This thesis presents an investigation of the lower-hybrid drift instability(LHDI) in a thin Harris current sheet with a guide field. This includes three-dimensional analytical and numerical analyses using the gyrokinetic electron, fully-kinetic ion(GeFi) description, which are compared with results from the Vlasov approach and simulations. Previous fully-kinetic studies solve the electron Valsov equation by integrating along the unperturbed phase-space orbits, including the complete electron-cyclotron motion. The LHDI satisfies ω << ω_ce and k_perpρ_e ∼ 1, where ω_ce and ρ_e are the electron cyclotron frequency and Larmor radius, respectively, and k_perp& is the wavevector perpendicular to the equilibrium magnetic field. By treating the electron response with gyrokinetic theory, the fast cyclotron motion is removed which greatly simplifies the derivation of the LHDI eigenvalue equations. This allows a more comprehensive LHDI analysis, which is carried out over the entire domain of unstable wavevectors. To our knowledge, an extensive scan of the operative domain of the LHDI in current sheets with a guide field has never been done.

The results will show that two types of electromagnetic LHDIs are active in the current sheet. The Type A LHDI is generally consistent with the existing theoretical descriptions of the LHDI, namely, quasi-electrostatic modes localized near the current sheet edges with k ρ_e ∼ 1, k_||=0, and ω ^2 ∼ ω_pi^2/(1+ω_pe^2 / ω_ce^2)$, where ω_pe and ω_pi are the electron and ion plasma frequencies, respectively. However, we will show that in sufficiently thin current sheets, i.e. strong equilibrium drifts, the Type A LHDI is destabilized by finite k_|| in the short wavelength domain, kρ _ce > 0.5. This destabilization increases the range of propagation angles, k_||/k_perp, for which the modes are operative, which reduces the localizing and stabilizing effects of magnetic shear. The dominant Type A modes are localized near the current sheet edge, z ∼ 1.5 L, due to the stabilizing resonant dissipation of the electron grad B drift, which is strongest near the current sheet center. At longer wavelengths, k^2 ρ_eρ_i ∼ 1, a second group of instabilities arise, which we define as Type B LHDIs. The Type B LHDIs are operative for a large range of propagation angles, and are suppressed when the electron grad B drift is removed. The dominant Type B instabilities are localized near the current sheet center, z ∼ 0.2L, with moderate k_||/k_perp and significant magnetic field perturbations. The Type B LHDIs resemble fluctuations observed in nature, and simulations, which have undergone limited analytical analysis. These modes are of general relevance to the evolution of thin current sheets, and may contribute to collisionless magnetic reconnection theory as a source of anomalous resistivity.