English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We calculate the energy radiated coherently by a system of $N$ charged nonrelativistic particles. It disagrees with the energy loss which is obtained ifone employs the Lorentz Abraham Dirac (LAD) equation for each particle, andsums up the contributions. This fact was already clearly stated in theclassical literature long ago. The reason for the discrepancy is the omissionof the mixing terms in the Poynting vector. For some simple systems we presenta generalized equation for the radiation reaction force which cures thisdefect. The counter examples show that the LAD equation cannot be generallyvalid and that all "proofs" must fail somewhere. We demonstrate this failurefor some popular examples in the literature.

Where the Lorentz-Abraham-Dirac equation for the radiation reaction force fails, and why the "proofs" break down