We review the general principles of the spectroscopy of plasmas containing quasimonochromatic electric fields (QEFs). We demonstrate that the underlying physics is very rich due to the complicated entanglement of four characteristic times: the typical time required for the formation of the quasienergy states, the lifetime of the excited state of the radiator, the typical time of the formation of the homogeneous Stark broadening by the electron microfield, and the typical time of the formation of the homogeneous Stark broadening by the dynamic part of the ion microfield. We exemplified how the shape and shift of spectral lines are affected by the mutual interactions of the three subsystems. Specifically, the interaction of the radiator with the plasma can be substantially influenced by the interaction of the radiator with the QEF, and vice versa, as well as by the interaction of the QEF and the plasma with each other. We also provide some applications of these various effects. Finally, we outline directions for future research.
We consider an infinite one dimensional array of alternating charges embedded in a two-dimensional configuration space and subjected to a weak static electric field transverse to the lattice axis. Expansion of the Coulomb interaction about a lattice site gives a transverse restoring stiffness
κ∝ζ(3)/L3, defining the oscillator length
ay, while Bloch periodicity is retained along the lattice direction and the transverse motion is represented in a harmonic basis. The Coulomb matrix elements are governed by the dimensionless scale
ηr−s, which couples the reciprocal-lattice transfer to the transverse oscillator length. A regularized one dimensional extension is also introduced through Coulomb regularization, yielding a finite diagonal offset and an exponentially decaying even-transfer coupling in reciprocal space. Small
ηr−s yields logarithmic, parity-dependent transverse-state coupling, while large
ηr−s approaches the one-dimensional Coulomb limit. In the finite-order spectrum, the latter approaches the Kronig Penney reference toward the band edge while retaining distinct Brillouin zone curvature. The formulation therefore identifies two characteristic quantities of the alternating lattice: the transverse restoring stiffness and the one-dimensional Madelung form, while retaining the two dimensional structure required to describe the response to a transverse electric field.
Keywords: alternating charge lattice; Bloch states; Coulomb interaction; transverse electric field; regularization; reciprocal space coupling; Brillouin zone spectrum.