  Toroidal Alfv\'en eigenmodes (TAEs) are gap modes induced by the toroidicity
of tokamak plasmas in absence of continuum damping. They can be excited by
energetic particles (EPs) when the EP drive exceeds other dampings. A TAE
benchmark case, which was proposed by the International Tokamak Physics
Activity (ITPA) group, is studied in this work. Numerical calculations of
linear growth of TAEs driven by EPs in a circular-shaped, large aspect ratio
tokamak have been performed using the Hybrid Kinetic-MHD (HK-MHD) model
implemented in the NIMROD code. This HK-MHD model couples a delta f
particle-in-cell (PIC) representation of EPs with the 3D MHD representation of
the bulk plasma through moment closure for the momentum conservation equation.
Both the excitation of TAEs and their transition to energetic particle modes
(EPMs) have been observed. The influence of EP density, temperature, density
gradient and position of the maximum relative density gradient, on the
frequency and the growth rate of TAEs are obtained, which are consistent with
those from eigen-analysis calculations and gyrokinetic simulations for an
initial Maxwellian distribution of EPs. The relative pressure gradient of EP at
the radial location of TAE gap, which represents the drive strength of EPs, can
strongly affect the growth rate of TAEs. When the density and temperature of EP
distribution are above certain threshold, the transition from TAE to EPM occurs
and the mode structure changes.
