A model for pickup ion transport in the heliosphere in the limit of uniform hemispheric distributions

Schwadron, N. A.

doi:10.1029/98ja01686

Cited by 39 publications

(44 citation statements)

References 16 publications

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“…This is consistent with long scattering mean free paths observed for interstellar pickup ions (6,1,10,12). It is perhaps surprising that the scattering mean free path is still so large close to the Sun.…”

Section: Discussionsupporting

confidence: 76%

“…This is a somewhat subtle assumption, but has been rigorously checked by comparing this solution with the results of a numerical model (10) which solves the complete transport equations. For the inner source density profile we take,…”

Section: A Modelmentioning

confidence: 99%

“…Since ions are picked in the sunward hemisphere, this suggests that the anisotropy in the pickup ions is caused by a difficulty for ions to scatter through 90 ° pitch-angle, where the pitch-angle is the angle between the instantaneous pickup ion velocity and the magnetic field direction. The full transport equation for pickup ions under the assumption of hemispheric distributions has been written down and solved by (8,10,12). The starting point is that distributions are uniform in the sunward hemisphere, f_, and in the antisunward hemisphere, f+.…”

Section: A Modelmentioning

confidence: 99%

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The inner source for pickup ions

Schwadron¹,

Gloeckler²,

Fisk³

et al. 1999

AIP Conference Proceedings

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Abstract.Pickup ions are observed by the Solar Wind Ion Composition Spectrometer on Ulysses which appear to have been picked up close to the Sun. A transport theory for the propagation of these ions is used to constrain the spatial profiles of the ion sources. The composition is like that of the solar wind which suggests that the inner source pickup ions result from solar wind particles that are embedded in dust grains and then released. Through comparison between modeled and observed distributions, it is possible to constrain the radial and latitudinal profiles of the inner source. Inner source protons are also observed and may constitute an energetically important population in the solar wind.

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Section: Discussionsupporting

confidence: 76%

Section: A Modelmentioning

confidence: 99%

Section: A Modelmentioning

confidence: 99%

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The inner source for pickup ions

Schwadron¹,

Gloeckler²,

Fisk³

et al. 1999

AIP Conference Proceedings

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“…approximation. As discussed by Schwadron (1998), the relaxation time approximation can be related to the quasi-linear scattering term away from 90¡. MHD turbulence acts to scatter solar energetic particles, anomalous and galactic cosmic rays, pickup ions in interplanetary space, and particles trapped in the magnetosphere.…”

Section: Modified Relaxation Time Model For the Fokker-planck Equationmentioning

confidence: 99%

“…The variables x and t denote the particle position and time, respectively. The scattering operator is given (df/dt) c either by a quasi-linear model (e.g., Jokipii 1966) or by a relaxation time approximation (e.g., 1994 ;Schwadron 1998). S Kota and L are source and loss terms, respectively.…”

Section: Introductionmentioning

confidence: 99%

Numerical Solution of the Time‐dependent Kinetic Equation for Anisotropic Pitch‐Angle Scattering

Lu¹,

Zank²,

Webb³

2001

ApJ

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A new powerful numerical method is developed for solving the time-dependent kinetic equation describing the anisotropic pitch-angle scattering of charged particles. The model includes the e †ects of adiabatic focusing in a radial magnetic Ðeld, adiabatic deceleration, anisotropic pitch-angle scattering, and convection in a magnetized plasma and signiÐcantly generalizes a model introduced by in Kota 1994. The pitch-angle scattering is assumed to scatter slowly through 90¡. By applying Legendre polynomial expansions to the particle transport equation, an inÐnite series of Ðrst-order di †erential equations for the harmonics of the distribution function is obtained. By means of a characteristic method (together with operator splitting), the solution of distributions at certain harmonics is computed. Solutions exhibiting coherent pulses are obtained, and these are identical to the exact analytic results obtained by However, the approach presented here allows for arbitrarily anisotropic initial data to be preKota. scribed, and it can also be used to study the dependence of particle distribution on pitch angle. It is shown that the presence of adiabatic focusing results in highly asymmetric particle propagation in opposite directions with typically more particles in the sunward hemisphere than in the antisunward hemisphere, although two oppositely propagating initial beams are introduced symmetrically. An abrupt transition can be found between hemispheres, and the distribution within each hemisphere is quasiisotropic. The model and approach discussed here lend themselves to the study of the propagation and transport of charged particles and pickup ions.

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Modeling interstellar pickup ion distributions in corotating interaction regions inside 1 AU

et al. 2015

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We present a modeling study of interstellar pickup ion (PUI) distributions in corotating interaction regions (CIRs). We consider gradual compressions associated with CIRs formed when fast speed streams overtake slower streams in the inner heliosphere. For the analysis, we adopt a simplified magnetohydrodynamic model of a CIR. The Energetic Particle Radiation Environment Module, a parallelized particle numerical kinetic code, is used to model PUI distributions using the focused transport equation, including adiabatic cooling/heating, adiabatic focusing, and parallel and perpendicular diffusion. The continuous injection of PUIs is handled as a source term with a ring distribution in velocity space that is produced from the local neutral density obtained from a hot model of the interstellar neutral gas. The simulated distributions exhibit a harder spectrum in the compression region and a softer spectrum in the rarefaction region than that in undisturbed solar wind. As an additional result, a v À5 power law tail distribution above the PUI cutoff speed (a knee in the distribution) emerges for a particular velocity gradient in the CIR. The tail above the PUI cutoff is sensitive to the CIR velocity gradient, and in one observational case studied, this relationship adequately explains the observed spectrum from 2 to 4 times the solar wind speed. This suggests that the velocity gradient associated with the CIR formation can efficiently create a seed population of PUIs before a shock forms even without stochastic acceleration. Thus, local CIR compressions without shocks may play a significant role in the acceleration process as suggested previously. CHEN ET AL.MODELING PICKUP ION DISTRIBUTION 9269 PUBLICATIONS

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A model for pickup ion transport in the heliosphere in the limit of uniform hemispheric distributions

Cited by 39 publications

References 16 publications

The inner source for pickup ions

The inner source for pickup ions

Numerical Solution of the Time‐dependent Kinetic Equation for Anisotropic Pitch‐Angle Scattering

Modeling interstellar pickup ion distributions in corotating interaction regions inside 1 AU

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