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Fredricks 1975
Fredricks, R.W. (1975). A model for generation of bow-shock-associated upstream waves. Journal of Geophysical Research 80: doi: 10.1029/JA080i001p00007. issn: 0148-0227.

It is shown that proton steams reflected from a bow shock structure that partially organizes their distribution in gyrophase in such a way that the reflected beam distribution function has the form Fb(&ngr;2, &ngr;, ϕ), where ϕ is the phase angle for motions perpendicular to the solar wind field B0, are capable of driving a left-hand (Alfv¿n) wave at rest frame frequencies &ohgr;<&OHgr;i. The driven wave amplitude becomes a sharply peaked function of &ohgr;/&OHgr;i=&khgr;, and the location &khgr;=&khgr;0 and peak amplitude of the wave B(&khgr;0) depend critically on the ratio of beam speed Vb to the Alfv¿n speed Ca and on the value of solar wind &bgr;. Driven wave amplitudes are estimated to be up to several gammas for beam speeds (in the rest frame) of Vb~2Vsw. The observed frequency and polarization depend upon Doppler shifting due to solar wind flow, and observed polarization could be either left-hand depending upon the vector properties of the solar wind velocity and magnetic field.

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Journal of Geophysical Research
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