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Introduction
Published in Igor G. Kondrat’ev, Alexander V. Kudrin, Tatyana M. Zaboronkova, Electrodynamics of Density Ducts in Magnetized Plasmas, 2019
Igor G. Kondrat’ev, Alexander V. Kudrin, Tatyana M. Zaboronkova
It is well established that whistlers are waves from lightning flashes near the earth’s surface. These are impulse signals which can penetrate the ionosphere and enter the magnetosphere. It has been shown by Storey in his pioneer work (Storey, 1953) that the ray direction of a whistler must be within about 20° of the direction of the earth’s magnetic field.* Any wave propagating in the whistler mode will therefore tend to travel almost along the geomagnetic field line. It was suggested that the whistler originating in a lightning flash in one hemisphere travels roughly along the geomagnetic field line, over the equator, and reaches earth in the other hemisphere somewhere near the opposite end of the line (a ‘short whistler’). It can be reflected by the earth and return along nearly the same path to a point near its origin (a ‘long whistler’). Sometimes multiple reflections of whistlers back and forth along the same line may occur. This is the mechanism proposed by Storey (1953) for guidance of the low-frequency electromagnetic waves through the magnetosphere. The mechanism is illustrated schematically in Figure 1.1. The curved line shows the geomagnetic field line and the forked arrow indicates a lightning flash, representing the source of the whistlers.
Electromagnetic Waves and Lasers
Published in Hitendra K. Malik, Laser-Matter Interaction for Radiation and Energy, 2021
In case of an R wave, the wave is in resonance(k=∞) with the cyclotron motion of the electrons at ω = ωc. The direction of rotation of the plane of polarization and the direction of gyration of the electrons for this wave are the same, causing the wave to lose energy in continuous acceleration of the electrons and making it incapable of propagating. This wave has a cutoff at ω=ωR and a stop-band between ωR and ωc and below ωc, i.e. whenω<ωc and it propagates at a velocity less than the speed of light c. The wave in this low frequency region is called the whistler mode. The whistler waves are extremely useful in the study of ionospheric phenomena. The L wave, on the other hand, has no resonance with the cyclotron motion of the electrons and has a lower cutoff frequency ωL compared with the cutoff frequency ωR of the R wave. This wave could have been in resonance with the motion of ions under the action of magnetic field B→0. Since we have neglected this motion, the term revealing the resonance is not appearing in the dispersion relation of the L wave.
Nonlinear whistler wave turbulence in pulsar wind nebula: FDTD simulations
Published in Waves in Random and Complex Media, 2023
Asif Shah, Saeed Ur Rehman, Q. Haque
Pulsars are rotating neutron stars characterized by an extremely high density, strong magnetic fields, and emit relativistic winds comprising of matter (electrons) and antimatter (positrons) particles [1,2]. When these winds interact with interstellar gas, luminous pulsar wind nebulae (PWN) are generated, having an electromagnetic spectrum in synchrotron and optical range [2]. Chandra observations have tracked PWN with radio and γ-rays under shocked conditions. The PWN structure and spectral characteristics depend on angular momentum, magnetic field, beam streaming speeds and properties of the ambient matter [3]. The AMS-02 experiment has observed positron and electron fluxes in PWN [4]. The interaction of PWN and reverse shock leads to the coexistence of thermal and nonthermal fluids [5]. It has been suggested that radio emissions from PWN are due to instantly accelerated electrons [6]. Resonant cyclotron absorption is thought to be an appropriate model for plasma acceleration in PWN [7]. Whistler waves are ubiquitous in space, astrophysical, and laboratory plasma systems and are thought to play a crucial part in plasma heating. Therefore, a large literature in the past several decades has explored different aspects of whistler waves. The whistler waves dissipate PWN energy [8]. Dispersive whistlers identify the magnetic reconnection rates [9]. Whistler mode evolves into transients in the presence of adiabatic electrons [10]. Satellites have simultaneously seen whistler waves at frequencies lower than the electron cyclotron frequency and anisotropic distributions of particles [11]. The production phenomena of whistler turbulence is useful for understanding intense electromagnetic fluctuations [12]. Recently, it is reported that whistler wave nonlinear steepening takes place very quickly [13]. Electron whistler mode triggers phase space diffusion and rapid pitch angle scattering [14]. The damping effects lead to spectral index modifications for whistler wave [15]. The particle beams act as a source of whistlers [16]. Landau resonance involves the mutual interactions of electrons with whistlers [17]. Whistler wave spectrum is closely associated with energy cascade during turbulence [18]. Recently, a variety of models have been employed to explore the nonlinear dynamics of oblique whistler waves [19–31]. But the nonlinear dynamics of whistler wave in PWN in the presence of counter streaming positron and electron beams is yet not studied in the literature. Therefore, this study is focused on the nonlinear dynamics of whistler wave in PWN. This study applies finite difference time domain (FDTD) simulation scheme which incorporates feedback between whistler wave, positron, and electron beams. The paper is organized as follows: Section 2 provides the basic set of fluid equations. The linear equations are presented in Section 3. The FDTD algorithm for nonlinear whistler waves in PWN is described in Section 4. The simulation results are discussed in Section 5. Section 6 is devoted to the summary.