A numerical electromagnetic linear dispersion relation for Maxwellian ring-beam velocity distributions

Umeda, Takayuki; Matsukiyo, Shuichi; Amano, Takanobu; Miyoshi, Yoshizumi

doi:10.1063/1.4736848

Cited by 26 publications

(32 citation statements)

References 16 publications

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“…The new approach we propose is motivated by the development of a dispersion solver that is based on ring beam velocity distributions (Min & Liu, ; Umeda et al, ), rather than the more conventional multiple bi‐Maxwellian distributions. The dispersion solver of Min and Liu treats particle distributions as a sum of multiple individual ring beam distributions of the form (Umeda et al, )

f_{j} ((),, v_{⊥}, v_{∥}) = \frac{n_{j}}{π^{3 / 2} θ_{∥ j} θ_{⊥ j}^{2} C_{j}} e^{- {(v_{∥} - v_{italicdj})}^{2} / θ_{∥ j}^{2}} e^{- {(v_{⊥} - v_{italicrj})}^{2} / θ_{⊥ j}^{2}}

where j denotes the individual ring beam, v dj is the parallel drift speed of the j th beam, v rj is the radius of the velocity space ring, θ || j and θ ⊥ j characterize the thermal spread of the ring in the directions parallel and perpendicular to the magnetic field, and C j is a constant of the form

C_{j} = e^{- v_{rj}^{2} / θ_{⊥ j}^{2}} + \sqrt{π} ((), \frac{v_{rj}}{θ_{⊥ j}}) ([], 1 + italicerf ((), \frac{v_{rj}}{θ_{⊥ j}}))

…”

Section: Characterization Of Distributionsmentioning

confidence: 99%

Ring/Shell Ion Distributions at Geosynchronous Orbit

et al. 2017

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One year's worth of plasma observations from geosynchronous orbit is examined for ion distributions that may simultaneously be subject to the ion Bernstein (IB) instability (generating fast magnetosonic waves) and the Alfvén cyclotron (AC) instability (generating electromagnetic ion cyclotron waves). Confirming past analyses, distributions with robust ∂fp(v⊥)/∂v⊥ > 0 near v|| = 0, which we denote as “ring/shell” distributions, are commonly found primarily on the dayside of the magnetosphere. A new approach to high‐fidelity representation of the observed ring/shell distribution functions in a form readily suited to both analytical moment calculation and linear dispersion analysis is presented, which allows statistical analysis of the ring/shell properties. The ring/shell temperature anisotropy is found to have a clear upper limit that depends on the parallel beta of the ring/shell (β||r) in a manner that is diagnostic of the operation of the AC instability. This upper limit is only reached in the postnoon events, which are primarily produced by the energy‐ and pitch angle‐dependent magnetic drifts of substorm‐injected ions. Further, it is primarily the leading edge of such injections, where the distribution is strongly ring‐like, that the AC instability appears to be operating. By contrast, the ratio of the ring energy to the Alfvén energy remains well within the range of 0.25–4.0 suitable for IB instability throughout essentially all of the events, except those that occur in denser cold plasma of the outer plasmasphere.

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f_{j} ((),, v_{⊥}, v_{∥}) = \frac{n_{j}}{π^{3 / 2} θ_{∥ j} θ_{⊥ j}^{2} C_{j}} e^{- {(v_{∥} - v_{italicdj})}^{2} / θ_{∥ j}^{2}} e^{- {(v_{⊥} - v_{italicrj})}^{2} / θ_{⊥ j}^{2}}

C_{j} = e^{- v_{rj}^{2} / θ_{⊥ j}^{2}} + \sqrt{π} ((), \frac{v_{rj}}{θ_{⊥ j}}) ([], 1 + italicerf ((), \frac{v_{rj}}{θ_{⊥ j}}))

…”

Section: Characterization Of Distributionsmentioning

confidence: 99%

Ring/Shell Ion Distributions at Geosynchronous Orbit

et al. 2017

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“…Such distributions provide a positive gradient parallel and perpendicular relative to the magnetic field. Umeda et al [2007Umeda et al [ , 2012 showed that electromagnetic chorus and electron cyclotron harmonic (ECH) waves could be generated by such distributions. Model chorus waves, for example, were unstable in two relatively narrow bands above and below f ce /2, similar to the observed frequency spectra in Figures 2 and 4.…”

Section: 1002/2013gl059165mentioning

confidence: 99%

Van Allen Probes observations of direct wave‐particle interactions

Fennell

Roeder

Kurth

et al. 2014

Geophysical Research Letters

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Quasiperiodic increases, or "bursts," of 17-26 keV electron fluxes in conjunction with chorus wave bursts were observed following a plasma injection on 13 January 2013. The pitch angle distributions changed during the burst events, evolving from sin N (α) to distributions that formed maxima at α = 75-80°, while fluxes at 90°and <60°remained nearly unchanged. The observations occurred outside of the plasmasphere in the postmidnight region and were observed by both Van Allen Probes. Density, cyclotron frequency, and pitch angle of the peak flux were used to estimate resonant electron energy. The result of~15-35 keV is consistent with the energies of the electrons showing the flux enhancements and corresponds to electrons in and above the steep flux gradient that signals the presence of an Alfvén boundary in the plasma. The cause of the quasiperiodic nature (on the order of a few minutes) of the bursts is not understood at this time.

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“…It should be noted that EN emissions are referred to as magnetosonic mode waves (Boardsen et al, ; Gul'elmi et al, ) and Rauch and Roux () referred to this wave as the class‐2 wave. EN emissions are generated through the ring distribution of the ring current protons (Ma et al, ; Min & Liu, ; Umeda et al, ). EN emissions are generated near the magnetic equator (e.g., Boardsen et al, ; Santolik et al, ) and propagate across the magnetic field lines (Ma et al, ).…”

Section: Introductionmentioning

confidence: 99%

EMIC Waves Converted From Equatorial Noise Due to M/Q = 2 Ions in the Plasmasphere: Observations From Van Allen Probes and Arase

Miyoshi

Matsuda

Kurita

et al. 2019

Geophysical Research Letters

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Equatorial noise (EN) emissions are observed inside and outside the plasmapause. EN emissions are referred to as magnetosonic mode waves. Using data from Van Allen Probes and Arase, we found conversion from EN emissions to electromagnetic ion cyclotron (EMIC) waves in the plasmasphere and in the topside ionosphere. A low‐frequency part of EN emissions becomes EMIC waves through branch splitting of EN emissions, and the mode conversion from EN to EMIC waves occurs around the frequency of M/Q = 2 (deuteron and/or alpha particles) cyclotron frequency. These processes result in plasmaspheric EMIC waves. We investigated the ion composition ratio by characteristic frequencies of EN emissions and EMIC waves and obtained ion composition ratios. We found that the maximum composition ratio of M/Q = 2 ions is ~10% below 3,000 km. The quantitative estimation of the ion composition will contribute to improving the plasma model of the deep plasmasphere and the topside ionosphere.

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A numerical electromagnetic linear dispersion relation for Maxwellian ring-beam velocity distributions

Cited by 26 publications

References 16 publications

Ring/Shell Ion Distributions at Geosynchronous Orbit

Ring/Shell Ion Distributions at Geosynchronous Orbit

Van Allen Probes observations of direct wave‐particle interactions

EMIC Waves Converted From Equatorial Noise Due to M/Q = 2 Ions in the Plasmasphere: Observations From Van Allen Probes and Arase

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