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GENERAL LINEAR DYNAMICS OF THE SHEET PINCH
NORMAL MODES WITH WAVE VECTOR PARALLEL
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Alfven wave Appendix approximation asymptotic becomes Chapter component consider constant crossing particle region density diamagnetic drift velocity discussed dispersion relation distribution function drift anisotropy modes eigenfunctions eigenvalue electric field electron temperature anisotropy equation equilibrium magnetic field expression Figure Figure Figure garden-hose instability geomagnetic gradient B drift growth rate imaginary inhomogeneous ion-acoustic wave limit linear localized mode long wavelength low frequency lowest even mode magnetic drift wave magnetic field lines magnetosphere magnetotail marginal stability maximum mirror instability negative neutral sheet crossing neutral surface noncrossing particles normal modes numerically obtain occurs odd modes parallel particle orbit particle trajectories perpendicular phase velocity plasma pressure plasma sheet propagation quadratic form quasilinear resonant electrons resonant particles scale length sheet pinch slow variation solutions spatial variation tail tearing mode term of Eq transverse drift anisotropy transverse waves variational principle vector potential Vlasov wave energy wave vector weak temperature anisotropy zero