Faraday–Fresnel rotation and splitting of orbital angular momentum carrying waves in a rotating plasma

Abstract

Rotational Fresnel drag – or orbital Faraday rotation – in a rotating magnetised plasma is uncovered and studied analytically for Trivelpiece–Gould and whistler–helicon waves carrying orbital angular momentum (OAM). Plasma rotation is shown to introduce a non-zero phase shift between OAM-carrying eigenmodes with opposite helicities, similarly to the phase shift between spin angular momentum eigenmodes associated with the classical Faraday effect in a magnetised plasma at rest. By examining the dispersion relation for these two low-frequency modes in a Brillouin rotating plasma, this Faraday–Fresnel rotation effect is traced back to the combined effects of Doppler shift, centrifugal forces and Coriolis forces. In addition, the longitudinal group velocity in the presence of rotation is shown to depend both on rotation and azimuthal mode, therefore predicting the Faraday–Fresnel splitting of the envelope of a wave packet containing a superposition of OAM-carrying eigenmodes with opposite helicities.

Rotating Alfvén waves in rotating plasmas

“…This coupling is expected to be strongest in the regions where the the dispersion curves of the modes absent rotation (torsional Alfvén waves) and absent magnetic field (inertial waves) intersect, which is highlighted in grey in figure 1. Since as already pointed out by Acheson & Hide (1973) the group velocity of these new modes for waves such that Ω • k = 0 has an azimuthal component, then we expect Fresnel-Faraday rotation as recently identified for Trivelpiece-Gould and Whistler-Helicon high-frequency electronic modes (Rax & Gueroult 2021).…”

Quasilinear theory of Brillouin resonances in rotating magnetized plasmas

“…The function is the solution of Poisson equation. Such solutions of Maxwell–Ampère and Poisson equations were recently identified for the whistler or helicon branch and the Trievelpiece–Gould modes in a rotating plasma (Rax & Gueroult 2021). As shown in Appendix A, the wave is both an SAM and OAM eigenfunction since and the scalar potential wave is an OAM eigenfunction.…”

“…2019 b , 2020). Lastly, adiabatic coupling between wave OAM and particles OAM leads to the Faraday–Fresnel rotation and splitting recently uncovered for Trievelpiece–Gould and helicon modes (Rax & Gueroult 2021). Moving on to resonant coupling, coupling between wave SAM and particles SAM is routinely used for electron and ion cyclotron resonance heating (ECRH/ICRH) in tokamaks (Rax 2011), and has also been proposed for mass separation or particle acceleration (Loeb & Friedland 1986; Pendergast et al.…”

“…In the case of interest the Fourier–Bessel expansion seems more natural given the cylindrical symmetry of the problem. An added motivation for this choice is that recent studies on the OAM Faraday–Fresnel effect (Rax & Gueroult 2021) have shown that the eigenmodes of the whistler branch in a rotating plasma are of the type described by (5.2) with in this case the ordinary Bessel function , and that the eigenmodes of the Trievelpiece–Gould branch in a rotating plasma are of the type described by (5.1) with in this case proportional to , with fulfilling in each case an appropriate dispersion relation. Lastly, the Fourier–Bessel expansion theorem states that all the other branches of the plasma waves spectrum in a rotating plasma can similarly be written with waves of the type (5.1) and (5.2), and that can be represented by as the sum = with .…”

“…On the latter, magnetized rotating plasma theory has been shown to be important in understanding pulsar dynamics and radiative transfer (Gueroult et al. 2019 b ), rotation augmented gyrotropy (Gueroult, Rax & Fisch 2020) or image rotation (aka Faraday–Fresnel effect) in plasmas (Rax & Gueroult 2021). The adiabatic theory of angular momentum perturbation in rotating magnetized plasmas also provides an interesting realization of a geometrical Berry type phase (Rax & Gueroult 2019).…”