Larmor power
The instantaneous total radiated power P = q²a²/(6πε₀c³) of an accelerating point charge, integrated over all solid angle. Synonym of the Larmor formula result; the quantity that appears as the rate of energy loss in radiation-reaction problems.
Definition
Larmor power is the instantaneous total electromagnetic power radiated by a non-relativistic accelerating point charge — the result of integrating the radiation Poynting flux over a sphere at infinity. Numerically P = q²a²/(6πε₀c³); for an electron (q = e, m = m_e) at acceleration a this evaluates to about 5.7×10⁻⁵⁴·(a / [m/s²])² watts, a number that makes clear why laboratory-scale accelerations radiate negligibly but particle-accelerator accelerations (~10²⁰ m/s² in a synchrotron bend) do not.
The quantity functions as an energy-conservation bookkeeper: it is the rate at which kinetic energy must be drained from the charge to pay for the outgoing radiation field. This bookkeeping is what motivates the radiation-reaction force of §10.6 — if power P is being radiated, an effective force F_rad must be doing negative work at the same rate, F_rad·v = −P. Working back from P = q²a²/(6πε₀c³) to the simplest local force expression that satisfies this energy-balance constraint on time-averaged over a cycle gives the Abraham-Lorentz result F_rad = (μ₀q²/6πc)·da/dt, which is proportional to the jerk rather than the acceleration itself. The relativistic generalisation (Liénard) retains the same functional dependence on acceleration squared but picks up a γ⁶ or γ⁴ prefactor depending on the angle between v and a. In astrophysical contexts (pulsar spin-down, synchrotron cooling of relativistic electrons in supernova remnants), the Larmor power integrated over the lifetime of a source sets the total radiated energy budget.