Magnetosonic wave instability by proton ring and shell distributions

Both proton ring and shell distributions, providing a positive gradient along the perpendicular direction, can trigger ion Bernstein instabilities and excite magnetosonic (MS) waves in the Earth’s inner magnetosphere. A thorough comparison of the ion Bernstein instability due to the proton ring and shell distributions has not been performed. In this study, we perform and compare the MS wave instabilities under different wave normal angles and parameters of ring and shell distributions. We find that (1) compared to shell-driven MS waves, ring-driven MS waves have narrower frequency and wavenumber ranges. (2) The peak growth rates of shell-driven MS waves are always near the first peaks of the square of first-kind Bessel function <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m1"><mml:msubsup><mml:mrow><mml:mi>J</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msubsup></mml:math> . While, The peak growth rates of ring-driven MS waves are near the first peaks of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m2"><mml:msubsup><mml:mrow><mml:mi>J</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msubsup></mml:math> , and shift to the cold plasma dispersion relation as ring velocity or wave normal angle increases. (3) MS wave growth rates increase as first peaks of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m3"><mml:msubsup><mml:mrow><mml:mi>J</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msubsup></mml:math> approach the cold plasma dispersion in frequency-wavenumber domain. This result can be used to explain dependences on ring (shell) velocity and wave normal angle. (4) The MS wave frequency range and growth rates decrease with increasing ring or shell temperature.