Electromagnetic plasma wave modes propagating along light-cone coordinates

TL;DR

This work develops a new class of exactly solvable, one-dimensional electromagnetic plasma wave modes propagating along light-cone coordinates $\eta=x-t$ and $\xi=x+t$, by solving the cold relativistic Maxwell–fluid equations in a separable form with $\rho$ and $\chi$ built from $\eta$ and $\xi$. The authors construct several families of wavepacket solutions using special functions—Airy, Parabolic Cylinder, Mathieu, and Bessel—each arising from different Weber/Mathieu-type separations along the light-cone, and analyze their energy transport properties. A detailed treatment of the Double Airy mode reveals a well-defined wavefront and tunable localization controlled by the scale parameter $\alpha$, with energy velocity remaining subluminal yet approaching $c$ for small $\alpha$, implying accelerating, near-light-front propagation. The paper also outlines generalizations to multi-dimensional wavepackets and discusses potential laboratory realizations and extensions to 3D, highlighting the practical relevance for structured light in plasmas and new pathways for manipulating electromagnetic energy in plasma media.

Abstract

We present new electromagnetic plasma modes that propagates in one time and one space coordinates. Differently to the usual plane wave solution, which is written in terms of separation of variables, all our solutions are along the light-cone coordinates. This allow us to find several new wavepacket solutions whose functionality properties rely on the conditions imposed on the choice for their light-cone coordinates dependence. The presented wavepacket solutions are constructed in terms of multiplications of Airy functions, Parabolic cylinder functions, Mathieu functions, or Bessel functions. We thoroughly analyze the case of a double Airy solution, which have new electromagnetic properties, as a defined wavefront, and velocity faster than the electromagnetic plane wave counterpart solution. It is also mentioned how more general structured wavepackets can be constructed from these new solutions.

Figures (3)

• Figure 1: Double Airy solution described in Sec. \ref{['douairy']} evolving for three times. Upper row for $\alpha=1$, and lower row for $\alpha=0.05$. Without loss of generality, we have chosen $\omega_p=1$.
• Figure 2: Double Airy solution described in Sec. \ref{['douairy']} for $t=120$ for three $\alpha$ values (and $\omega_p=1$). Vertical lines represent their respective wavefront positions.
• Figure 3: Wavepacket \ref{['wavepacketG']} for the Double Airy solution, with $\zeta(\alpha)=\exp(-\delta\, \alpha^2)$. We consider $t=120$ and $\omega_p=1$. Blue line is for $\delta=1$. Red line is for $\delta=10$. Green line is for $\delta=100$.