An efficient and positivity‐preserving layer method for modeling radiation belt diffusion processes

Tao, X.; Zhang, L.; Wang, C.; Li, X.; Albert, J. M.; Chan, A. A.

doi:10.1002/2015ja022064

Cited by 16 publications

(21 citation statements)

References 34 publications

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“…First, similar to Li et al [2015], the new pitch angle diffusion coefficient is small near the loss cone, and the new energy diffusion coefficient peaks near 0 ∼ 70 ∘ ; therefore, bounce resonance with magnetosonic waves alone cannot cause rapid loss of relativistic electrons. Instead, it might lead to acceleration of MeV electrons, and this effect is as significant as that from gyroresonance (mainly from Landau resonance) [Tao et al, 2016]. Second, the new D 0 0 is significant for 0 ∼ 90 ∘ ; when combined with other waves that are only effective at pitch angle scattering when 0 ≲ 70 ∘ , bounce resonance with magnetosonic waves can help transport near-equatorially mirroring electrons toward small pitch angles, leading to decrease of electron flux at high 10.1002/2016GL070139 pitch angles.…”

Section: Discussionmentioning

confidence: 99%

Theoretical bounce resonance diffusion coefficient for waves generated near the equatorial plane

Tao

2016

Geophysical Research Letters

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Theoretical bounce resonance diffusion coefficient for waves generated near the equatorial plane with arbitrary wave normal angle distributions is derived. Previous studies either assumed waves to cover the whole bounce trajectory or to have only one wave normal angle for a given frequency. In this work, we theoretically derive a new bounce resonance diffusion coefficient without these limitations. We demonstrate that the pitch angle diffusion from bounce resonance is significant for near‐equatorially mirroring particles using a published magnetosonic wave model. Our results suggest that the bounce resonance diffusion by magnetosonic waves could be an important mechanism for pitch angle scattering of near‐equatorially mirroring particles; therefore, it might be important to include bounce resonance with magnetosonic waves in global radiation belt modeling.

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Section: Discussionmentioning

confidence: 99%

Theoretical bounce resonance diffusion coefficient for waves generated near the equatorial plane

Tao

2016

Geophysical Research Letters

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“…For simplicity, the initial electron pitch angle distribution is assumed to be a sin ( α eq ) distribution (Tao et al, ). For the boundary conditions, PSD is assumed to be zero at E k = 10 MeV and at the loss cone, to be constant at E k = 10 keV, and əF/əα eq = 0 at α eq = 90°.…”

Section: Effect Of Low‐harmonic Ms Waves On the Radiation Belt Electronsmentioning

confidence: 99%

Effect of Low‐Harmonic Magnetosonic Waves on the Radiation Belt Electrons Inside the Plasmasphere

Cui

et al. 2019

JGR Space Physics

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In this paper, we presented two observational cases and simulations to indicate the relationship between the formation of butterfly‐like electron pitch angle distributions and the emission of low‐harmonic (LH) fast magnetosonic (MS) waves inside the high‐density plasmasphere. In the wave emission region, the pitch angle of relativistic (>1 MeV) electrons becomes obvious butterfly‐like distributions for both events (near‐equatorially mirroring electrons are transported to lower pitch angles). Unlike relativistic (>1 MeV) electrons, energetic electrons (<1 MeV) change slightly, except that relatively low‐energy electrons (<~150 keV) show butterfly‐like distributions in the 21 August 2013 event. In theory, the LH MS waves can affect different‐energy electrons through the bounce resonance, Landau resonance, and transit time scattering. By performing the Fokker‐Planck diffusion simulations, we demonstrate that the bounce resonance with the LH MS waves mainly leads to the butterfly pitch angle distribution of MeV electrons, whereas the Landau resonance and transit time scattering mainly affect energetic electrons in the high‐density region.

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“…To demonstrate the effect of pitch angle scattering on electron flux evolution, we use the layer method from Tao et al () to solve the bounce‐averaged pitch angle and energy diffusion equation,

\frac{∂f}{∂t} = \frac{1}{G} \frac{\partial}{\partial α_{0}} G ((), D_{α_{0} α_{0}} \frac{∂f}{\partial α_{0}} + D_{α_{0} p} \frac{∂f}{∂p}) + \frac{1}{G} \frac{\partial}{∂p} G ((), D_{α_{0} p} \frac{∂f}{\partial α_{0}} + D_{pp} \frac{∂f}{∂p}),

where f is the phase space density and

G = p^{2} T (α_{0}) \sin (2 α_{0})

is related to the Jacobian. The initial and boundary conditions are the same as those used by Tao et al ().…”

Section: Analysis Of Bounce Resonance Diffusion Coefficientsmentioning

confidence: 99%

\frac{∂f}{∂t} = \frac{1}{G} \frac{\partial}{\partial α_{0}} G ((), D_{α_{0} α_{0}} \frac{∂f}{\partial α_{0}} + D_{α_{0} p} \frac{∂f}{∂p}) + \frac{1}{G} \frac{\partial}{∂p} G ((), D_{α_{0} p} \frac{∂f}{\partial α_{0}} + D_{pp} \frac{∂f}{∂p}),

where f is the phase space density and

G = p^{2} T (α_{0}) \sin (2 α_{0})

is related to the Jacobian. The initial and boundary conditions are the same as those used by Tao et al (). The diffusion coefficients,

D_{α_{0} α_{0}}, D_{α_{0} p}

, and D p p , are shown in Figure , and they are obtained from the bounce resonance diffusion coefficient D W W as

D_{α_{0} α_{0}} = D_{WW} {((), \frac{\partial α_{0}}{∂W})}^{2}, D_{α_{0} p} = D_{WW} \frac{\partial α_{0}}{∂W} \frac{∂p}{∂W}, and D_{pp} = D_{WW} (())

…”

Section: Analysis Of Bounce Resonance Diffusion Coefficientsmentioning

confidence: 99%

Validation and Analysis of Bounce Resonance Diffusion Coefficients

Tao

2018

JGR Space Physics

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Theoretical bounce resonance diffusion coefficients for waves generated near the equatorial plane are analyzed theoretically and validated numerically using guiding‐center test particle simulations. A previous study demonstrated numerically the sensitivity of the diffusion coefficients to the peak wave normal angle and the maximum wave latitude for electrons in bounce resonance with equatorially confined magnetosonic waves. We demonstrate analytically that the sensitivity of the diffusion coefficients to the peak wave normal angle is due to the narrow width of the wave normal angle distribution of the particular wave model used by the previous study. We also show that there is no dependence on the maximum latitude if particle's mirroring points are located within the wave boundary. By analyzing the contribution of each harmonic resonance to the total diffusion coefficients, we show that the discontinuities of the diffusion coefficients as a function of the equatorial pitch angle (α0) occur when the contribution of a harmonic resonance goes to 0. Using a two‐dimensional pitch angle and energy diffusion simulation, we demonstrate that bounce resonance with magnetosonic waves can cause pitch angle scattering of equatorially mirroring electrons, leading to a smooth variation of flux with α0 for α0∼90∘. We conclude that bounce resonance with magnetosonic waves might be an important mechanism in pitch angle scattering and acceleration of electrons in the radiation belt.

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An efficient and positivity‐preserving layer method for modeling radiation belt diffusion processes

Cited by 16 publications

References 34 publications

Theoretical bounce resonance diffusion coefficient for waves generated near the equatorial plane

Theoretical bounce resonance diffusion coefficient for waves generated near the equatorial plane

Effect of Low‐Harmonic Magnetosonic Waves on the Radiation Belt Electrons Inside the Plasmasphere

Validation and Analysis of Bounce Resonance Diffusion Coefficients

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