Nonlinear Scalar Interactions in the EMDrive: Petiau's Elliptic-Function Approach

TL;DR

The paper tackles the apparent momentum-violation signals associated with EMDrive by proposing a beyond-Maxwell framework in which the electromagnetic field kinetically couples to a light scalar via $g\phi F_{\mu\nu}\tilde{F}^{\mu\nu}$. Using Petiau's elliptic-function solutions to nonlinear wave equations, the authors construct exact nonlinear cavity modes and combine them through Jacobi addition theorems to generate spatially asymmetric field configurations. They derive a cubic nonlinear wave equation for the cavity field, compute a modified stress tensor, and show a small but finite momentum flux that, in principle, can produce thrust for certain scalar masses and couplings, with enhancement possible in high-$Q$ cavities. The approach yields testable predictions, including a scaling $\Delta T \propto g^2 B_0^4/m^2$, connections to axion-like particle searches, and clear null tests, thereby linking EMDrive-like thrust to ultralight dark-matter scenarios and guiding future precision cavity experiments.

Abstract

The EMDrive, a controversial electromagnetic propulsion concept, challenges momentum conservation in standard Maxwell electrodynamics. We propose a beyond-Maxwell framework by coupling the electromagnetic field to a light scalar field, inspired by axion-like particle models and effective field theory. Using Guy Petiau's 1958 elliptic-function solutions for nonlinear wave equations, we construct exact cavity modes and combine them via Jacobi addition theorems. These nonlinear modes produce an asymmetric momentum flux, suggesting a theoretical pathway for EMDrive thrust. We compute the stress-tensor asymmetry numerically and show that while standard axion-like particles yield negligible effects, light scalars beyond current constraints could produce measurable thrust. The framework provides testable predictions connecting EMDrive physics to dark matter searches.

Figures (1)

• Figure 1: Top: Nonlinear field solution $\psi_{12}(\xi)$ in the EMDrive cavity ($k=0.8$, $\lambda=0.1$). The asymmetric profile ($\delta_1=0$, $\delta_2=5$) results from scalar-photon coupling and Jacobi addition theorem. Parameters: $\omega=1.0$, $A=2.794$, $B=1.334$, cavity length $L=4K(k)/B \approx 5.983$. Bottom: Modified stress tensor $T_{zz}(\xi)$ corresponding to the field profile in the top. The momentum flux imbalance $\Delta T = T_{zz}(L/2) - T_{zz}(0) = -8.0 \times 10^{-4}$ indicates net thrust toward $\xi=0$. Vertical lines mark positions where stress asymmetry is evaluated.