Scalar-Longitudinal Modes of Extended Electrodynamics in Perfectly Conducting Cavities and Trapped Modes of Divergence Cleaning
Abstract
In extended electrodynamics, the Lorenz condition is not imposed and C=∇·A+μ0ε0∂Φ/∂ t is a dynamical field, which adds a scalar-longitudinal (SL) family to the TE, TM and TEM modes of a cavity. With C=0 on the wall of a closed perfectly conducting cavity, the classical resonances remain unchanged, while the SL modes are the Dirichlet eigenmodes of the volume, with B=0 and an electric field along ∇ C. In uniform cavities they share the frequencies of the TM modes that vary along the axis, and for a connected wall the fundamental remains classical. Matching at a conductor described by its constitutive laws gives ∂ C/∂ n=0 instead and couples the scalar-bearing modes to the Maxwell field. The results belong to the C=0 problem, the condition that separates the sectors and the one divergence cleaning imposes. The rectangular, circular cylinder and coaxial cavities provide benchmarks, together with the damping time that gives the slowest scalar mode its fastest decay.
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BibTeX
@misc{rentzber2026scalarlongitudinal,
title = {{Scalar-Longitudinal Modes of Extended Electrodynamics in Perfectly Conducting Cavities and Trapped Modes of Divergence Cleaning}},
author = {Natan Rentzber and Jacob Howard and Fernando Minotti and Anatoliy Pinchuk and Giovanni Modanese},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.33953},
eprint = {2610.33953},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.33953},
}
RIS
TY - UNPB
TI - Scalar-Longitudinal Modes of Extended Electrodynamics in Perfectly Conducting Cavities and Trapped Modes of Divergence Cleaning
AU - Natan Rentzber
AU - Jacob Howard
AU - Fernando Minotti
AU - Anatoliy Pinchuk
AU - Giovanni Modanese
PY - 2026
DA - 2026/10/24
PB - arXiv
DO - 10.48550/arxiv.2610.33953
UR - https://arxiv.org/abs/2610.33953
AB - In extended electrodynamics, the Lorenz condition is not imposed and C=∇·A+μ_0ε_0∂Φ/∂ t is a dynamical field, which adds a scalar-longitudinal (SL) family to the TE, TM and TEM modes of a cavity. With C=0 on the wall of a closed perfectly conducting cavity, the classical resonances remain unchanged, while the SL modes are the Dirichlet eigenmodes of the volume, with B=0 and an electric field along ∇ C. In uniform cavities they share the frequencies of the TM modes that vary along the axis, and for a connected wall the fundamental remains classical. Matching at a conductor described by its constitutive laws gives ∂ C/∂ n=0 instead and couples the scalar-bearing modes to the Maxwell field. The results belong to the C=0 problem, the condition that separates the sectors and the one divergence cleaning imposes. The rectangular, circular cylinder and coaxial cavities provide benchmarks, together with the damping time that gives the slowest scalar mode its fastest decay.
ER -