  Cyclotron Radiation Emission Spectroscopy (CRES) is a technique for measuring
the kinetic energy of charged particles through a precision measurement of the
frequency of the cyclotron radiation generated by the particle's motion in a
magnetic field. The Project 8 collaboration is developing a next-generation
neutrino mass measurement experiment based on CRES. One approach is to use a
phased antenna array, which surrounds a volume of tritium gas, to detect and
measure the cyclotron radiation of the resulting $\beta$-decay electrons. To
validate the feasibility of this method, Project 8 has designed a test stand to
benchmark the performance of an antenna array at reconstructing signals that
mimic those of genuine CRES events. To generate synthetic CRES events, a novel
probe antenna has been developed, which emits radiation with characteristics
similar to the cyclotron radiation produced by charged particles in magnetic
fields. This paper outlines the design, construction, and characterization of
this Synthetic Cyclotron Antenna (SYNCA). Furthermore, we perform a series of
measurements that use the SYNCA to test the position reconstruction
capabilities of the digital beamforming reconstruction technique. We find that
the SYNCA produces radiation with characteristics closely matching those
expected for cyclotron radiation and reproduces experimentally the
phenomenology of digital beamforming simulations of true CRES signals.
