<p><strong>Abstract.</strong> We examine how the growth of magnetospheric whistler-mode waves depends on the cold (background) electron number density <i>N</i>₀. The analysis is carried out by varying the cold-plasma parameter <i>a</i> = (electron gyrofrequency)²/(electron plasma frequency)² which is proportional to 1/<i>N</i>₀. For given values of the thermal anisotropy <i>A</i>_T and the ratio <i>N</i>_h/<i>N</i>₀,

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... e <i>N</i>_h is the hot (energetic) electron number density, we find that, as <i>N</i>₀ decreases, the maximum values of the linear and nonlinear growth rates decrease and the threshold wave amplitude for nonlinear growth increases. Generally, as <i>N</i>₀ decreases, the region of (<i>N</i>_h/<i>N</i>₀, <i>A</i>_T)-parameter space in which nonlinear wave growth can occur becomes more limited; that is, as <i>N</i>₀ decreases, the parameter region permitting nonlinear wave growth shifts to the top right of (<i>N</i>_h/<i>N</i>₀, <i>A</i>_T) space characterized by larger <i>N</i>_h/<i>N</i>₀ values and larger <i>A</i>_T values. The results have implications for choosing input parameters for full-scale particle simulations and also in the analysis of whistler-mode chorus data.</p>