<i>L</i>parameter, A new approximation

Hilton, Henry H.

doi:10.1029/ja076i028p06952

Cited by 28 publications

(15 citation statements)

References 4 publications

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“…We use the Olson-Pfitzer tiltdependent static field model [Olson and Pfitzer, 1977] to estimate the magnetic field at each satellite, BSAT, and to calculate the integral invariant I (related to the "bounce" invariant, d [Lyons and Williams, 1984]) for a particle mirroring at the satellite. An oe value and magnetic latitude are associated with each satellite location by labeling the Olson-Pfitzer field line passing through the satellite with the L value of the Earth's (tilted) dipole magnetic field having the same values of BSAT and I [Hilton, 1971]. This method provides a useful ordering of the data for purposes of discussion.…”

Section: Introductionmentioning

confidence: 99%

Substorm injection of relativistic electrons to geosynchronous orbit during the great magnetic storm of March 24, 1991

Ingraham¹,

Cayton²,

Belian³

et al. 2001

J. Geophys. Res.

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Abstract. The great March 1991 magnetic storm and the immediately preceding solar energetic particle event (SEP) were among the largest observed during the past solar cycle, and have been the object of intense study. We investigate here, using data from eight satellites, the very large delayed buildup of relativistic electron flux in the outer zone during a 1.5-day period beginning 2 days after onset of the main phase of this storm. A notable feature of the March storm is the intense substorm activity throughout the period of the relativistic flux buildup, and the good correlation between some temporal features of the lower-energy substorm-injected electron flux and the relativistic electron flux at geosynchronous orbit. Velocity dispersion analysis of these fluxes between geosynchronous satellites near local midnight and local noon shows evidence that both classes of electrons arrive at geosynchron0us nearly simultaneously within a few hours of local midnight. From this we conclude that for this storm period the substorm inductive electric field transports not only the usual (50-300 keV) substorm electrons but also the relativistic (0.3 to several MeV) electrons to geosynchronous orbit. A simplified calculation of the electron oe x B and gradient/curvature drifts indicates that sufficiently strong substorm dipolarization inductive electric fields ( • 10 mV/m) could achieve this, provided sufficient relativistic electrons are present in the source region. Consistent with this interpretation, we find that the injected relativistic electrons have a pitch angle distribution that is markedly peaked perpendicular to the magnetic field. Furthermore, the equatorial phase space density at geosynchronous orbit (L = 6.7) is greater than it is at GPS orbit at the equator (L = 4.2) throughout this buildup period, indicating that a source for the relativistic electrons lies outside geosynchronous orbit during this time. Earthward transport of the relativistic electrons by large substorm dipolarization fields, since it is unidirectional, would constitute a strong addition to the transport by radial diffusion and, when it occurs, could result in unusually strong relativistic fluxes, as is reported here for this magnetic storm.

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Section: Introductionmentioning

confidence: 99%

Substorm injection of relativistic electrons to geosynchronous orbit during the great magnetic storm of March 24, 1991

Ingraham¹,

Cayton²,

Belian³

et al. 2001

J. Geophys. Res.

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“…[55] A decade later, Hilton [1971] introduced a new approximation to calculate L when I and B are known. He approximated F(X) by…”

Section: Discussionmentioning

confidence: 99%

“…In this reference dipole field, L is the radial distance where the magnetic drift shell intersects the equatorial plane. [15] It should be emphasized again that no secular variations should ever be applied to the value M d as was suggested by Hilton [1971] at the end of his brief report. Indeed, making the value of M d dependent on the epoch would generate irretrievable confusion and inconsistency when building unified RB models from data collected over widely different periods of time; it would also generate intricate confusion among the users retrieving predicted fluxes from such heterogeneous RB models for any later epoch or mission dates [Lemaire et al, 1990a[Lemaire et al, , 1990b.…”

Section: Invariant Coordinate Systemsmentioning

confidence: 99%

Using invariant altitude (h_inv) for mapping of the radiation belt fluxes in the low‐altitude environment

Cabrera¹,

Lemaire

2007

Space Weather

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[1] Mapping of the radiation belt environment in the classical (B, L) invariant coordinates is rather poorly resolved at low altitudes where the SAMPEX and DEMETER missions are collecting scientific data. This lack of adequate spatial resolution at low altitudes has been pointed out since 1986. A simple solution to this standing problem is proposed in this article. We recall alternative coordinates that were proposed in the 90s to improve the spatial resolution of binning meshes and radiation belt maps in the lowaltitude region, i.e., near the atmospheric cutoff. Next, we define a new coordinate: the ''invariant altitude,'' h inv , that we recommend instead of B or other invariant drift shell coordinates like B/B 0 or a 0 , the equatorial pitch angle. In McIlwain's reference dipole, the new coordinate, h inv , corresponds to the altitude (in units of km) of mirror points of particles which have given values of B and I or L, calculated by using a geomagnetic field model like the International Geomagnetic Reference Field. The advantages and limitations of the new h inv coordinate are presented. For illustration, the distributions of the omnidirectional fluxes of electrons and protons predicted by the standard AE8 and AP8 radiation belt models are displayed using this new invariant coordinate, as well as by using alternative invariant coordinates like B/B 0 or a 0 . A set of orbits of the SAMPEX, DEMETER, and CRRES spacecraft are displayed in these different coordinate systems to illustrate the advantage of using the invariant altitude h inv to map the radiation belt environment at low altitudes.Citation: Cabrera, J., and J. Lemaire (2007), Using invariant altitude (h inv ) for mapping of the radiation belt fluxes in the lowaltitude environment, Space Weather, 5, S04007,

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“…First, the observed counting rates are extracted from the compressed 240-s accumulations, and 8 geomagnetic coordinates are appended to the three geographic coordinates already present in the data file. The magnetic field magnitude, B, at the position of the space vehicle is evaluated from the T89 model using the current IGRF internal field and the external field corresponding to planetary activity index Kp in the range 2− to 2+; next, the magnetic filed line that passes through the satellite is traced from the satellite to its northern and southern foot points on Earth's surface; the position and value of the minimum magnitude B 0 along this field line is recorded, and the bounce invariant for particles mirroring at the satellite is evaluated; these quantities and Hilton's asymptotic expansion (Hilton, 1971) determine an approximate value (a very good one) for McIlwain's L parameter; two cylindrical coordinates for an equivalent dipole field are also calculated, the distance from the dipole axis, and the distance from the magnetic equatorial plane of the dipole field. Second, the input or true counting rate (the observed counting rate corrected for deadtime) for each channel is modelled as a sum of two contributions: non-electron background counts plus counts that result from a spectrum of incident electrons.…”

Section: Analysis: a Density-temperature Description Of Electrons In mentioning

confidence: 99%

Density and temperature of energetic electrons in the Earth's magnetotail derived from high-latitude GPS observations during the declining phase of the solar cycle

Denton

Cayton

2011

Ann. Geophys.

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Abstract. Single relativistic-Maxwellian fits are made to high-latitude GPS-satellite observations of energetic electrons for the period January 2006-November 2010; a constellation of 12 GPS space vehicles provides the observations. The derived fit parameters (for energies ∼0.1-1.0 MeV), in combination with field-line mapping on the nightside of the magnetosphere, provide a survey of the energetic electron density and temperature distribution in the magnetotail between McIlwain L-values of L = 6 and L = 22. Analysis reveals the characteristics of the density-temperature distribution of energetic electrons and its variation as a function of solar wind speed and the Kp index. The density-temperature characteristics of the magnetotail energetic electrons are very similar to those found in the outer electron radiation belt as measured at geosynchronous orbit. The energetic electron density in the magnetotail is much greater during increased geomagnetic activity and during fast solar wind. The total electron density in the magnetotail is found to be strongly correlated with solar wind speed and is at least a factor of two greater for high-speed solar wind (V SW = 500-1000 km s −1 ) compared to low-speed solar wind (V SW = 100-400 km s −1 ). These results have important implications for understanding (a) how the solar wind may modulate entry into the magnetosphere during fast and slow solar wind, and (b) if the magnetotail is a source or a sink for the outer electron radiation belt.

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Lparameter, A new approximation

Cited by 28 publications

References 4 publications

Substorm injection of relativistic electrons to geosynchronous orbit during the great magnetic storm of March 24, 1991

Substorm injection of relativistic electrons to geosynchronous orbit during the great magnetic storm of March 24, 1991

Using invariant altitude (h_inv) for mapping of the radiation belt fluxes in the low‐altitude environment

Density and temperature of energetic electrons in the Earth's magnetotail derived from high-latitude GPS observations during the declining phase of the solar cycle

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Lparameter, A new approximation

Cited by 28 publications

References 4 publications

Substorm injection of relativistic electrons to geosynchronous orbit during the great magnetic storm of March 24, 1991

Substorm injection of relativistic electrons to geosynchronous orbit during the great magnetic storm of March 24, 1991

Using invariant altitude (hinv) for mapping of the radiation belt fluxes in the low‐altitude environment

Density and temperature of energetic electrons in the Earth's magnetotail derived from high-latitude GPS observations during the declining phase of the solar cycle

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Using invariant altitude (h_inv) for mapping of the radiation belt fluxes in the low‐altitude environment