Methodsmentioning

confidence: 99%

“…Shown in Figure 1a is B m as a function of K (vertical axis) calculated at each field line passing an x-y grid point. For inversion of K(B m ) to B m (K), Sheldon and Gaffey [1993] used a 10th degree polynomial expression, which resulted in only 3% maximum deviation. To make the implementation simpler and obtain better accuracy, we instead use spline interpolation for the inversion.…”

Section: Methodsmentioning

confidence: 99%

“…Fast computation of a particle trajectory is achieved by the principle of energy conservation. Later the (U, B, K) coordinates were used for describing convective evolution of the particle distribution and for categorizing topologically different drift orbits [Sheldon and Gaffey, 1993]. In this paper we will use this particle tracing algorithm in the calculation of L * .…”

Section: Introductionmentioning

confidence: 99%

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A novel technique for rapid L^* calculation using UBK coordinates

2013

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[1] The magnetic drift invariant (L * ) is an important quantity used for tracking and organizing particle dynamics in the radiation belts, but its accurate calculation has been computationally expensive in the past, thus making it difficult to employ this quantity in real-time space weather applications. In this paper, we propose a new, efficient method to calculate L * using the principle of energy conservation. This method uses Whipple's (U, B, K) coordinates to quickly and accurately determine trajectories of particles at the magnetic mirror point from two-dimensional isoenergy contours. The method works for any magnetic field configuration and is able to accommodate constant electric potential along field lines. We compare the result of this method with those of International Radiation Belt Environment Modeling library (IRBEM-LIB) to demonstrate the performance of this new method. The method requires a preparation step, and thus may not be the optimal method for a single trajectory calculation; however, it presents a huge performance gain when adiabatically propagating a large population of particles in a given magnetic field configuration.

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“…The electrostatic potential U is assumed to be constant along a field line, and therefore is independent of pitch angle. However Bm is clearly pitch angle dependent, and must be known for every value of the second adiabatic invariant J or K [Sheldon and Gaffey, 1993]. Birmingham [1984] discusses the conditions under which the first two invariants are not conserved, which for a "realistic" model field, e.g.…”

Section: Hamiltonian Convectionmentioning

confidence: 99%

Particle transport in the magnetosphere: A new diffusion model

Sheldon

Eastman

1997

Geophysical Research Letters

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Abstract. Previous transport models of the plasmasphere, ring current and radiation belts have considered either diffusive or convective transport, but not both. Since the K7B drift speed is proportional to energy, analyses of particles with E> 100 keV have generally used only •7B drift and diffusive transport. Conversely, particles of E<30 keV have been treated with only E xB drift and convective transport. The ring current, which lies between these two regimes, cannot be described by either mechanism alone, so that these standard models, though widely used and otherwise applicable, fail in detail to describe the trapped ion population convection model, but we need a robust definition of diffusion as well.In addition to simulations, there is compelling empirical evidence that no present convection or diffusion model can adequately explain the data. One example from the AMPTE mission will suffice. On days 138-143 of 1987, the CI-IEM instrument observed the quietest ring current in its four-year mission, as determined by both ground based indices and in situ measured densities. A plot of those six radial passes (see Figure 1) shows a distinct peak around L=2.8 that surfaced as the magnetosphere quieted (Days 139-142), but appears as observed with modem instrumentation. We develop a , diffused during more active periods (Day 138). Now this formalism that can describe both diffusive and convective transport in a completely general way, including UT, LT, radial, and pitch angle dependence, with arbitrary magnetic and electric field models. The formalism is general enough to rederive the electric or magnetic diffusion coefficients for trapped particles without the simplifying assumption of axial symmetry or a vanishing convection electric field, thus improving on the standard coefficients derived nearly 30 years ago. More importantly, we include the previously neglected diffusion term due to a localized, non-global perturbation of the fields, and show that under some circumstances this term may dominate over the resonant diffusion caused by global perturbations.

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Particle tracing in the magnetosphere: New algorithms and results

Cited by 23 publications

References 15 publications

Empirical model for μ scattering caused by field line curvature in a realistic magnetosphere

Empirical model for μ scattering caused by field line curvature in a realistic magnetosphere

A novel technique for rapid L^* calculation using UBK coordinates

Particle transport in the magnetosphere: A new diffusion model

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Particle tracing in the magnetosphere: New algorithms and results

Cited by 23 publications

References 15 publications

Empirical model for μ scattering caused by field line curvature in a realistic magnetosphere

Empirical model for μ scattering caused by field line curvature in a realistic magnetosphere

A novel technique for rapid L* calculation using UBK coordinates

Particle transport in the magnetosphere: A new diffusion model

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A novel technique for rapid L^* calculation using UBK coordinates