Do polar-cap pair discharges reproduce observed pulsar radio spectra?

In plain words

Bursts of electron-positron pair creation above the magnetic poles may generate the radio waves directly; whether they produce the right brightness and spectrum is untested.

Precise statement

Using global 3D kinetic plasma simulations with quantum-electrodynamic pair production at realistic field strength ($B \sim 10^{12}\,\mathrm{G}$) and scale separation, compute the radio luminosity, spectrum and polarization from polar-cap discharges and compare with population averages (spectral index $\sim -1.6$, luminosity versus spin-down power). Answer: yes or no with a quantitative comparison.

What would settle it

Simulations reaching realistic scale separation whose extrapolated spectra and luminosities agree or disagree with survey statistics.

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