Jupiter Radiation Belt Energy Budget: Synchrotron Luminosity, Electron Energy Content and Loss Timescales from Radio Observations

This paper computes a quantitative budget for the magnetosphere of Jupiter from published spacecraft values, using a deliberately transparent calculation whose every step can be checked from the deposited script. The headline results are: synchrotron_power_W = 1e+11; total_electron_energy_J = 1.6e+19; synchrotron_loss_time_years = 5.08; electron_energy_density_J_m3 = 1.6e-08; particle_to_magnetic_energy_ratio = 0.0403. The radiative loss timescale comes out of order years, and longer under other representative choices in the published range, which tells us synchrotron radiation, for all its observability, is a minor energy drain on the belts: the electrons are far more likely to be lost by scattering into the atmosphere or by radial transport than by radiating. The particle energy density is a small fraction of the magnetic energy density, confirming that the field is the organising agent and the particles a trace population energetically, however hazardous they are to spacecraft. The treatment states its inputs, its geometric and physical assumptions, and the sensitivity of each conclusion to those choices, so that the results function as a consistency test on the published values as much as a derivation from them. Where the computed budget agrees with independent determinations, the agreement corroborates both; where it strains, the strain identifies the input or assumption most likely to need revision.