Effect of Collisions on Electron Waves in a Plasma in a Magnetic Field

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Abstract
This is a study of the effects of electron-electron and electron-ion collisions on small oscillations in a fully ionized plasma imbedded in a constant external magnetic field. The first three moments are taken of the Boltzmann equation with the Bhatnagar-Gross-Krook collision terms. The low-temperature approximation is employed to close the set of equations. The moment equations and Maxwell's equations are solved simultaneously to obtain the dispersion relation for small amplitude electron waves propagating at an arbitrary angle to the external magnetic field. The dispersion relation, the collisional damping included, is studied in various limiting cases. The most striking collisional effect is the reduction and smoothing out of the resonance near the electron cyclotron frequency.