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Summary form only given, as follows. At present, the realization of high-density operation with potential confinement is one of the most important issues on the tandem mirror research. The plasma production with ion-cyclotron-range of frequency (ICRF) waves is common in both fusion and plasma applications. In plasmas with relatively low density and small radius the wavelength is in the same order of the plasma size and eigenmodes are formed in both radial and axial directions. Because the wavelength depends strongly on the density, the density is likely to be clamped at the optimum value for the eigenmode formation. The saturation of the density increase is sometimes observed in GAMMA 10. To raise the limit for the density clamping, higher frequency ICRF waves (high harmonic fast waves HHFWs) of which frequencies are from 6 to 10 times ion cyclotron frequency at the midplane of the central cell have been introduced. HHFWs are effectively used for the current drive experiments on the spherical torus. When HHFWs are applied, several eigenmodes with different radial structures will be possibly excited and the restriction of the density clamping becomes moderate. The increase of the density from the saturation level has been clearly observed in the experiments. The excitation of waves with higher mode structure in the radial direction is measured when the apparent density increase is observed.