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The effect of resonances in the photon emission rate in the radiative heat generation and transfer and the Casimir friction at the sliding of two polar dielectric plates has been studied. The resonances have different origin in the frequency ranges of the normal and anomalous Doppler effects. In the frequency range of the normal Doppler effect, the resonances are due to resonant photon tunneling between surface phonon/plas-mon polaritons of plates. Such resonances exist only at a relative sliding velocity v = 0 for two identical plates. However, the resonances may occur at v ≠ 0 for different plates. In the frequency range of the anomalous Doppler effect, the resonances are due to the excitation generation in both plates. While the resonances are finite in the frequency range of the normal Doppler effect, singular resonances are possible even in the presence of dissipation in the system in the frequency range of the anomalous Doppler effect. The resonances for identical and different sliding plates have been considered.

International audience; We present a new method to semianalytically calculate the radiation efficiency of electromagnetic waves emitted at specific frequencies by electrostatic wave turbulence in solar wind and coronal plasmas with random density fluctuations. This method is applied to the case of electromagnetic emission radiated at the fundamental plasma frequency ω p by beam-driven Langmuir wave turbulence during Type III solar bursts. It is supposed that the main radiation mechanism is the linear conversion of electrostatic to electromagnetic waves on the background plasma density fluctuations, at constant frequency. The radiation efficiency (emissivity) of such a process is larger than that obtained in the framework of models where the low frequency density fluctuations and the corresponding ion sound waves are not external but produced by the electrostatic wave turbulence itself through nonlinear wave-wave interactions. Results show that the radiation efficiency of Langmuir wave turbulence into electromagnetic emissions at ω p is nearly constant asymptotically, with the electromagnetic energy density growing linearly with time, and is proportional to the average level of density fluctuations. Comparisons with another analytical method developed by the authors and with space observations are satisfactory.

A new method to calculate semi-analytically the radiation efficiency of electromagnetic waves emitted at specific frequencies by electrostatic wave turbulence in solar plasmas with random density fluctuations is presented. It is applied to the case of electromagnetic emissions radiated at the fundamental plasma frequency ωp by beam-driven Langmuir wave turbulence during Type III solar bursts. It is supposed that the main radiation mechanism is the linear conversion of electrostatic to electromagnetic waves on the background plasma density fluctuations, at constant frequency. Due to the presence of such inhomogeneities, the rates of electromagnetic radiation are modified compared to the case of uniform plasmas. Results show that the radiation efficiency of Langmuir wave turbulence into electromagnetic emissions at ωp is nearly constant asymptotically, the electromagnetic energy density growing linearly with time, and is proportional to the average level of density fluctuations. Comparisons with another analytical method developed by the authors and with space observations are satisfactory.

International audience; Type III solar radio bursts have been commonly observed in the solar wind and coronal plasmas. Electron beams accelerated in the Sun's atmosphere generate weakly magnetized Langmuir (upper-hybrid) wave turbulence producing in turn electromagnetic emissions at the electron plasma frequency ωp and its harmonic 2ωp, via successive processes involving interactions between the background plasma, the waves and the beam particles. The impact of the random density fluctuations inherent to the background plasma on these processes requires the development of novel approaches and models. Owing to a new theoretical modeling, the radiation efficiency of electromagnetic waves radiated at ωp from a plasma source with random density fluctuations and developed upper-hybrid wave turbulence is calculated analytically and numerically. It is shown that the maximum radiation efficiency at frequency ωp scales as the average level of density fluctuations and as the ratio (c/vT)–2 (where vT is the thermal velocity). These scaling laws are found owing to two different and novel methods of determination of the electromagnetic radiation by turbulent inhomogeneous plasma sources through waves' transformations on randomly fluctuating density irregularities. These results contribute significantly to the understanding of the processes involved in the generation of Type III solar radio bursts. Their presentation is preceded by a summary of previous studies on the dynamics of beam-driven Langmuir turbulence in inhomogeneous solar plasmas.

It has been shown that the rotation of a spherical nanoparticle with the radius R near the surface of a semi-infinite homogeneous medium can result in singular resonance in fluctuation-induced electromagnetic phenomena (Casimir force, Casimir friction, and radiative heat generation). Fluctuation electromagnetic effects increase strongly near this resonance even in the presence of dissipation in the system. The resonance occurs at distances of the particle from the surface d < d0R(3/4e″1(ω1)e″2 (ω2))1/3 (where e″i(ωi) is the imaginary part of the dielectric function of the particle or the medium at the frequency of a surface phonon or plasmon polariton ωi), when the rotation frequency coincides with poles in the photon generation rate at Ω ≈ ω1 + ω2. These poles are due to the multiple scattering of electromagnetic waves between the particle and surface under conditions of the anomalous Doppler effect. These poles exist even in the presence of dissipation. At d < d0, depending on the particle rotation frequency, the Casimir force can change sign; i.e., the attraction of the particle to the surface changes to repulsion. The results can be important for the development of experimental methods for the detection of quantum friction.

The quantum heat generation, interaction force, and friction torque for two rotating spherical nanoparticles with the radius R are calculated. In contrast to a static case where an upper bound in the radiative heat transfer between two particles exists, the quantum heat generation for two rotating particles diverges at distances between particles d < d 0 = R(3/e″(ω0))1/3 (where e″(ω0) is the imaginary part of the dielectric function for the material of a particle at the resonance frequency ω0), when the rotation frequency coincides with poles in the excitation generation rate at Ω = 2ω0. These poles are due to the anomalous Doppler effect and the mutual polarization of particles and exist even in the presence of dissipation in particles. The anomalous heat generation is associated with the conversion of mechanical rotation energy into heat mediated by quantum friction. Similar singularities also exist for the interaction force and friction torque. The results can be of significant importance for biomedical applications.

A systematic study of the properties of Langmuir turbulence generated by electron beams via bump-on-tail instabilities in strongly nonhomogeneous plasmas is presented. A statistical analysis of the Langmuir waves' amplitudes using numerical simulations based on two theoretical models is performed: a dynamical one and a probabilistic one. The former describes the self-consistent dynamics of wave-particle and wave-wave interactions. The latter is a modified version of the quasi-linear theory. To analyze the simulation data provided by the probabilistic model, a Pearson technique is used to classify the calculated probability distribution functions (PDFs) of the logarithm of the waves' amplitudes. It is demonstrated that the core parts of the PDFs belong to the Pearson types I, IV, and VI distributions, while the high-amplitude parts of the PDFs follow power law or exponential decay. Analysis of the PDFs calculated using the numerical simulations based on the dynamical model leads to the following additional results. In the small-amplitude parts of the PDFs, a universal scaling parameter is found, with a value not depending on the average levels of the density fluctuations and of the Langmuir turbulence. Second, the PDFs are obtained in the presence of wave decay processes. When those are weak, the PDFs show at large fields' amplitudes an exponential asymptotic behavior; during time evolution, the corresponding scaling parameter decreases until a universal probability distribution is reached, indicating that the wave decay processes are sufficiently strong. Such exponential type of distribution is a specific signature of transition states in the Langmuir turbulence.

Calculations of the radiative and phonon heat transfer between metals in an extreme near field in presence of electrostatic potential difference are given. Potential difference leads to a coupling between the radiation field and acoustic waves in solid, as a result of which the heat flux between two gold plates associated with p -polarized electromagnetic waves increases by many orders of magnitude as the potential difference varies from 0 to 10V. The radiative heat transfer is compared with the phonon heat transfer associated with the electrostatic and van der Waals interactions between the surface displacements. For large potential difference and small distances the radiative heat transfer is reduced to the electrostatic phonon heat transfer. A particular case of surface acoustic waves - Rayleigh waves is studied in details. Conditions are obtained for the existence of surface phonon polaritons associated with the interaction of Rayleigh waves with an electromagnetic field. The surface Rayleigh and bulk acoustic waves can give contributions of the same order. The obtained results can be used to control heat fluxes at the nanoscale using the potential difference and to create coherent radiation sources based on the properties of the Rayleigh waves, 12pages, 4 figure

Quantum Cherenkov radiation and quantum friction at the motion of a small neutral particle parallel to the surface of a transparent dielectric with the refractive index n have been studied in a fully relativistic theory. Radiation appears at velocities above the threshold value, v > v c = c/n. The friction force in the particle–plate configuration has been derived from the friction force in the plate–plate configuration under the assumption that one of the plates is significantly decharged. A decrease in the kinetic energy of the particle near the threshold velocity is due to its radiation and near the speed of light is determined by the heat power absorbed by the particle in the rest frame. The powers of quantum and classical Cherenkov radiation can be comparable in the relativistic case.

The effect of resonances in the photon emission rate in radiative heat generation and transfer, and Casimir friction at the relative sliding of two plates of polar dielectrics is studied. Resonances are of a different origin in the frequency range of the normal (NED) and anomalous (AED) Doppler effect. In the NED domain, resonances are associated with resonant photon tunneling between surface phonon/plasmon polaritons. In the AED domain resonances are associated with the instantaneous generation of excitations in both plates. While in the NED domain the resonances are finite, in the ADE domain singular resonances are possible even in the presence of dissipation in the system.

Within the framework of a linear theory, the instability of an electron beam with a finite radius in a cold magnetised boundless plasma is considered. It is shown that a finite beam dimension influences the generation of quasi-potential waves in two aspects: the perpendicular wave number is quantised so that the frequencies of the waves are subjected to strong selection; a new kind of instability appears due to wave energy losses by emission into surrounding space. Growth rate dependence of wave numbers and frequencies is investigated for typical parameters of experiments with electron beams in space.

The random density fluctuations observed in the solar wind plasma crucially influence on the Langmuir wave turbulence generated by energetic electron beams ejected during solar bursts. Those are powerful phenomena consisting of a chain of successive processes leading ultimately to strong electromagnetic emissions. The small-scale processes governing the interactions between the waves, the beams and the inhomogeneous plasmas need to be studied to explain such macroscopic phenomena. Moreover, the complexity induced by the plasma irregularities requires to find new approaches and modelling. Therefore theoretical and numerical tools were built to describe the Langmuir wave turbulence and the beam&rsquo, s dynamics in inhomogeneous plasmas, in the form of a self-consistent Hamiltonian model including a fluid description for the plasma and a kinetic approach for the beam. On this basis, numerical simulations were performed in order to shed light on the impact of the density fluctuations on the beam dynamics, the electromagnetic wave radiation, the generation of Langmuir wave turbulence, the waves&rsquo, coupling and decay phenomena involving Langmuir and low frequency waves, the acceleration of beam electrons, their diffusion mechanisms, the modulation of the Langmuir waveforms and the statistical properties of the radiated fields&rsquo, distributions. The paper presents the main results obtained in the form of a review.

International audience; This paper studies the self-consistent interactions between whistler envelope solitons and electron beams in inhomogeneous plasmas, using a Hamiltonian model of wave-particle interaction where nonlinear equations describing the dynamics of whistler and ion acoustic waves and including a beam current term are coupled with Newton equations. It allows describing the parallel propagation of narrowband whistlers interacting with arbitrary particle distributions in irregular plasmas. It is shown that the whistler envelope soliton does not exchange energy with all the resonant electrons as in the case of whistler turbulence but mostly with those moving in its close vicinity (locality condition), even if the downstream particle distribution is perturbed. During these interactions, the soliton can either damp and accelerate particles, or absorb beam energy and cause electron deceleration. If the energy exchanges are significant, the envelope is deformed; its upstream front can steepen, whereas oscillations can appear on its downstream side. Weak density inhomogeneities as the random fluctuations of the solar wind plasma have no strong impact on the interactions of the whistler soliton with the resonant particles.

The friction force at the motion of a small relativistic neutral particle with respect to blackbody radiation has been calculated within fluctuation electrodynamics. It has been shown that the acceleration of the particle is determined by the friction force in the rest reference frame of the particle (K’ reference frame), which is not generally equal to the friction force in the reference frame specified by blackbody radiation (K reference frame). The difference between friction forces in different reference frames is due to a change in the rest mass of the particle owing to the absorption and emission of radiation by the particle. The friction force in the K’ reference frame is determined only by the interaction of the particle with blackbody radiation. Consequently, it depends only on the temperature of this radiation and is independent of the temperature of the particle. The interaction of the particle with its own thermal radiation in the K reference frame also contributes to the friction force. At a constant temperature of the particle, the friction forces in the K’ and K reference frames are equal to each other. The friction force of blackbody radiation for an atom is determined by the radiative broadening of an electron line of the atom, which is calculated by taking into account the interaction of the atom with its radiation. In the ultrarelativistic case (1 − β → 0), the friction force for the atom diverges as (1 − β)−3 and the (average) temperature of the atom is T2 ≈ (1− β)−3/8T1, where T1 is the temperature of blackbody radiation and β = V/c. Discrepancies in the theory of the friction force caused by blackbody radiation have been discussed.

We calculate the quantum heat generation, the interaction force and the frictional torque for two rotating spherical nanoparticles with a radius $R$. In contrast to the static case, when there is an upper limit in the radiative heat transfer between the particles, for two rotating nanoparticles the quantum heat generation rate diverges when the angular velocity becomes equal to the poles in the photon emission rate. These poles arise for the separation $d, Comment: 7 pages, 3 figures

The spectral correlation function for the fluctuating electromagnetic field outside a semi-infinite solid with a planar surface can be calculated using the generalized Kirchhoff law for isotropic materials.

International audience; The paper studies the influence of the background plasma density fluctuations on the dynamics of the Langmuir turbulence generated by electron beams, for parameters typical for solar type III beams and plasmas near 1 AU. A self-consistent Hamiltonian model based on the Zakharov and the Newton equations is used, which presents several advantages compared to the Vlasov approach. Beams generating Langmuir turbulence can be accelerated as a result of wave transformation effects or/and decay cascade processes; in both cases, the beam-driven Langmuir waves transfer part of their energy to waves of smaller wavenumbers, which can be reabsorbed later on by beam particles of higher velocities. As a consequence, beams can conserve a large part of their initial kinetic energy while propagating and radiating wave turbulence over long distances in inhomogeneous plasmas. Beam particles can also be accelerated in quasi-homogeneous plasmas due to the second cascade of wave decay, the wave transformation processes being very weak in this case. The net gains and losses of energy of a beam and the wave turbulence it radiates are calculated as a function of the average level of plasma density fluctuations and the beam parameters. The results obtained provide relevant information on the mechanism of energy reabsorption by beams radiating Langmuir turbulence in solar wind plasmas.

In this section, we consider the basic principles of radiative heat transfer. The general theory of the fluctuating electromagnetic field is applied for the calculation of the radiative heat transfer in the plate–plate and particle–plate configurations using the Green’s function and scattering matrix approaches. The Green’s function approach is used to calculate the radiative heat transfer between anisotropic materials and the scattering matrix approach is used to calculate the radiative heat transfer between plates in relative motion.

When a charged particle uniformly moves through a medium with the velocity higher than the velocity of light in that medium, the VavilovCherenkov radiation is produced by the medium.

Asymptotic state of an open quantum system can undergo qualitative changes upon small variation of system parameters. We demonstrate it that such 'quantum bifurcations' can be appropriately defined and made visible as changes in the structure of the asymptotic density matrix. By using an $N$-boson open quantum dimer, we present quantum diagrams for the pitchfork and saddle-node bifurcations in the stationary case and visualize a period-doubling transition to chaos for the periodically modulated dimer. In the latter case, we also identify a specific bifurcation of purely quantum nature.

As will be shown in the subsequent sections, reflection and emission of electromagnetic waves from surfaces of solids significantly depend on the presence of localized surface modes, which include surface electromagnetic waves. This particular type of waves exists at the interface between two different media. An electromagnetic surface wave propagates along the interface and decreases exponentially in the perpendicular direction.

In this section, two approaches in the theory of Casimir friction in the plate-plate configuration are considered. The first approach is based on the fluctuation electrodynamics proposed by Rytov [5–7]. In this approach the fluctuating electromagnetic field is considered as a classical field that can be calculated from Maxwell’s equation with the fluctuating current density as the source of the field, and with appropriate boundary conditions.

In this section, the friction force acting on a small neutral particle moving relative to a flat surface of a solid is considered in the framework of the fluctuation electrodynamic in non-relativistic and relativistic cases. The friction force in the particle–plate configuration is deduced from the friction force in the plate–plate configuration, assuming one of the plates to be sufficiently rarefied. The effect of the multiple scattering of the electromagnetic field between a particle and substrate is also studied. These effects can be important for physisorbed molecules. For physisorbed molecules, high-order processes, which are not included in the theory of Casimir friction, can dominate the damping rate of physisorbed molecules. The results of the theoretical calculations are compared with experimental data. The special case of Casimir friction force acting on a small neutral particle moving relative to the black-body radiation is also analyzed.

To obtain a simple picture of the origin of the Casimir force, we begin this section by considering a system of two plane-parallel plates of ideal conductors, following the original Casimir paper [39]. These planes produce a waveguide. The number of electromagnetic modes in the waveguide is discrete and depends on the width of the waveguide. From quantum electrodynamics, it is known that each mode with frequency \(\omega \) has a minimum energy \(\hbar \omega /2\) referred to as vacuum fluctuations or zero point motion.

Coulomb drag is a frictional coupling between electric currents flowing in spatially separated conducting layers. It is caused by interlayer electron-electron interactions. The frictional drag between quantum wells makes it possible to probe directly the inter-particle interaction.

There are two approaches for studying the fluctuating electromagnetic field. In the first approach, proposed by Rytov [5–7], it is assumed that the fluctuating electromagnetic field is created by the thermal and quantum fluctuations of current density \(\mathbf {j}^f\) inside the medium.

Casimir has shown that quantum fluctuations of the electromagnetic field produce an attractive force between macroscopic bodies. It has recently been shown that two non-contacting bodies moving relative to each other experience a friction due to the same quantum fluctuations of the electromagnetic field. However, until recent time there was no experimental evidence for or against this effect, because the predicted friction forces are very small, and precise measurements of quantum forces are incredibly difficult with present technology. The existence of quantum friction is still debated even among theoreticians. However, the situation drastically changed with the discovery of a new material—graphene. We recently proposed that quantum friction can be detected in frictional drag experiments between graphene sheets, and in the transport properties of nonsuspended graphene on an SiO\(_2\) substrate in a high electric field.

The dependence of the thermal component of the Casimir force and Casimir friction between graphene sheets on the drift velocity of charge carriers in one of the sheets has been analyzed. It has been shown that the drift motion results in the measurable change in the thermal Casimir force owing to the Doppler effect. The thermal Casimir force, as well as Casimir friction, increases strongly in the case of resonant photon tunneling, when the energy of an emitted photon coincides with the excitation energy of an electron-hole pair. In the case of resonant photon tunneling, the dominant contribution to the Casimir friction even at temperatures above room temperature comes from quantum friction caused by quantum fluctuations. Quantum friction can be detected in an experiment on the friction drag between graphene sheets in a high electric field.

The possibility of the mechanical detection of the Casimir friction using noncontact force microscope is discussed. On a ${\mathrm{SiO}}_{2}$ tip situated above a graphene-covered ${\mathrm{SiO}}_{2}$ substrate will act the frictional drag force mediated by a fluctuating electromagnetic field produced by a current in the graphene sheet. This friction force will produce the bending of the cantilever, which can be measured by state-of-art noncontact force microscope. Both the thermal and quantum contributions to the Casimir frictional drag force can be studied using this experimental setup. This result paves the way for the mechanical detection of the Casimir friction and for the application of the frictional drag effect in micro- and nanoelectromechanical devices (MEMS and NEMS).

International audience; Particle diffusion in velocity space is studied on the basis of 1D simulations of Langmuir turbulence generated by electron beams in solar wind plasmas. Using a large amount of particle trajectories calculated with a great accuracy and over long times and analyzing them with statistical algorithms, the diffusion coefficients of particles in wave packets are estimated, as well as their relation to the waves' intensities and spectra and their dependence on the average level of background plasma density fluctuations. Results are compared with analytical solutions provided by the quasilinear theory of weak turbulence.

International audience; Langmuir wave decay in solar wind plasmas typical of type III bursts' source regions near 1 AU have been reported by several spacecraft observations. In such plasmas, due to the presence of random density fluctuations, wave decay occurs usually simultaneously and compete with other coupling effects between the fields and the density irregularities, as reflection, scattering and/or refraction processes. Numerical simulations show that resonant three-wave coupling processes including several cascades of Langmuir wave decay can occur in such plasmas, leading to wave energy transfer to smaller wavenumbers k, as shown in the frame of weak turbulence theory. However, in such conditions, and contrary to what occurs in homogeneous plasmas, the decay process is localized in space at a given time. Moreover, wave-wave coupling plays a significant role in the modulation of the Langmuir waveforms, in agreement with recent space observations.

International audience; The self-consistent evolution of Langmuir turbulence generated by electron beams in solar wind plasmas with density inhomogeneities is calculated by numerical simulations based on a 1D Hamiltonian model. It is shown, owing to numerical simulations performed with parameters relevant to type III solar bursts' conditions at 1 AU, that the presence of long-wavelength random density fluctuations of sufficiently large average level crucially modifies the well-known process of beam interaction with Langmuir waves in homogeneous plasmas.