Kinetic plasma waves carrying orbital angular momentum

D. R. Blackman, R. Nuter, Ph. Korneev, and V. T. Tikhonchuk

Phys. Rev. E 100, 013204 – Published 15 July 2019

Abstract

The structure of Langmuir plasma waves carrying a finite orbital angular momentum is revised in the paraxial approximation. It is shown that the kinetic effects related to higher-order momenta of the electron distribution function lead to coupling of Laguerre-Gaussian modes and result in a modification of the wave dispersion and damping. The theoretical analysis is compared to the three-dimensional particle-in-cell numerical simulations for a mode with orbital momentum $l = 2$ . It is demonstrated that propagation of such a plasma wave is accompanied with generation of quasistatic axial and azimuthal magnetic fields which result from the orbital and longitudinal momenta transported with the wave, respectively.

Received 25 March 2019

DOI:https://doi.org/10.1103/PhysRevE.100.013204

Physics Subject Headings (PhySH)

Electrostatic waves & oscillations Laser-plasma interactions Optical vortices

Particle-in-cell methods Plasma kinetic theory

Plasma Physics

Authors & Affiliations

D. R. Blackman ¹, R. Nuter¹, Ph. Korneev^2,3, and V. T. Tikhonchuk^1,4

¹CELIA, University of Bordeaux, CNRS, CEA, F-33405 Talence, France
²National Research Nuclear University “MEPhI” (Moscow Engineering Physics Institute), Moscow 115409, Russia
³P. N. Lebedev Physics Institute, Russian Academy of Sciences, 119991 Moscow, Russia
⁴ELI-Beamlines, Institute of Physics, Czech Academy of Sciences, 25241 Dolní Břežany, Czech Republic

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Issue

Vol. 100, Iss. 1 — July 2019

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Images

Figure 1
Dispersion (a) and damping (b) of the OAM plasma wave calculated using Eqs. (30) and (31). Values on these graphs are calculated using the wave width $w_{b, 0} / λ_{D} = 12$ (red triangles), 25 (blue circles), and 100 (green diamonds) and for the OAM conditions $l = 2, p = 0$ . The black crossed line on (a) shows the standard Bohm-Gross dispersion corresponding to $w_{b, 0} / λ_{D} \to \infty$ , while the black dashed line on (b) shows the damping rate in the limit $k^{2} λ_{De} w_{b, 0} ≫ 1$ .
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Figure 2
Results from a PIC simulation 16 periods after the initial 10-period setup phase. The plots on the top are of $δ n_{e} / n_{e 0}$ , the middle of $E_{θ}$ , and the bottom of $E_{r}$ . The electric fields are normalized by the plasma field $E_{p} = m_{e} c ω_{p e} / e$ . The plots on the left, (a), (c), and (e), show transverse slices (with no image filter applied) taken from the center of the PIC code box, with the propagation $(z)$ axis going into the page. The dashed lines shown in the transverse slices are the line outs used to plot the graphics on the right. The plots on the right, (b), (d), and (f), are line outs from the slices (filtered green, unfiltered light green) compared with theoretical predictions with an $a_{0} = 0.2$ (black dashed lines) plotted against the position along the line outs $d$ plotted in (a), (c), and (e); this corresponds to $y \cos ϕ$ where $ϕ$ is the angle the line out would make with the $y$ axis.
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Figure 3
Three 3D views of the electron density deviation in the plasma wave, calculated in the ocean PIC code for the plasmon mode $p = 0, l = 2$ , data taken 16 periods after the initial 10 period setup phase. The views along the propagation axis, and across the transverse axis, are shown with a parallel projection, and the final tilted image uses a convergent projection. The red and blue surfaces show surfaces of constant $δ n_{e} / n_{e 0}$ , and the light green surface corresponds to a positive density perturbation with a value of $80 %$ the amplitude of the plasmon. The dark blue surface shows a negative density perturbation with the same absolute value as the red surface. In addition to the surfaces of constant density the magnetic field lines for the interior (interior red thin lines) and exterior (exterior light thin purple lines) regions of the plasmon are shown. The magnetic field lines are calculated using the magnetic field values taken from the PIC code and the mayavi2 [15] streamline package; the first figure includes arrows to denote the direction of propagation of the magnetic field lines.
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Figure 4
Results from the same PIC simulation as in Fig. 2. The plots on the top show the azimuthal magnetic field $B_{θ}$ and the bottom show the axial magnetic field $B_{z}$ , both normalized to the field $B_{p} = m_{e} ω_{p e} / e$ . The plots on the left show the central transverse slice from the PIC box (filtered using a Gaussian filter with a width equal to one cell and the plots on the right show line outs from these slices (light green unfiltered data, green filtered data) compared with a theoretical model using $a_{0} = 0.2$ (black dashed line). Due to this being a second-order effect there is considerable noise seen in the magnetic field, despite there being $\sim 100$ particles per cell in the simulation. Nevertheless, after a filter is applied to the axial field, a good match to the theoretical model can be seen.
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Figure 5
The upper plot shows the amplitude of the electric field components, with red triangles showing the axial, blue diamonds the azimuthal, green circles the radial electric fields, and finally black crosses showing the electron density component. The vertical dashed line shows the point in the simulation where the amplification process stops. The horizontal dashed lines show the component amplitudes for a reference $a_{0} = 0.2$ in the same color and marker scheme. The lower plot shows the amplitude of magnetic field components in the PIC simulation. Red lines with triangles correspond to the axial field, and blue lines with diamonds to the azimuthal field, with the solid line corresponding to the PIC simulation; the darker solid line corresponds to an average over a Gaussian window over three periods. No radial magnetic field is observable.
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