  Aims. The simulation of three-wave interaction based plasma emission, thought
to be the underlying mechanism for Type III solar radio bursts, is a
challenging task requiring fully-kinetic, multi-dimensional models. This paper
aims to resolve a contradiction in past attempts, whereby some studies indicate
that no such processes occur. Methods. We self-consistently simulate
three-waved based plasma emission through all stages by using 2D, fully
kinetic, electromagnetic particle-in-cell simulations of relaxing electron
beams using the EPOCH2D code. Results. Here we present the results of two
simulations; Run 1 (nb/n0 = 0.0057, vb/{\Delta}vb = vb/Ve = 16) and Run 2
(nb/n0 = 0.05, vb/{\Delta}vb = vb/Ve = 8), which we find to permit and prohibit
plasma emission respectively. We show that the possibility of plasma emission
is contingent upon the frequency of the initial electrostatic waves generated
by the bump-in-tail instability, and that these waves may be prohibited from
participating in the necessary three-wave interactions due to frequency
conservation requirements. In resolving this apparent contradiction through a
comprehensive analysis, in this paper we present the first self-consistent
demonstration of fundamental and harmonic plasma emission from a single-beam
system via fully kinetic numerical simulation. We caution against simulating
astrophysical radio bursts using unrealistically dense beams (a common approach
which reduces run time), as the resulting non-Langmiur characteristics of the
initial wave modes significantly suppresses emission. Comparison of our results
also indicates that, contrary to the suggestions of previous authors, an
alternative plasma emission mechanism based on two counter-propagating beams is
unnecessary in an astrophysical context.
