  The excitation of toroidicity induced Alfv{\'e}n eigenmodes (TAEs) using
prescribed external electromagnetic perturbations (hereafter ``antenna") acting
on a confined toroidal plasma as well as its nonlinear couplings to other modes
in the system is studied. The antenna is described by an electrostatic
potential resembling the target TAE mode structure along with its corresponding
parallel electromagnetic potential computed from Ohm's law. Numerically stable
long-time linear simulations are achieved by integrating the antenna within the
framework of a mixed representation and pullback scheme [A. Mishchenko, et al.,
Comput. Phys. Commun. \textbf{238} (2019) 194]. By decomposing the plasma
electromagnetic potential into symplectic and Hamiltonian parts and using Ohm's
law, the destabilizing contribution of the potential gradient parallel to the
magnetic field is canceled in the equations of motion. Besides evaluating the
frequencies as well as growth/damping rates of excited modes compared to
referenced TAEs, we study the interaction of antenna-driven modes with fast
particles and indicate their margins of instability. Furthermore, we show first
nonlinear simulations in the presence of a TAE-like antenna exciting other TAE
modes, as well as Global Alfv\'en Eigenmodes (GAE) having different toroidal
wave numbers from that of the antenna.
