Diagnosis of Strong Beam-Plasma Turbulence Conditions from Electromagnetic Emission

Electromagnetic emission from strong beam-plasma experiments displays scaling with the beam-instability growth rate ${\gamma }_b$. We relate this to the underlying turbulence through a simple model balancing rates of electrostatic energy transfer from the beam to the plasma. A transition from subsonic to supersonic turbulence appears as a break in the scaling of emitted power with ${\gamma }_b$. The implied values of the electrostatic-wave energy density obtained by measurement of the scattering of the relativistic beam agree qualitatively with the model, and yield $W\equiv \frac{E^2}{4\pi \mathrm{nkT}}\cong 0.01 \mathrm{to} 1$. The scattering waves apparently have phase velocities near the beam velocity.