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The magnitudes of the harmonic fields which are generated when an alternating electric field is applied to a plasma are calculated. The plasma has a density gradient and is immersed in a uniform static magnetic field. The harmonics are very strongly excited near the upper hybrid frequency. A fluid theory is employed to describe the highly non linear behavior near resonance and a kinetic theory is used to find the effect of a finite temperature. It is found that kinetic effects are important if the radius of gyration is comparable in size to the scale length.