Abstract
Abstract. An optimal approach reducing the population of MeV electrons in the magnetosphere is presented. Under a double resonance condition, whistler wave is simultaneously in cyclotron resonance with keV and MeV electrons. The injected whistler waves is first amplified by the background keV electrons via loss-cone negative mass instability to become effective in precipitating MeV electrons via cyclotron resonance elevated chaotic scattering. The numerical results show that a small amplitude whistler wave can be amplified by more than 25 dB. The amplification factor reduces only about 10 dB with a 30 dB increase of the initial wave intensity. Use of an amplified whistler wave to scatter 1.5 MeV electrons from an initial pitch angle of 86.5°to a pitch angle <50° is demonstrated. The ratio of the required wave magnetic field to the background magnetic field is calculated to be about 8×10−4.
Highlights
In the magnetosphere, energetic electrons are trapped by the Earth’s magnetic dipole field to undergo a bouncing motion about the geomagnetic equator
The relativistic cyclotron resonance condition is a quadratic equation in the electron momentum, there exists a double resonance situation (Kuo et al, 2007), namely, a whistler wave is simultaneously in cyclotron resonance with the keV electrons and with the MeV electrons
To simplify the formulation while retaining the essential physics, the magnetic dipole field is modeled by a parabolic scalar potential, φ=−mωb2z2/2e, superimposed over a uniform magnetic field, B0=B0z, where z is the distance from the equatorial plane
Summary
Energetic electrons are trapped by the Earth’s magnetic dipole field to undergo a bouncing motion about the geomagnetic equator. The relativistic cyclotron resonance condition is a quadratic equation in the electron momentum, there exists a double resonance situation (Kuo et al, 2007), namely, a whistler wave is simultaneously in cyclotron resonance with the keV electrons and with the MeV electrons This suggests an optimal approach, which applies the chaotic scattering process under a double resonance condition, for the control of the population of MeV electrons trapped in the magnetosphere. This approach first uses keV electrons (having a loss-cone velocity distribution) to energize the incident whistler waves, which become more effective to precipitate MeV electrons into loss cones, via cyclotron resonance enhanced chaotic scattering.
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