We study the enhanced damping of Trivelpiece-Gould modes in a nonneutral plasma column, due to application of a Debye-shielded cylindrically symmetric squeeze potential [phi]₁. Damping of these plasma modes is caused by additional Landau resonances at energies En for which the particle bounce frequency [omega]b(En) and the wave frequency [omega] satisfy [omega] = n[omega]b(En). In the first chapter we assume a smooth squeeze of finite width and find that additional resonances induced by the squeeze cause substantial damping, even in the large wave phase velocity compared to thermal velocity regime. For [omega]/ k >> (T /m) and [phi]₁ << T , the resonance damping rate has a I[phi]₁I² dependence. This dependence agrees with the simulations and experimental results. In chapter 2 a narrow partition-like squeeze is added to an unsqeezed 1D plasma and we evaluate the plasma heating, caused by cylindrically symmetric plasma modes. As in chapter 1, collisionless heating is enhanced by the squeeze, due to additional resonances, even when [omega]/k >> (T /m). Adding collisions to the theory broadens these resonances and also creates a boundary layer at the separatrix between trapped and passing particles. This further enhances the heating at [omega]/k vs < 1, where vs is the separatrix velocity. We study the nonlinear interaction of TG waves in chapter 3. We obtain corrections to the forms and frequencies of weakly nonlinear modes. Futhermore, we study the decay instability between a dominant axial mode m = 2 and a small amplitude mode m = 1, using both analytical and numerical techniques. In chapter 4, we study nonlinear interactions of the novel Electron Acoustic Waves in a 1D plasma. Here, we use a weakly nonlinear analysis of a 1D Vlasov-Poisson system, in a modified Maxwellian equilibrium, flattened at the phase velocity of the waves. Using numerical simulation of the 1D Vlasov-Poisson system, we study the unstable collapse of an EAW mode m = 2 to an EAW mode m = 1 and compare the numerically-obtained exponential growth rates to the analytically obtained results