  Electromagnetic fundamental and harmonic emission is ubiquitously observed
throughout the heliosphere, and in particular it is commonly associated with
the occurrence of Type II and III solar radio bursts. Classical analytic
calculations for the plasma-emission process, though useful, are limited to
idealized situations; a conclusive numerical verification of this theory is
still lacking, with earlier studies often providing contradicting results on
e.g. the precise parameter space in which fundamental and harmonic emission can
be produced. To accurately capture the chain of mechanisms underlying plasma
emission - from precursor plasma processes to the generation of electromagnetic
waves over long times - we perform large-scale, first-principles simulations of
beam-plasma instabilities. By employing a very large number of computational
particles we achieve very low numerical noise, and explore (with an array of
simulations) a wide parameter space determined by the beam-plasma density ratio
and the ion-to-electron temperature ratio. In particular, we observe direct
evidence of both fundamental and harmonic plasma emission when the
beam-to-background density ratio $\le$0.005 (with beam-to-background energy
ratio ~0.5), tightly constraining this threshold. We observe that,
asymptotically, in this regime ~0.1% of the initial beam energy is converted
into harmonic emission, and ~0.001% into fundamental emission. In contrast with
previous studies, we also find that this emission is independent of the
ion-to-electron temperature ratio. In addition, we report the direct detection
of third-harmonic emission in all of our simulations, at power levels
compatible with observations. Our findings have important consequences for
understanding the viable conditions leading to plasma emission in space
systems, and for the interpretation of observed electromagnetic signals
throughout the heliosphere.
