Cherenkov Instability Research Articles

Beyond the ordinary acoustoelectric effect: Superluminal phenomena in the acoustic realm and phonon-mediated Bloch gain

It has been shown that coherent phonons can be used as a potent tool for controlling and enhancing optoelectronic and transport properties of nanostructured materials. Recent studies revealed that interaction of acoustic phonons and fast-moving carriers in semiconductor heterostructures can be accompanied by electron-phonon instabilities that cause ordinary and induced Cherenkov effects. However, the development of such instabilities is still poorly understood. Our study shows that other supersonic phenomena, beyond the Cherenkov instability, are possible for nonequilibrium charge transport in the miniband semiconductor superlattices (SLs) driven by an acoustic plane wave. Using semiclassical nonperturbative methods and elements of the bifurcation theory, we find the conditions for the onset of dynamical instabilities (bifurcations) which are caused by the emission of specific SL phonons by supersonic electrons, and their back action on the electrons. Notably, the underlying radiation mechanism is connected either to normal or anomalous Doppler effects in full accordance with the Ginzburg-Frank-Tamm theory. The appearance of induced Doppler effects is also discussed in relation to the formation of electron bunches propagating through the spatially periodic structure of the SL. When the amplitude of the acoustic wave exceeds a certain threshold, the dynamical instabilities developed in the system are manifested as drift velocity reversals, resonances in sound attenuation, and absolute negative mobility. We demonstrate that the discovered superluminal Doppler phenomena can be utilized for tunable broadband amplification and generation of GHz-THz electromagnetic waves, which creates a ground for the development of novel phononic devices.

Suppression of errors in simulated ultrarelativistic bunch propagation using the X -dispersionless Maxwell solver

Because of the inherent value of high-energy particle beams for the study of quantum electrodynamics effects, it is of great importance to accurately model the physics in numerical simulations. Numerical effects may alter the dynamics of a simulation and may change the physics of energy losses on account of the radiation reaction (RR) force. In this work, the numerical Cherenkov effect in combination with the RR force are analyzed in the vacuum propagation of an ultrarelativistic electron bunch. It is revisited that the use of the standard Yee solver in the present setup triggers the numerical Cherenkov instability. With the instability at hand, the simulation results of the Yee solver are compared to data obtained by the $X$-dispersionless Maxwell solver, also known as the rhombi-in-plane (RIP) solver. There, the numerical instability is suppressed by several orders of magnitude. Afterward, the impact of radiation reaction on the dynamics is studied for both cases. It is shown that the combination of the Yee solver and the RR force enhances the error significantly and the electron bunch loses about 90% of its energy as a result. These huge energy losses can be observed only if both the Lorentz force and the RR force are enabled in the code. In contrast, the RIP Maxwell solver is not plagued by these issues and accurately calculates the dynamics of the electron bunch.

Superluminal phase velocity approach for suppression of Numerical Cherenkov Instability in Maxwell solver

A modification of a standard finite-difference time-domain (FDTD) Maxwell solver is proposed based on the inclusion of the terms of the higher order in the finite differences approximation. By selecting the coefficients of this hybrid scheme the numeric dispersion of the electromagnetic waves can be fine-tuned. It is shown that a particular choice of the coefficients leads to the phase velocity of all the waves being slightly larger than speed of light. Results of the 3D Particles-In-Cells (PIC) simulations demonstrate that the proposed scheme of the Maxwell solver is efficient to mitigate the Numerical Cherenkov Instability (NCI) when simulating ultrarelativistic charged beams.

Spoof-Plasmon Instability in Terahertz Region Excited by Magnetized Electron Beam

Spoof plasmon is surface waves extended along corrugated surfaces and the terahertz equivalent of optical surface plasmon polaritons for metals. The spoof plasmon may be effectively excited by an electron beam. The beam is perturbed three-dimensionally during the interaction with the spoof plasmon. In this work, we present numerical analysis on the spoof-plasmon instability driven by a magnetized electron beam in a terahertz region. The slow cyclotron as well as Cherenkov instabilities of the spoof plasmon are excited due to the 3-D perturbation. The two instabilities grow large and merge by increasing the beam current and decreasing the magnetic field. The merged instability divides again into the two instabilities for an extremely high beam current. The spoof-plasmon instabilities are examined by revealing modes involved using the saddle-point analysis.

Scalable spectral solver in Galilean coordinates for eliminating the numerical Cherenkov instability in particle-in-cell simulations of streaming plasmas.

Discretizing Maxwell's equations in Galilean (comoving) coordinates allows the derivation of a pseudospectral solver that eliminates the numerical Cherenkov instability for electromagnetic particle-in-cell simulations of relativistic plasmas flowing at a uniform velocity. Here we generalize this solver by incorporating spatial derivatives of arbitrary order, thereby enabling efficient parallelization by domain decomposition. This allows scaling of the algorithm to many distributed compute units. We derive the numerical dispersion relation of the algorithm and present a comprehensive theoretical stability analysis. The method is applied to simulations of plasma acceleration in a Lorentz-boosted frame of reference.

Time-step dependent force interpolation scheme for suppressing numerical Cherenkov instability in relativistic particle-in-cell simulations

The WT scheme, a piecewise polynomial force interpolation scheme with time-step dependency, is proposed in this paper for relativistic particle-in-cell (PIC) simulations. The WT scheme removes the lowest order numerical Cherenkov instability (NCI) growth rate for arbitrary time steps allowed by the Courant condition. While NCI from higher order resonances is still present, the numerical tests show that for smaller time steps, the numerical instability grows much slower than using the optimal time step found in previous studies. The WT scheme is efficient for improving the quality and flexibility of relativistic PIC simulations.

Diagnosing numerical Cherenkov instabilities in relativistic plasma simulations based on general meshes

Numerical Cherenkov radiation (NCR) or instability is a detrimental effect frequently found in electromagnetic particle-in-cell (EM-PIC) simulations involving relativistic plasma beams. NCR is caused by spurious coupling between electromagnetic-field modes and multiple beam resonances. This coupling may result from the slow down of poorly-resolved waves due to numerical (grid) dispersion and from aliasing mechanisms. NCR has been studied in the past for finite-difference-based EM-PIC algorithms on regular (structured) meshes with rectangular elements. In this work, we extend the analysis of NCR to finite-element-based EM-PIC algorithms implemented on unstructured meshes. The influence of different mesh element shapes and mesh layouts on NCR is studied. Analytic predictions are compared against results from finite-element-based EM-PIC simulations of relativistic plasma beams on various mesh types.

Instability of flux flow and production of vortex-antivortex pairs by current-driven Josephson vortices in layered superconductors

We report numerical simulations of the nonlinear dynamics of Josephson vortices driven by strong dc currents in layered superconductors. Dynamic equations for interlayer phase differences in a stack of coupled superconducting layers were solved to calculate a drag coefficient $\eta(J)$ of the vortex as a function of the perpendicular dc current density $J$. It is shown that Cherenkov radiation produced by a moving vortex causes significant radiation drag increasing $\eta(v)$ at high vortex velocities $v$ and striking instabilities of driven Josephson vortices moving faster than a terminal velocity $v_c$. The steady-state flux flow breaks down at $v>v_c$ as the vortex starts producing a cascade of expanding vortex-antivortex pairs evolving into either planar macrovortex structures or branching flux patterns propagating both along and across the layers. The pair production triggered by a rapidly moving vortex is most pronounced in a stack of underdamped planar junctions where it can occur at $J>J_s$ well below the interlayer Josephson critical current density. Both $v_c$ and $J_s$ were calculated as functions of the quasiparticle damping parameter, and the dc magnetic field applied parallel to the layers. The effects of vortex interaction on the Cherenkov instability of moving vortex chains and lattices in annular stacks of Josephson junctions were considered. It is shown that a vortex driven by a current density $J>J_s$ in a multilayer of finite length excites self-sustained large-amplitude standing waves of magnetic flux, resulting in temporal oscillations of the total magnetic moment. We evaluated a contribution of this effect to the power $W$ radiated by the sample and showed that $W$ increases strongly as the number of layers increases.

Linear theory of instabilities generated by an electron beam in a metamaterial-loaded waveguide

We present the linear theory of the starting current of Cherenkov-cyclotron and Cherenkov instabilities generated by an electron beam passing through a metamaterial-loaded waveguide. Effective medium theory is used to represent the metamaterial structure properties. The theory predicts that the instabilities compete with the Cherenkov-cyclotron mode dominating at a lower magnetic field and the Cherenkov instability at a higher magnetic field. The theoretical results are compared to results from recent experiments at MIT using a 490 kV, 84 A electron beam in magnetic fields of 300 G to 1500 G. For an effective medium model fitted to the MIT experimental parameters, theory predicts that the Cherenkov-cyclotron mode will dominate below 780 G and the Cherenkov mode above 780 G, in good agreement with experimental observations of switching between these modes at 750 G. The analytical theory allows a better understanding of the mode competition and the dependence of the instabilities on key parameters such as voltage, current, and magnetic fields.

Coherent Cherenkov-cyclotron radiation excited by an electron beam in a two-spiral metamaterial waveguide

We present the analysis of a microwave generator that uses two-spiral metamaterial (MTM) plates in a below cutoff WR340 waveguide that interacts with a high-power electron beam, motivated by recent results obtained by researchers at MIT. Particle-in-cell simulations using the MAGIC code demonstrated that power levels of 12 MW are achieved in a backward wave mode at a frequency of 2.47 GHz from an anomalous Doppler instability using a 1 μs pulsed electron beam of energy 400 keV, current 82 A in a 415 G magnetic field. In addition, a backward wave with 9 MW output power is achieved at a frequency of 2.54 GHz attributed to a Cherenkov instability using a 1 μs pulsed electron beam of energy 400 keV, current 82 A in a 1200 G magnetic field. MAGIC simulations demonstrate that the beam-wave interaction electronic efficiency can be as high as 27.4%. Nonlinear simulations indicate that beam interception leads to secondary electron emission from surfaces, which makes the anomalous Doppler instability and Cherenkov instability more complicated by a shift in frequency. This work seeks to clarify some discrepancy between particle-in-cell simulations and experiments at MIT over a range of guide magnetic field.

Waves in inhomogeneous plasmas and liquid and gas flows. Analogies between electro- and gas-dynamic phenomena

Two rather closely analogous classes of phenomena — plasma and hydrodynamic — are reviewed. Topics covered include: surface waves in an inhomogeneous plasma layer and in an inhomogeneous incompressible fluid flow; the instability of the tangential discontinuity of an inhomogeneous gas flow and the negative mass instability of an electron-beam-carrying plasma; radiative Cherenkov instabilities of an electron beam in a plasma and of a gas flow in a gas; the instability of plasma flows and of incompressible fluid flows with inhomogeneous velocity profiles. Special attention is given to the collisionless damping of plasma surface waves. It is shown that no such damping occurs for surface waves in gas flows.

A description on plasma background effect in growth rate of THz waves in a metallic cylindrical waveguide, including a dielectric tube and two current sources

The propagation of slow waves in a dielectric tube surrounded by a long cylindrical metallic waveguide is investigated. The dielectric tube located in a background region of plasma under two different states A and B. In the A-state the dielectric tube hollow filled with the plasma and in the B-state the outer surface of dielectric tube has been covered by the plasma layer. There are two relativistic electron beams with opposite velocities injected in the waveguide as the energy sources. Using the fluid theory for the plasmas, the Cherenkov instability in the mentioned waveguide will be analyzed. The dispersion relations of E-mode waves for the states A, B have been obtained. The time growth rate of surface waves are compared with each other for two cases A and B. The effect of plasma region on time growth rate of the waves, will be investigated. In all cases it will be shown, while an electron beam is responsible for instability, another electron beam plays a stabilizing role.

Cherenkov instability of a magnetized beam-plasma system with allowance for a momentum spread of beam electrons

Cherenkov instability is considered in a completely magnetized homogeneous beam-plasma system featuring a thermal momentum spread of beam electrons. The thermal spread in the beam is described in the scope of both the hydrodynamic approach and the kinetic equation method by giving the electron momentum distribution function in the form of theMaxwellian and semi-Maxwellian distributions. It is shown that two beam-plasma instability regimes, the single-particle and collective Cherenkov effects (Compton and Raman regimes) differing by the physical mechanism and the increments, are possible in a system (waveguide) with homogeneous transverse beam and plasma density profiles. Solutions to dispersion equations for these and a more general regime are obtained and analyzed.

Study on Operation of a Surface-Wave Oscillator Around the $\pi$ -Point Region

We numerically and experimentally studied the operation of a W-band (75–110 GHz) surface-wave oscillator driven by the electron beam energy of less than 100 keV. Two numerical methods of the real wavenumber analysis and the saddle point analysis are studied to examine the operation of the oscillator. We analyzed the Cherenkov instability for the interaction of the space charge modes and the structure modes EH01. We showed that the instabilities are of absolute instabilities when the oscillator operates around the $\pi $ -point region. In the experiment, radiations due to the absolute instability are detected around the $\pi $ -point region when the length of the slow-wave structure (SWS) is short enough. On the other hand, the absolute instability generates no meaningful radiation in the $\pi $ -point region for the long length of SWS.

Coherent Cherenkov-Cyclotron Radiation Excited by an Electron Beam in a Metamaterial Waveguide.

An electron beam passing through a metamaterial structure is predicted to generate reversed Cherenkov radiation, an unusual and potentially very useful property. We present an experimental test of this phenomenon using an intense electron beam passing through a metamaterial loaded waveguide. Power levels of up to 5MW are observed in backward wave modes at a frequency of 2.40GHz using a one microsecond pulsed electron beam of 490keV, 84A in a 400G magnetic field. Contrary to expectations, the output power is not generated in the Cherenkov mode. Instead, the presence of the magnetic field, which is required to transport the electron beam, induces a Cherenkov-cyclotron (or anomalous Doppler) instability at a frequency equal to the Cherenkov frequency minus the cyclotron frequency. Nonlinear simulations indicate that the Cherenkov-cyclotron mode should dominate over the Cherenkov instability at a lower magnetic field where the highest output power is obtained.

Elimination of numerical Cherenkov instability in flowing-plasma particle-in-cell simulations by using Galilean coordinates.

Particle-in-cell (PIC) simulations of relativistic flowing plasmas are of key interest to several fields of physics (including, e.g., laser-wakefield acceleration, when viewed in a Lorentz-boosted frame) but remain sometimes infeasible due to the well-known numerical Cherenkov instability (NCI). In this article, we show that, for a plasma drifting at a uniform relativistic velocity, the NCI can be eliminated by simply integrating the PIC equations in Galilean coordinates that follow the plasma (also sometimes known as comoving coordinates) within a spectral analytical framework. The elimination of the NCI is verified empirically and confirmed by a theoretical analysis of the instability. Moreover, it is shown that this method is applicable both to Cartesian geometry and to cylindrical geometry with azimuthal Fourier decomposition.

Stable discrete representation of relativistically drifting plasmas

Representing the electrodynamics of relativistically drifting particle ensembles in discrete, co-propagating Galilean coordinates enables the derivation of a Particle-In-Cell algorithm that is intrinsically free of the numerical Cherenkov instability for plasmas flowing at a uniform velocity. Application of the method is shown by modeling plasma accelerators in a Lorentz-transformed optimal frame of reference.

New longitudinal mode and compression of pair ions in plasma

Positive and negative ions forming the so-called pair plasma differing in sign of their charge but asymmetric in mass and temperature support a new acoustic-like mode. The condition for the excitation of ion sound wave through electron beam induced Cherenkov instability is also investigated. This beam can generate a perturbation in the pair ion plasmas in the presence of electrons when there is number density, temperature, and mass difference in the two species of ions. Basic emphasis is on the focusing of ion sound waves, and we show how, in the area of localization of wave energy, the density of pair particles increases while electrons are pushed away from that region. Further, this localization of wave is dependent on the shape of the pulse. Considering the example of pancake and bullet shaped pulses, we find that only the former leads to compression of pair ions in the supersonic regime of the focusing region. Here, possible existence of regions where pure pair particles can exist may also be speculated which is not only useful from academic point of view but also to mimic the situation of plasma (electron positron asymmetric and symmetric) observed in astrophysical environment.

Simulations for Plasma and Laser Acceleration

Computer simulations have had a profound impact on the design and understanding of past and present plasma acceleration experiments, and will be a key component for turning plasma accelerators from a promising technology into a mainstream scientific tool. In this article, we present an overview of the numerical techniques used with the most popular approaches to model plasma-based accelerators: electromagnetic particle-in-cell, quasistatic and ponderomotive guiding center. The material that is presented is intended to serve as an introduction to the basics of those approaches, and to advances (some of them very recent) that have pushed the state of the art, such as the optimal Lorentz-boosted frame, advanced laser envelope solvers and the elimination of numerical Cherenkov instability. The particle-in-cell method, which has broader interest and is more standardized, is presented in more depth. Additional topics that are cross-cutting, such as azimuthal Fourier decomposition or filtering, are also discussed, as well as potential challenges and remedies in the initialization of simulations and output of data. Examples of simulations using the techniques that are presented have been left out of this article for conciseness, and because simulation results are best understood when presented together, and contrasted with theoretical and/or experimental results, as in other articles of this volume.

Recent advances in high-performance modeling of plasma-based acceleration using the full PIC method

Numerical simulations have been critical in the recent rapid developments of plasma-based acceleration concepts. Among the various available numerical techniques, the particle-in-cell (PIC) approach is the method of choice for self-consistent simulations from first principles. The fundamentals of the PIC method were established decades ago, but improvements or variations are continuously being proposed. We report on several recent advances in PIC-related algorithms that are of interest for application to plasma-based accelerators, including (a) detailed analysis of the numerical Cherenkov instability and its remediation for the modeling of plasma accelerators in laboratory and Lorentz boosted frames, (b) analytic pseudo-spectral electromagnetic solvers in Cartesian and cylindrical (with azimuthal modes decomposition) geometries, and (c) novel analysis of Maxwell׳s solvers׳ stencil variation and truncation, in application to domain decomposition strategies and implementation of perfectly matched layers in high-order and pseudo-spectral solvers.