This work reports on numerical calculations concerning the kinetic properties of low-n, low-m toroidal Alfvén eigenmodes (TAEs) in tokamak plasmas for fusion relevant parameters. The selfconsistent and non-perturbative code Ligka [Ph. Lauber, Ph.D. Thesis, TU München, (2003)] is employed. It is based on a linear gyro-kinetic model consisting of the quasi-neutrality equation and the moment equation for the perturbed current. It is shown that in a certain limit the underlying equations of Ligka can be simplified to the equations known as the 'reduced kinetic model'. An antenna-like version of Ligka allows one to systematically find all shear-Alfvén-type modes in a given frequency interval, such as kinetic TAEs (KTAEs) and kinetically modified TAEs. The coupling to the kinetic Alfvén wave (KAW) is found in the form of continuum damping and radiative damping. For the cases examined here, no mode conversion in the centre is found. In the case of a large non-ideal parameter, damping rates around 0.5 - 1% are found, close to experimental measurements.