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A theoretical prediction of ion plasma oscillations in a neutral sheet

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Starting from the Vlasov equation the steady state and stability properties of the electron sheet in the Cowley neutral sheet model of the geomagnetic tail are considered. Electrostatic ion plasma oscillations propagating from dusk to dawn are found to be unstable provided the thermal spread normal to the current is sufficiently large. Assuming the population of the neutral sheet to be supplied by the polar wind it is shown how a localisation of the cross tail electric field could lead to the instability first appearing around midnight. It is conjectured that the localisation of the cross tail electric field could continually feed the instability, so leading to enough turbulence to give enhanced reconnection of the magnetic field.

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f :

distribution function

B :

magnetic field strength far from the neutral sheet

a :

sheet half thickness


total potential drop across the tail which is localised to the dusk end of the tail in Cowley's model


potential for the steady state electric field normal to the electron current sheet. This potential exists in that region of the tail that excludes the localised region of cross tail electric field

\(\bar V\) :

average velocity across the tail of electrons in the current sheet

v τ :

average velocity of the electrons normal to the current sheet

p :

canonical momentum of a particle


energy of a particle

KT :

electron energy normal to the sheet (1/2m e v τ 2 )

KT i :

ion energy (1/2m i V 2)


electron gyrofrequency far from the neutral sheet

Ωi :

ion gyrofrequency far from the neutral sheet

Ay :

steady state vector potential for the magnetic field

A :

−Ay/aB 0 (normalised vector potential)


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When perturbing the steady state, dashes have been used to denote the time dependent first order quantities. Where no confusion could arise the dashes are dropped, e.g.Ey=Ey′ since there is no zero orderEy in the region considered in the stability analysis.

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Bowers, E.C. A theoretical prediction of ion plasma oscillations in a neutral sheet. Astrophys Space Sci 21, 399–423 (1973). https://doi.org/10.1007/BF00643105

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  • Magnetic Field
  • Steady State
  • Theoretical Prediction
  • Stability Property
  • Vlasov Equation