Cold Fluid Theory Research Articles

Dispersion surface and electromagnetic responses of the magnetosonic/whistler mode in the high-β collisionless plasmas

Near-parallel and highly oblique magnetosonic/whistler (M/W) mode waves are frequently observed in solar wind and interplanetary shocks. These observed waves are usually analyzed by the plasma kinetic and fluid theories. This study compares the dispersion surface and electromagnetic responses of the M/W mode wave under both kinetic and fluid theories in the plasmas with βp = βe ≃ 1 in detail. In comparison with the kinetic theory, it proposes that the hot fluid theory is suitable to obtain the dispersion relation, the ratio of the parallel to perpendicular magnetic fluctuation Bz/B⊥, and the ratio of the electric to magnetic fluctuation E/B. Except the near-parallel low-frequency M/W mode, the hot fluid theory would be used to calculate the ratio between two magnetic fluctuations perpendicular to the wave vector B1/B2, the magnetic helicity σ, and the ratio of the parallel to perpendicular electric fluctuation Ez/E⊥ of the M/W mode waves. The cold fluid theory is good at describing the magnetic responses including Bz/B⊥, B1/B2, and σ, but it underestimates ω, E/B, and Ez/E⊥ for the obliquely propagating M/W mode wave. Furthermore, both hot and cold fluid theories can obtain the ratio of the longitudinal to transverse electric fluctuation relative to the wave vector EL/EP of the obliquely propagating low-frequency M/W mode. These results provide an indicator about how to choose the adequate theory to analyze the observations of the M/W mode waves in the solar wind and interplanetary shocks. Besides, from the dispersion surface in kinetic theory, it shows that the relative weak damping arises for the low-frequency branch at the angle around 0°, 60°, and 90° and for the high-frequency branch with ω ∼ [ωcp, 300ωcp] at the normal angle smaller than 60°, which indicates the possible angle and frequency of the freely propagating M/W mode waves.

Two-stream instability assessment of fast ignition driven by quasi-monoenergetic ions

During the past decade, the generation of energetic ion beams by high-intensity laser-plasma interactions has attracted much interest due to their many applications in high energy density physics and fast ignition. The interaction of the energetic beam with the pre-compressed DT plasma may be accompanied by micro-instabilities along normal and parallel to the beam direction. In application of ions heavier than hydrogen isotopes in fast ignition, we expect that the number of required ions reduces considerably. Here, we present a one-dimensional relativistic beam-plasma instability formulation to investigate the stabilization mode of a flow aligned two-stream instability spectrum where both cold-fluid and kinetic linear theory results are reported. In the latter, the saddle point expansion of the relativistic drift-Maxwellian distribution was applied. The stabilization mode was then extracted by using the Nyquist method. We have also restricted our stability analyses to quasi-monoenergetic ion beams of type Li3+, C6+, Al13+, and V23+ with optimal energies of 140 MeV, 450 MeV, 2.2 GeV, and 5.5 GeV, respectively, proposed by numerical simulations in fast ignition [Honrubia et al. Laser Part. Beams 32, 419 (2014)]. The stable mode is attained by two free system parameters, i.e., beam/plasma density ratio, α, and background plasma temperature, Tp. In the case of low Zb ions, by different degree levels, both parameters push the system to complete stability. However, in the case of high Zb ions, complete stabilization is achieved just through few orders of magnitude lower α. It has also been shown that in complete stabilization of the system, the α parameter scales as an inverse square of ions' atomic number, ∝Zb−2.

Theoretical and Experimental Investigation on Intense Sheet Electron Beam Transport With Its Diocotron Instability in a Uniform Magnetic Field

In this paper, the cold-fluid model theory of an intense sheet electron beam is developed to investigate the diocotron instability during its transport in a uniform magnetic field. The model shows that if the magnetic field strength and the beam filling factor are increased separately, the diocotron instability will be suppressed, which extends the sheet-beam transport distance effectively. To verify the above conclusion, a set of complicated instruments, the electron beam measuring and analyzing system (EBMAS), was developed to measure the beam cross section, beam current density, and the 3-D trajectory. The sheet electron beam transport process in a uniform magnetic field with its diocotron instability is investigated on the basis of EBMAS measurements. The measured results agree very well with theoretical calculation and numerical simulation. A sheet-electron-beam tube based on a uniform magnetic field was then manufactured to drive a future W-band sheet-beam klystron (WSBK). Tuning the sheet-beam parameters over a broad range, including a cathode voltage range of 20-82 kV, current range of 0.5-4.27 A, and with a beam cross section of about 10 mm $\times\,$ 0.5 mm, the experimental beam transmission rate is above 98% through a beam tunnel of 100 mm in length.

Cyclotron waves in a non-neutral plasma column

A kinetic theory of linear electrostatic plasma waves with frequencies near the cyclotron frequency Ωcs of a given plasma species s is developed for a multispecies non-neutral plasma column with general radial density and electric field profiles. Terms in the perturbed distribution function up to O(1/Ωcs2) are kept, as are the effects of finite cyclotron radius rc up to O(rc2). At this order, the equilibrium distribution is not Maxwellian if the plasma temperature or rotation frequency is not uniform. For rc→0, the theory reproduces cold-fluid theory and predicts surface cyclotron waves propagating azimuthally. For finite rc, the wave equation predicts that the surface wave couples to radially and azimuthally propagating Bernstein waves, at locations where the wave frequency equals the local upper hybrid frequency. The equation also predicts a second set of Bernstein waves that do not couple to the surface wave, and therefore have no effect on the external potential. The wave equation is solved both numerically and analytically in the WKB approximation, and analytic dispersion relations for the waves are obtained. The theory predicts that both types of Bernstein wave are damped at resonances, which are locations where the Doppler-shifted wave frequency matches the local cyclotron frequency as seen in the rotating frame.

Effect of electron heating on self-induced transparency in relativistic-intensity laser-plasma interactions

The effective increase of the critical density associated with the interaction of relativistically intense laser pulses with overcritical plasmas, known as self-induced transparency, is revisited for the case of circular polarization. A comparison of particle-in-cell simulations to the predictions of a relativistic cold-fluid model for the transparency threshold demonstrates that kinetic effects, such as electron heating, can lead to a substantial increase of the effective critical density compared to cold-fluid theory. These results are interpreted by a study of separatrices in the single-electron phase space corresponding to dynamics in the stationary fields predicted by the cold-fluid model. It is shown that perturbations due to electron heating exceeding a certain finite threshold can force electrons to escape into the vacuum, leading to laser pulse propagation. The modification of the transparency threshold is linked to the temporal pulse profile, through its effect on electron heating.

Collective energy absorption of ultracold plasmas through electronic edge-modes

We investigate the collective dynamics of electrons in ultracold neutral plasmas driven by an oscillating radio-frequency field. We point out the importance of a sharp density drop at the plasma boundary that arises due to unavoidable charge imbalances, and show that this plasma edge provides the major mechanism for energy absorption from the external field. Using a cold fluid theory, we derive the corresponding absorption frequency and validate our findings by microscopic molecular dynamics simulations. The proposed edge-mode is shown to provide a consistent explanation for the observed absorption spectra measured in different experiments. Understanding the response of the electronic plasma component to weak external driving is essential since it grants experimental access to the time-evolving density and temperature of ultracold plasmas.

Whistler-Langmuir oscillitons and their relation to auroral hiss

Abstract. A new type of oscilliton (soliton with superimposed spatial oscillations) is described which arises in plasmas if the electron cyclotron frequency Ωe is larger than the electron plasma frequency ωe, which is a typical situation for auroral regions in planetary magnetospheres. Both high-frequency modes of concern, the Langmuir and the whistler wave, are completely decoupled if they propagate parallel to the magnetic field. However, for oblique propagation two mixed modes are created with longitudinal and transverse electric field components. The lower mode (in the literature commonly called the whistler mode, e.g. Gurnett et al., 1983) has whistler wave characteristics at small wave numbers and asymptotically transforms into the Langmuir mode. As a consequence of the coupling between these two modes, with different phase velocity dependence, a maximum in phase velocity appears at finite wave number. The occurrence of such a particular point where phase and group velocity coincide creates the condition for the existence of a new type of oscillating nonlinear stationary structure, which we call the whistler-Langmuir (WL) oscilliton. After determining, by means of stationary dispersion theory, the parameter regime in which WL oscillitons exist, their spatial profiles are calculated within the framework of cold (non-relativistic) fluid theory. Particle-in-cell (PIC) simulations are used to demonstrate the formation of WL oscillitons which seem to play an important role in understanding electron beam-excited plasma radiation that is observed as auroral hiss in planetary magnetospheres far away from the source region.

Investigation of the diocotron instability of an infinitely wide sheet electron beam by using the macroscopic cold-fluid model theory

This paper investigates the diocotron instability of an infinitely wide relativistic sheet electron beam in conducting walls propagating through a uniform magnetic field by using the macroscopic cold-fluid model theory. Assuming low-frequency perturbations with long axial wavelengths, the eigenvalue equation and the dispersion relation are acquired for a sheet electron beam with sharp boundary profile and uniform density. The results presented in this paper has developed the use of the macroscopic cold-fluid model theory by extending the parameter of the electron cyclotron frequency ωc to a wider usage range, which is restricted to be much larger than the plasma frequency ωp in the previous research work. Theoretical analyses and numerical calculations indicate that the transport of the sheet electron beam will be completely stabilized by augmenting the normalized beam thickness to a conductor gap larger than a threshold λb, which is greatly dependent on the parameter ωc/ωp. The larger ωc/ωp is, the smaller λb will be needed. Moreover, the system parameters, including the wave number kx of the perturbations and the relativistic mass factor γb, will also influence the growth rate of diocotron instability obviously.

Collective excitations of a spherically confined Yukawa plasma

The complete spectrum of eigenmodes of a spherically confined Yukawa plasma is presented, based on first-principle molecular dynamics simulations. These results are compared with a recent fluid theory for the multipole modes of this system [H. Kählert and M. Bonitz, Phys. Rev. E 82, 036407 (2010)] and with the exact N-particle eigenmodes in the crystalline phase. Simulations confirm the existence of high-order modes found in cold fluid theory. We investigate the influence of screening, coupling, and friction on the mode spectra in detail. Good agreement between theory and simulation is found for weak to moderate screening and low-order modes. In addition, a number of new modes are observed which are missing in the fluid theory. The relations between the breathing mode in the fluid theory, simulation, and the crystal eigenmode are investigated in further detail.

Investigation on focus and transport characteristics of high transmission rate sheet electron beam

The investigation on focus and transport characteristics of sheet electron beam has been a key technique for the development of high-power microwave and millimeter-wave vacuum electronic devices. Compared with the period permanent magnetic system to transport the sheet electron beam, the uniform magnetic focusing system has many advantages, such as easily adjusting and matching the magnet with the beam, focusing the intensity electron beam, no cut off beam voltage restriction, etc. However, the Diocotron instability of the sheet electron beam in the uniform magnetic field can produce the distortion, deformation, vortex and oscillation to destroy the beam transportation. In this paper, the single-particle model and the cold-fluid model theory and calculation are used to indicate that if the electron optics system parameters of the sheet beam are designed more carefully, the magnitude of uniform magnetic field and the filling factor of the beam in transport tunnel are increased appropriately, the Diocotron instability can be reduced, even vanished completely to transport the sheet beam effectively in a long distance. To verify the above conclusion, the electron gun with the ellipse cathode and the electron optics system are designed and optimized with the three-dimensinal simulation software in detail. After the complex assembly and weld process with the small geometry and high precision, the W-band sheet electron beam tube is manufactured and tested. The sheet beam cross section of 10 mm0.7 mm is achieved experimentally with the one-dimensional compression and formation of electron gun. Also, with a beam voltage of 2080 kV, and beam current of 0.644.60 A,the experimental transmission rate of sheet beam electron tube manufactured is more than 95% with a drift length of 90 mm, which is higher than the periodic cusp magnetic field transport experiment result of 92% obtained recently.

Multidimensional electron beam-plasma instabilities in the relativistic regime

The interest in relativistic beam-plasma instabilities has been greatly rejuvenated over the past two decades by novel concepts in laboratory and space plasmas. Recent advances in this long-standing field are here reviewed from both theoretical and numerical points of view. The primary focus is on the two-dimensional spectrum of unstable electromagnetic waves growing within relativistic, unmagnetized, and uniform electron beam-plasma systems. Although the goal is to provide a unified picture of all instability classes at play, emphasis is put on the potentially dominant waves propagating obliquely to the beam direction, which have received little attention over the years. First, the basic derivation of the general dielectric function of a kinetic relativistic plasma is recalled. Next, an overview of two-dimensional unstable spectra associated with various beam-plasma distribution functions is given. Both cold-fluid and kinetic linear theory results are reported, the latter being based on waterbag and Maxwell–Jüttner model distributions. The main properties of the competing modes (developing parallel, transverse, and oblique to the beam) are given, and their respective region of dominance in the system parameter space is explained. Later sections address particle-in-cell numerical simulations and the nonlinear evolution of multidimensional beam-plasma systems. The elementary structures generated by the various instability classes are first discussed in the case of reduced-geometry systems. Validation of linear theory is then illustrated in detail for large-scale systems, as is the multistaged character of the nonlinear phase. Finally, a collection of closely related beam-plasma problems involving additional physical effects is presented, and worthwhile directions of future research are outlined.

Kinetic equilibrium of a periodically twisted ellipse-shaped charged-particle beam

A Vlasov equilibrium of the Kapchinskij-Vladimirskij form is obtained for a periodically twisted ellipse-shaped charged-particle beam in a nonaxisymmetric periodic magnetic focusing field. The single-particle Hamiltonian dynamics is analyzed self-consistently. A constant of motion analogous to the Courant-Snyder invariant is found. The equilibrium distribution function is constructed. The statistical properties of the beam equilibrium are studied. In the zero-temperature limit, the generalized envelope equations derived from the kinetic equilibrium theory recover the generalized envelope equations obtained in the cold-fluid equilibrium theory. Examples of periodically twisted elliptic beam equilibria are presented, and potential applications are discussed. For ribbon-beam amplifier and ribbon-beam klystron applications, the kinetic equilibrium theory predicts that the effect of beam temperature on the beam envelopes is negligibly small.

Cold-fluid theory of equilibrium and stability of a high-intensity periodically twisted ellipse-shaped charged-particle beam

It is shown that there exists an exact paraxial cold-fluid equilibrium of a high-intensity, space-charge-dominated charged-particle beam with a periodically twisted elliptic cross section in a nonaxisymmetric periodic magnetic field. Generalized envelope equations, which determine the beam envelopes, ellipse orientation, density, and internal flow velocity profiles, are derived. Nonrelativistic and relativistic examples of such beam equilibria are presented. The equilibrium and stability of such beams are demonstrated by self-consistent particle-in-cell (PIC) simulations.

Observation of a structural transition for Coulomb crystals in a linear Paul trap.

A structural transition for laser cooled ion Coulomb crystals in a linear Paul trap just above the stability limit of parametrically resonant excitation of bulk plasma modes has been observed. In contrast to the usual spheroidal shell structures present below the stability limit, the ions arrange in a "string-of-disks" configuration. The spheroidal envelopes of the string-of-disks structures are in agreement with results from cold fluid theory usually valid for ion Coulomb crystals if the ion systems are assumed to be rotating collectively.

Nonuniform non-neutral plasma in a trap.

An analytical model for breathing oscillations in a nonuniform non-neutral plasma slab is developed. The plasma is relatively small and warm with the smallest dimension only of several Debye lengths. Nonuniformity in the equilibrium results in a frequency shift associated with pressure and boundary effects. The plasma size and temperature, being related to the frequency shift, can therefore be evaluated from frequency measurements. In particular, for small nonuniform plasmas the frequency of the breathing mode is twice that predicted by the cold fluid theory. Nonlinear oscillations are also considered and the pressure is shown to have an important effect on the dynamics. Analytical solutions for linear and nonlinear oscillations are obtained and compared with that from one-dimensional particle-in-cell simulations. Good agreement is found.

A tutorial presentation of the two stream instability and Landau damping

A tutorial presentation is given of the interaction between a high frequency electrostatic wave and a plasma. The analysis is carried out in several consecutive simple steps, starting from electrostatic plasma waves in a cold plasma and successively introducing complications like streaming electrons, the two stream instability and eventually the Landau damping phenomenon. The analysis is based only on cold plasma fluid theory and does not involve kinetic Vlasov theory.

Instabilities Driven by an Intense Beam in a Plasma-Filled Dielectric-Lined Waveguide Immersed in a Finite Axial Magnetic Field

A linear analysis is described on stabilities driven by an intense relativistic electron beam in an infinitely long, plasma-filled, and dielectric-lined circular waveguide immersed in a finite strength axial magnetic field. A dispersion equation is derived from the cold fluid theory and solved numerically. Beam-plasma instabilities due to interaction between beam modes and the Trivelpiece-Gould modes appear as well as the Cherenkov and the cyclotron Cherenkov instabilities. Parametric researches are carried out varying magnetic field strength, plasma density, and dielectric constant. Effects of a finite magnetic field and plasma filling are discussed in connection with the possibilities of using this system as a microwave radiation source.

Variational principle for crossed-field devices

We present a Rayleigh–Ritz variational model of the electron sheath in crossed-field devices. Using laminar layer orbits, this model predicts equilibria in agreement with the classical Brillouin model. Other predictions include the existence of existence of non-classical, stable equilibria as well as limit cycles. This variational model also predicts the existence of a stable propagating diocotron mode, which is absent from the Brillouin model but is present in the double-box model of Kaup and Thomas. Comparisons of these results with those of the cold-fluid theory are discussed.

Spectral Analysis of the Flow of a Neutralized Electron Beam

The flow of a neutralized electron beam in the classical Pierce beam–plasma system is examined. The system comprises two grounded electrodes containing a stationary background population of neutralizing ions, and electrons are steadily injected with speed V0 from the left-hand electrode at which the charge density is maintained constant. According to cold fluid theory, the system is governed by a single dimensionless parameter α = Lωp/V0, where L is the separation of the electrodes and ωp the plasma frequency. We cast the governing partial differential equations of the cold fluid model in general spectral form, and, by the technique of Galerkin truncation, we reduce the system to low-order systems of ordinary differential equations. Specifically, we reduce the Pierce system to four-dimensional and six-dimensional systems. We examine the nonlinear dynamics of the electron flow, and we find that the nature of the long-term oscillations can be critically dependent on both the value of the parameter α and the initial conditions. While oscillations are typically quasi-periodic, chaotic behavior is also common. For instance, chaotic oscillations in the four-dimensional system can be induced, for any value of α in the range 2.6π ≤ α ≤ 3π, by a suitable choice of initial conditions. That the initial conditions in the Pierce beam–plasma system can play a significant role in influencing the long-term behavior is a main result of our study. We compare our results with computer simulations of the full system, and conclude that whether or not the complex nonlinear dynamics of the Pierce system can be captured in a low-order ordinary differential system remains a challenging question.

Linear analysis of cyclotron-cherenkov and cherenkov instabilities in dielectric-loaded coaxial waveguides

We present, based on the cold fluid theory, linear analysis of the Cherenkov and cyclotron-Cherenkov instabilities which are driven when a linear electron beam is injected into a dielectric-loaded waveguide immersed in an axial magnetic field. In the analysis we consider azimuthally symmetric TM0n modes. We derive dispersion relations for three types of waveguide, and compare computationally obtained linear growth rates of both instabilities. For the type A, which consists of a metallic cylinder with dielectric liner on its inner surface, the growth rate of the Cherenkov instability is larger than that of the cyclotron-Cherenkov instability. For the type B, which consists of a dielectric core and an outer metallic cylinder, both growth rates are comparable. And for the type C, which consists of a metallic core with dielectric liner on its surface and an outer metallic cylinder, the growth rate of the latter instability is higher than that of the former instability. Finally, for the type C, obtained are dependences of the oscillation frequency and the growth rates of both instabilities on the following parameters: the beam energy, the beam current, the axial magnetic field, the dielectric constant, and the thickness of the dielectric.