2015
DOI: 10.1002/2015ja021482
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Limitation of energetic ring current ion spectra

Abstract: We address the problem of determining the limiting energetic ring current ion spectrum resulting from electromagnetic ion cyclotron (EMIC)‐wave‐ion interactions. We solve the problem in a relativistic regime, incorporating a cold background multi‐ion plasma component and without assuming a predetermined form for the ion energy distribution. The limiting (Kennel‐Petschek) spectrum is determined by the condition that the EMIC waves acquire a specified gain over a given convective length scale for all frequencies… Show more

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Cited by 5 publications
(10 citation statements)
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“…We suppose that the EMIC waves generated by the distribution (1) undergo a specified gain G in amplitude during propagation over a convective path length LR E along a magnetic field line, where L denotes magnetic shell and R E is the Earth's radius. Then, as detailed by Summers and Shi (), it can be shown that a limiting energy distribution g ( p ) = g * ( p ) can be achieved where g * is determined by the equation, lefttrueX0[]11italicγω/Ωp1γ0ω/Ωp2X0Xssγ1+sωΩp()1+sγ()ωΩp2()1italicγω/Ωp1γ0ω/Ωp2X0g*pdX,=1mpc212π3Gmpc2cBEeRE1γ0ω/normalΩp2L4X0 where ω is the (real) wave frequency, X = p 2 , γ=1+X, and Ω p = eB 0 /( m p c ) is the proton gyrofrequency where e is the electronic charge. We assume that the background magnetic field strength B 0 equals the equatorial dipole value, B 0 = B E / L 3 .…”
Section: Calculation Of the Limiting Energy Spectrummentioning
confidence: 99%
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“…We suppose that the EMIC waves generated by the distribution (1) undergo a specified gain G in amplitude during propagation over a convective path length LR E along a magnetic field line, where L denotes magnetic shell and R E is the Earth's radius. Then, as detailed by Summers and Shi (), it can be shown that a limiting energy distribution g ( p ) = g * ( p ) can be achieved where g * is determined by the equation, lefttrueX0[]11italicγω/Ωp1γ0ω/Ωp2X0Xssγ1+sωΩp()1+sγ()ωΩp2()1italicγω/Ωp1γ0ω/Ωp2X0g*pdX,=1mpc212π3Gmpc2cBEeRE1γ0ω/normalΩp2L4X0 where ω is the (real) wave frequency, X = p 2 , γ=1+X, and Ω p = eB 0 /( m p c ) is the proton gyrofrequency where e is the electronic charge. We assume that the background magnetic field strength B 0 equals the equatorial dipole value, B 0 = B E / L 3 .…”
Section: Calculation Of the Limiting Energy Spectrummentioning
confidence: 99%
“…Equation , which is an integral equation for g * , is valid for all frequencies ω over which wave growth occurs. The equation can be readily transformed into a linear Volterra integral equation of the first kind (see Summers & Shi, ) and can be solved by standard numerical techniques, as given, for instance, by Press et al (). Once the solution for g * has been found, the limiting omnidirectional differential proton flux (from ) is then given by J4π*()E=2π3/2normalΓ()s+1normalΓ()s+3/2mpc2X0.2emg*()p, where E=()1+X1mpc2.…”
Section: Calculation Of the Limiting Energy Spectrummentioning
confidence: 99%
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