The growth rate of field-aligned electromagnetic ion cyclotron (EMIC) waves in the terrestrial magnetosphere is investigated using an anisotropic kappa particle distribution to model the energetic ring current ions. Under such conditions, the wave dispersion relationship can be expressed in terms of the recently introduced modified plasma dispersion function. This function is analogous to the plasma dispersion function defined by Fried and Conte which has previously been used extensively to investigate wave instability in a hot Maxwellian plasma. Calculations for kappa distributions under magnetospheric conditions indicate that the previous results, obtained with a Maxwellian distribution, tend to overestimate the peak convective growth rate of L mode waves. Nonetheless, the dominant spectral properties of EMIC waves, as reported from AMPTE observations, can be understood in terms of cyclotron resonant instability using realistic magnetospheric parameters. Significant convective amplification is mainly confined to the outer (L>=5) magnetosphere. In the afternoon sector, where plasma densities can exceed 107 m-3, intense wave growth is possible in two bands, one above and one below the helium gyrofrequency ΩHe+. Conversely, on the nightside or for early morning conditions, lower ambient plasma density only allows instability above ΩHe+. High concentration of thermal helium can strongly suppress instability in the band above ΩHe+, but it has little effect on wave growth in the band below ΩHe+.