Mirror and azimuthal drift frequencies for geomagnetically trapped particles

Hamlin, D.A.; Karplus, Robert; Vik, R. C.; Watson, Kenneth

doi:10.1029/jz066i001p00001

Cited by 274 publications

(167 citation statements)

References 1 publication

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“…), guiding center bounce period. Equation (1) for the dipole field drift r a t e can be shown (with some amount of algebra) to be exactly equivalent to the expression derived by Hamlin, Karplus, Vik, and Watson [1961]. Northrop's result is aesthetically pleasing in that only the familiar particle parameters e , W , J , and T appear in it; our results for the drifts in more general fields share this property.…”

Section: Introductionsupporting

confidence: 60%

Guiding Center Drifts in Time-Dependent Meridional Magnetic Fields

Birmingham

1968

The Physics of Fluids

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The problem of a particle trapped in a time dependent meridional magnetic m i r r o r field and at the same time subjected to a time dependent perpendicular electric field ( E * B = 0) is considered. Bounce averaged guiding center theory is used to derive expressions for the drift velocity components. These drift expressions depend in a straightforward iashion on the struciures d ilie iiiagE&2e and electric fields and on the particle charge, kinetic energy, longitudinal invariant, and bounce period. In the special case of a static magnetic field, no electric field, and J = 0 particles, the drift equations a r e integrated and the bounce averaged guiding center trajectory obtained.iii GUIDING CENTER DRIFTS IN TIME-DEPENDENT

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Section: Introductionsupporting

confidence: 60%

Guiding Center Drifts in Time-Dependent Meridional Magnetic Fields

Birmingham

1968

The Physics of Fluids

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“…[26] In equations (2) and (3), T(a) and P(a) are given approximately by T(a) = 1.30 − 0.56 sin a and P(a) = 0.35 + 0.15 sin a [Hamlin et al, 1961], in which a is the ion's equatorial pitch angle, m i is the ion mass, L is the McIlwain L shell value [McIlwain, 1961], R E is the Earth's radius, B E is the equatorial magnetic field strength at the surface of the Earth, is the azimuthal angle (positive eastward with midnight at 0°), and W E denotes the angular frequency of the Earth's rotation. In addition, y 0 is an electric potential indicating the dawn-dusk convection electric fields [Volland, 1973;Stern, 1975], which is always described as an empirical K p -dependent function [Maynard and Chen, 1975]:…”

Section: Discussionmentioning

confidence: 99%

“…For the fundamental mode, we have N = 0, ±2, ±4,…. [25] The bounce frequency w b of ions with energy W (in Joule) in a dipole field is given by [Hamlin et al, 1961] …”

Section: Discussionmentioning

confidence: 99%

The role of ULF waves interacting with oxygen ions at the outer ring current during storm times

Yang

Zong

et al. 2011

J. Geophys. Res.

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[1] The modulations of the outer ring current O + ion fluxes by ULF Pc5 waves are investigated by multisatellite observations during storm times. The O + ions have energies up to tens of keV. We concentrate on the process in terms of drift-bounce resonance of O + ions with ULF standing waves to understand whether the ring current O + ions could be accelerated/decelerated by ULF waves. Two case studies are performed, in which the Cluster satellites travel the outer ring current region in the morning sector with radial distances of about 5.5 R E . Distinct O + ion flux oscillations are observed associated with fundamental mode ULF standing waves. On 25 October 2002, both satellites SC1 and SC4 observe strong poloidal and toroidal standing waves at approximately the same region one by one with a time lag of 45 min. The O + ion flux oscillations at around 20 keV are dominantly coherent with the poloidal standing wave at 3.4 mHz with cross phases of near 90°with respect to the magnetic field waves. The O + phase space density spectra at 10 to 25 keV, measured by both satellites, deviate significantly from the typical power law distribution. We suggest that the O + ions at 10 to 25 keV are accelerated due to drift-bounce resonance with the poloidal standing wave. On 4 November 2002, satellite SC1 observes considerable poloidal and toroidal standing waves. The O + ion flux oscillation at around 7 keV is well correlated with both of the two wave modes at 3.7 mHz with cross phases of about 90°with respect to the magnetic field waves. The O + spectra at 4 to 8 keV deviates remarkably from the background power law distribution. When satellite SC4 closely encounters the same region 40 min later, the wave activities at 3.7 mHz are found to be rather weak and the O + spectra is close to the background power law distribution. We suggest that the spectra variation of SC1 results from the deceleration of O + ion at 4 to 8 keV via drift-bounce resonances during the strong wave activities. The observations made in this study reveal the effective role of ULF standing waves in accelerating/decelerating the ring current O + ions.Citation: Yang, B., Q.-G. Zong, S. Y. Fu, X. Li, A. Korth, H. S. Fu, C. Yue, and H. Reme (2011), The role of ULF waves interacting with oxygen ions at the outer ring current during storm times,

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“…The overall trajectories of energetic protons in the magnetosphere can be calculated by combining the gradientcurvature drift as given by Hamlin et al [1961] with the E x B drift [e.g., Chisham, 1996] Improvements to our model could be made by using more realistic magnetic and electric fields. Replacing the dipole field in our model with a more realistic magnetic field will introduce effects such as drift-shell splitting.…”

Section: • -•0 L2 Sin ½ -L 'mentioning

confidence: 99%

Modeling the properties of high‐m Alfvén waves driven by the drift‐bounce resonance mechanism

Ozeke¹,

Mann²

2001

J. Geophys. Res.

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Abstract. High-m Alfv6n waves can be driven by drift-bounce resonance with energetic protons in the magnetosphere. We calculate the trajectories of protons in a dipole magnetosphere, including the effects of corotarion and convection electric fields. We propose that the boundary between open and closed orbits, following a partidle injection, can represent a region where unstable particle distributions with df/dW > 0 can develop. Hence we can model the energetically favorable locations

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Mirror and azimuthal drift frequencies for geomagnetically trapped particles

Cited by 274 publications

References 1 publication

Guiding Center Drifts in Time-Dependent Meridional Magnetic Fields

Guiding Center Drifts in Time-Dependent Meridional Magnetic Fields

The role of ULF waves interacting with oxygen ions at the outer ring current during storm times

Modeling the properties of high‐m Alfvén waves driven by the drift‐bounce resonance mechanism

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