We present nonlinear resistive MHD simulations of the response of a rotating plasma to an error field when the plasma has weakly damped linear tearing modes (TM's), stabilized by pressure gradient and favorable curvature. Favorable curvature leads to the Glasser effect: the occurrence of real frequencies and stabilization with positive stability index $Δ'$. A cylinder with hollow pressure is used to model the toroidal favorable curvature. Linear simulations with rotation and an error field $\tildeψ_w$ show, in agreement with analytic results, that the peak reconnected flux occurs for a rotation rate near the TM phase velocity. Nonlinear simulations with small $\tildeψ_w$ show that the real frequency and stabilization by favorable average curvature are masked by a nonlinear effect that occurs for very thin islands: flattening of the pressure across the island, mainly due to sound wave propagation. This flattening causes the disappearance of real frequencies destabilization of the mode, allowing it to grow to large amplitude similar to a $β=0$ unstable TM. The flattening of the current for larger islands saturates the mode nonlinearly. In the post-saturation phase, the interaction of the error field with the destabilized spontaneous tearing mode, which rotates with the plasma, leads to oscillations in the Maxwell torque and therefore modulations in the plasma rotation. The islands also rotate with modulated phase velocity, undergoing small-amplitude oscillations due to these modulations. We also present a quasilinear model with an unstable spontaneous TM and error fields, showing that the superposition of these fields results in similar oscillations.
A scheme of wake field generation for positron acceleration using hollow or donut shaped electron driver beams is studied. An annular shaped, electron free region forms around a hollow driver beam creating a favorable region (longitudinal field is accelerating and transverse field is focusing and radially linear) for positron acceleration. Accelerating gradients of the order of 10 GV/m are produced by a hollow electron beam driver with FACET like parameters. The peak accelerating field increases linearly with the total charge in the beam driver while the axial size of the favorable region ($\s…
The dielectric function for electron gas with parabolic energy bands is derived in a fractional dimensional space. The static response function shows a good dimensional dependance. The plasma frequencies are obtained from the roots of the dielectric functions. The plasma dispersion shows strong dimensional dependence. It is found that the plasma frequencies in the low dimensional systems are strongly dependent on the wave vector. It is weakly dependent in the three dimensional system and has a finite value at zero wave vector.
We study the collision frequencies of particles in the weakly and highly ionized plasmas with the power-law q-distributions in nonextensive statistics. We derive the average collision frequencies of neutral-neutral particle, electron-neutral particle, ion-neutral particle, electron-electron, ion-ion and electron-ion, respectively, in the q-distributed plasmas. We show that the average collision frequencies depend strongly on the q-parameter in a complex form and thus their properties are significantly different from that in Maxwell-distributed plasmas. These new average collision frequencies a…
The collision frequencies of electron-neutral-particle in the weakly ionized complex plasmas with the non-Maxwellian velocity distributions are studied. The average collision frequencies of electron-neutral-particle in the plasmas are derived accurately. We find that these collision frequencies are significantly dependent on the power-law spectral indices of non-Maxwellian distribution functions and so they are generally different from the collision frequencies in the plasmas with a Maxwellian velocity distribution, which will affect the transport properties of the charged particles in the pla…
Investigation of the specific oscillations with frequencies 15-30 kHz on the T-10 tokamak (R= 150cm, a = 30 cm) with Heavy Ion Beam Probe (HIBP) diagnostic was conducted in regimes with off-axis ECRH (B = 2.33 T, Ip= 220 kA, r_ECRH=12 cm). Previous experiments in OH regimes have shown that "20 kHz" modes are mainly the potential fluctuations. These oscillations are seen on the signals of HIBP, Langmuir probes and reflectometry. They should cause the fluctuations of the poloidal rotation, i.e. the torsional plasma oscillations with m=0, called as the zonal flows. The HIBP sample volume was loca…
We study the ion response to an initial perturbation in a weakly ionized plasma with ion flow driven by a dc electric field. The analysis is made by extending the classical Landau work [J. Phys. (USSR) 10, 25 (1946)] to the ion kinetic equation including ion-neutral collisions and a dc electric field. We show, in particular, that the complex frequencies of ion waves can be directly found from a known expression for the ion susceptibility [Phys. Rev. E 71, 016405 (2005); Phys. Rep. 27, 997 (2001)]; this is not obvious from its original derivation, because it only aims to describe the ion respon…
Proposals to reach the next generation of laser intensities through Raman or Brillouin backscattering have centered on optical frequencies. Higher frequencies are beyond the range of such methods mainly due to the wave damping that accompanies the higher density plasmas necessary for compressing higher frequency lasers. However, we find that an external magnetic field transverse to the direction of laser propagation can reduce the required plasma density. Using parametric interactions in magnetized plasmas to mediate pulse compression both reduces the wave damping and alleviates instabilities,…
The local magnetic field in a Penning-Malmberg trap is found by measuring the temperatures that result when electron plasmas are illuminated by microwaves pulses. Multiple heating resonances are observed as the pulse frequencies are swept. The many resonances are due to electron bounce and plasma rotation sidebands. The heating peak corresponding to the cyclotron frequency resonance is identified to determine the magnetic field. A new method for quickly preparing low density electron plasmas for destructive temperature measurements enables a rapid and automated scan of microwave frequencies. T…
The asymptotic behavior of the equilibrium radiation in Maxwellian plasma is investigated for the region of low frequencies. It is shown, that already for a weakly non-ideal plasma the equilibrium radiation can essentially deviate from the Planck law. The deviation from the Planck distribution is described by the transverse dielectric permittivity which takes into account both frequency and spatial dispersion. The influence of plasma non-ideality increases with increase of the non-ideality parameter in the in the dielectric permittivity. The spectral energy distribution of the equilibrium radi…
Resonant field amplification or error field penetration involves driving a weakly stable tearing perturbation in a rotating toroidal plasma. In this paper it is shown that the locking characteristics for modes with finite real frequencies $ω_{r}$ are quite different from the conventional results. A calculation of the tearing mode amplitude assuming modes with frequencies $\pmω_{r}$ in the plasma frame shows that it is maximized when the frequency of the stable backward propagating mode ($-ω_{r}$) in the lab frame is zero, i.e. when $v=ω_{r}/k$. Even more importantly, the locking torque is exac…
We present a new theoretical approach for collisional absorption of laser energy in dense plasmas which accommodates arbitrary frequencies and high intensities of the laser field. We establish a connection between laser absorption by inverse Bremstrahlung and the stopping power. This relation is then applied to include strong correlations beyond the mean field approach. The results show an excellent agreement with molecular dynamics simulations up to very high coupling strength.
Tearing modes with real frequencies in the plasma frame (i.e. in addition to the Doppler shift due to $E\times B$ rotation) are of potential importance because of their effect on the locking process. In particular, it has recently been shown [J. M. Finn, A. J. Cole, and D. P. Brennan, Phys. Plasmas (Letters), 22:120701, 2015] that the Maxwell torque on the plasma in the presence of an applied error field is modified significantly for tearing modes having real frequencies near marginal stability. In addition, it is known [J. M. Finn and R. A. Gerwin, Phys. Plasmas, 3:2344, 1996] that resistive …
A first-principle study of the collective oscillation spectrum of a strongly correlated one-component plasma in a strong magnetic field is presented. The spectrum consists of six fundamental modes which are found to be in good agreement with results from the Quasi-Localized Charge approximation. At high frequencies additional modes are observed that include Bernstein-type oscillations and their transverse counterparts which are of importance for the high-frequency optical and transport properties of these plasmas.
Sufficient conditions are found on the ion velocity distribution $f_i$ and potential amplitude for stability of steady electron holes moving at slow speeds, coinciding with the bulk of $f_i$. Fully establishing stability requires calculation of the ion response to shift potential perturbations having an entire range of oscillatory frequencies, because under some conditions real frequencies intermediate between the ion and electron responses prove to be unstable even when the extremes are not. The mechanism of this overstability is explained and calculated in detail. Electron holes of peak pote…
The physics of plasmas containing positive and negative ions is discussed with special attention to the recently produced pair-ion plasma containing ions of equal mass and opposite charge. The effects of the density gradient in the direction perpendicular to the ambient magnetic field vector, observed in the experiment, are discussed. In addition, the possible presence of electrons is discussed in the context of plasma modes propagating at an angle with respect to the magnetic field vector. The electrons may either be added to the plasma or enter the plasma attached to negative ions and then b…
The electron cyclotron emission (ECE) in fusion devices is non-trivial to model in detail at frequencies well below the fundamental resonance where the plasma is optically thin. However, doing so is important for evaluating the background for microwave diagnostics operating in this frequency range. Here we present a general framework for estimating the ECE levels of fusion plasmas at such frequencies using ensemble-averaging of rays traced through many randomized wall reflections. This enables us to account for the overall vacuum vessel geometry, self-consistently include cross-polarization, a…
Photon bursts with a wavelength smaller than the plasma inter-particle distance can drive plasma wakes via Compton scattering. We investigate this fundamental process analytically and numerically for different photon frequencies, photon flux, and plasma magnetization. Our results show that Langmuir and extraordinary modes are driven efficiently when the photon energy density lies above a certain threshold. The interaction of photon bursts with magnetized plasmas is of distinguished interest as the generated extraordinary modes can convert into pure electromagnetic waves at the plasma/vacuum bo…
A self-consistent particle-in-cell simulation study is performed to investigate the effect of driving frequency on the electric field non-linearity, electron heating mechanism and electron energy distribution function (EEDF) in a low pressure symmetric capacitively coupled plasma (CCP) discharge at a constant electron plasma frequency. The driving frequency is varied from 27.12 MHz to 100 MHz for a discharge gap of 3.2 cm in argon at a gas pressure of 1 Pa. The simulation results provide insight of higher harmonic generations in a CCP system for a constant electron response time. The spatio-te…
The classic problem of the dynamic evolution of Langmuir electron waves in a collisionless plasma and their Landau damping is cast as a second-order, self-adjoint problem with a continuum spectrum of real and positive squared frequencies. The corresponding complete basis of singular normal modes is obtained, along with their orthogonality relation. This yields easily the general expression of the time-reversal-invariant solution for any initial-value problem. An example is given for a specific initial condition that illustrates the Landau damping of the macroscopic moments of the perturbation.
We present measurements of high-order harmonics and relativistic electrons emitted into the vacuum from a plasma mirror driven by temporally-shaped ultra-intense laser waveforms, produced by collinearly combining the main laser field with its second harmonic. We experimentally show how these observables are influenced by the phase delay between these two frequencies at the attosecond timescale, and relate these observations to the underlying physics through an advanced analysis of 1D/2D Particle-In-Cell simulations. These results demonstrate that sub-cycle shaping of the driving laser field pr…
The propagation of plasma waves in a new non-linear, logarithmic electrodynamics model is performed. A cold, uniform, collisionless fluid plasma model is applied. Electrostatic waves in magnetized plasma are shown to correspond to modified Trivelpiece-Gould modes, together with changes of the plasma and upper-hybrid frequencies, driven by the logarithmic electrodynamics effects. Electromagnetic waves are described by a generalized Appleton-Hartree dispersion relation. The cases of propagation parallel or perpendicular to the equilibrium magnetic field are analyzed in detail. In particular, gen…
The dispersion characteristics of an circularly polarized electromagnetic wave of arbitrary amplitude, propagating in a highly (thermally and kinematically) relativistic plasma, are shown to approach those of a linear wave in an unmagnetized, non-relativistic plasma. Further aided by high relativistic temperatures, the cut-off frequency tends to become negligibly small; as a result, waves with frequencies well below the nominal plasma and the cyclotron frequencies find the plasma to be essentially transparent. This relativistic phenomenon may greatly advance our ability to understand and model…
The concept of available energy of a collisionless plasma is discussed in the context of magnetic confinement. The available energy quantifies how much of the plasma energy can be converted into fluctuations (including nonlinear ones) and is thus a measure of plasma stability, which can be used to derive linear and nonlinear stability criteria without solving an eigenvalue problem. In a magnetically confined plasma, the available energy is determined by the density and temperature profiles as well as the magnetic geometry. It also depends on what constraints limit the possible forms of plasma …
Magnetosonic waves propagating perpendicular to an external magnetic field are studied with attention to the effect of multiple ion species. First, power spectra of magnetic field fluctuations and autocorrelation functions in thermal equilibrium plasmas are numerically obtained. In a multi-ion-species plasma, besides $ω\simeq kv_{\rm A}$ mode, numerous waves are present near many different ion cyclotron frequencies. The autocorrelation function of the quasi-mode consisting of these waves is not recovered to its initial value, owing to the phase mixing of these waves. Next, with particle simula…
Rf plasma production in Whistler waves range of frequency f/fci >1 is applied on the compact helical system (CHS) in a steady state operation with low toroidal magnetic field strength, where f and fci are rf and ion cyclotron frequencies, respectively. Maximum rf power and pulse width are is170kW and 10 msec at 9MHz, respectively. The line averaged plasma density <ne> as high as 2x10^18 m-3 (He plasma) is produced in the region of toroidal magnetic field strength on magnetic axis B=100G~1.5kG and the electron temperature measured at plasma periphery is about 20eV. The wave magnetic field stren…
The properties of linear instabilities in the Large Plasma Device [W. Gekelman et al., Rev. Sci. Inst., 62, 2875 (1991)] are studied both through analytic calculations and solving numerically a system of linearized collisional plasma fluid equations using the 3D fluid code BOUT [M. Umansky et al., Contrib. Plasma Phys. 180, 887 (2009)], which has been successfully modified to treat cylindrical geometry. Instability drive from plasma pressure gradients and flows is considered, focusing on resistive drift waves, the Kelvin-Helmholtz and rotational interchange instabilities. A general linear disp…
Plasma supports electromagnetic waves propagation for frequencies higher than plasma frequency but features dielectric permittivity less than 1. This property leads to photon density of states (DOS) lower than in vacuum and should result in subnatural spectral linewidths, sub-Planckian spectrum of thermal radiation, and sub-Rayleigh scattering as well as in lower inelastic photon scattering including Raman scattering. Lamb shift will be altered as well though the decisive contribution from high-energy modes in this case makes the photon DOS effect rather small since plasma DOS converges with t…
Rotation of tokamak-plasmas, not at the mechanical equilibrium, is investigated utilizing a theorem of thermodynamics, established by Prigogine. This theorem, suitably applied to toroidally confined plasmas, suggests that the global barycentric rotations of the plasma, in the toroidal and poloidal directions, are pure reversible processes. In case of negligible viscosity and by supposing the validity of the balance equation for the internal forces, we show that the plasma, even not in the mechanical equilibrium, may freely rotate as a rigid body in the toroidal direction with an angular freque…
The normal modes of a three-dimensional Yukawa plasma in an isotropic, harmonic confinement are investigated by solving the linearized cold fluid equations. The eigenmodes are found analytically and expressed in terms of hypergeometric functions. It is found that the mode frequencies solely depend on the dimensionless plasma parameter $ξ=κR$, where $R$ is the plasma radius and $κ$ the inverse screening length. The eigenfrequencies increase monotonically with $ξ$ and saturate in the limit $ξ\to\infty$. Compared with the results in the Coulomb limit~[D. H. E. Dubin, Phys. Rev. Lett. \textbf{66},…
We present a new model for simulating the electromagnetic fluctuations with frequencies much lower than the ion cyclotron frequency in plasmas confined in general magnetic configurations. This novel model (termed as GK-E&B) employs nonlinear gyrokinetic equations formulated in terms of electromagnetic fields along with momentum balance equations for solving fields. It, thus, not only includes kinetic effects, such as wave-particle interaction and microscopic (ion Larmor radius scale) physics; but also is computationally more efficient than the conventional formulation described in terms of pot…
Resistive instabilities of current sheets in stratified plasmas with a gravitational field
Institute for Fusion Studies, Department of Physics, The University of Texas at Austin（德克萨斯大学奥斯汀分校物理系聚变研究所）；Department of Physics, Faculty of Science, Assiut University（阿西尤特大学理学院物理系）
The low frequency magnetic field spectrum in the primordial plasma is of particular interest as a possible origin of magnetic fields in the universe (e.g., Tajima et al. 1992 and Cable and Tajima 1992). We derive the magnetic field spectrum in the primordial plasma, in particular, at the epoch of primordial nucleosynthesis. The pioneering study of Cable and Tajima (1992) of the electromagnetic fluctuations, based on the Fluctuation-Dissipation Theorem, is extended. Our model describes both the thermal and collisional effects in a plasma. It is based on a kinetic description with the BGK collis…
A strongly mismatched regime of self-guided nonlinear laser-plasma acceleration in the bubble regime is modeled for optimization of Laser to Particle energy efficiency with application to recently proposed laser positron accelerator. The strong mismatch, in contrast with the matched condition, arises from the incident laser spot-size being much larger than that needed for equilibration of the laser ponderomotive and electron-ion charge-separation force in the plasma bubble. This is shown to be favorable for optimization of large self-injected electron charge and ultra-low transverse emittance.…
It is assumed, in general, that the electromagnetic spectrum in the Primordial Universe was a blackbody spectrum in vacuum. We derive the electromagnetic spectrum, based on the Fluctuation-Dissipation Theorem that describes the electromagnetic fluctuations in a plasma. Our description includes thermal and collisional effects in a plasma. The electromagnetic spectrum obtained differs from the blackbody spectrum in vacuum at low frequencies. In particular, concentrating on the primordial nucleosynthesis era, it has more energy for frequencies less than 3 to $6ω_{pe}$, where $ω_{pe}$ is the elect…
This is a brief overview of the main physical ideas for application of field effect transistors for generation and detection of TeraHertz radiation. Resonant frequencies of the two-dimensional plasma oscillations in FETs increase with the reduction of the channel dimensions and reach the THz range for sub-micron gate lengths. When the mobility is high enough, the dynamics of a short channel FET at THz frequencies is dominated by plasma waves. This may result, on the one hand, in a spontaneous generation of plasma waves by a dc current and on the other hand, in a resonant response to the incomi…
A Synthetic Aperture Microwave Imaging (SAMI) system has been designed and built to obtain 2-D images at several frequencies from fusion plasmas. SAMI uses a phased array of linearly polarised antennas. The array configuration has been optimised to achieve maximum synthetic aperture beam efficiency. The signals received by antennas are down-converted to the intermediate frequency range and then recorded in a full vector form. Full vector signals allow beam focusing and image reconstruction in both real time and a post processing mode. SAMI can scan over 16 preprogrammed frequencies in the rang…
It is shown through analytical modeling and numerical simulations that external magnetic fields can relax the self-trapping thresholds in plasma based accelerators. In addition, the transverse location where self-trapping occurs can be selected by adequate choice of the spatial profile of the external magnetic field. We also find that magnetic-field assisted self-injection can lead to the emission of betatron radiation at well defined frequencies. This controlled injection technique could be explored using state-of-the-art magnetic fields in current/next generation plasma/laser wakefield accel…
Waveform shaping and frequency synthesis based on waveform modulation is ubiquitous in electronics, telecommunication technology, and optics. For optical waveforms, the carrier frequency is on the order of several hundred THz, while the modulation frequencies used in conventional devices like electro- or acousto-optical modulators are orders of magnitude lower. As a consequence, any new frequencies are typically very close to the fundamental. The synthesis of new frequencies in the extreme ultraviolet (XUV), e.g. by using relativistic oscillating mirrors, requires modulation frequencies in the…
Four-wave mixing and secondary radiations generated by nonharmonic two-color filaments in air: Influence of the Kerr and plasma nonlinearities
Vilnius University（维尔纽斯大学）；Université de Bordeaux-CNRS-CEA（波尔多大学-CNRS-CEA）；The Extreme Light Infrastructure ERIC, ELI Beamlines Facility（极强光基础设施ERIC，ELI光束线设施）
Inhomogeneous plasmas filaments instabilities are investigated by using the techniques of classical differential geometry of curves where Frenet torsion and curvature describe completely the motion of curves. In our case the Frenet frame changes in time and also depends upon the other coordinates taking into account the inhomogeneity of the plasma. The exponential perturbation method so commonly used to describe cosmological perturbatons is applied to magnetohydrodynamic (MHD) plasma equations to find longitudinal modes describing Alfven waves propagation modes describing plasma waves in the m…
We visualize plasma bubbles driven by 0.67 PW laser pulses in plasma of density $n_e \approx 5\times10^{17}$ ${\rm cm}^{-3}$ by imaging Faraday rotation patterns imprinted on linearly-polarized probe pulses of wavelength $λ_{pr} = 1.05 μ$m and duration $τ_{pr} = 2$ ps or $1$ ps that cross the bubble's path at right angles. When the bubble captures and accelerates tens to hundreds of pC of electron charge, we observe two parallel streaks of length $cτ_{pr}$ straddling the drive pulse propagation axis, separated by $\sim45$ $μ$m, in which probe polarization rotates by $0.3^\circ$ to more than $5…
We study the response of a semi-bounded one-component fully degenerate electron plasma to an initial perturbation in the electrostatic limit. We show that the part of the electric potential corresponding to surface waves in such plasma can be represented, at large times, as the sum of two terms, one term corresponding to "conventional" (Langmuir) surface waves and the other term representing a new type of surface waves resulting from specific analytic properties of degenerate plasma's dielectric response function. These two terms are characterized by different oscillation frequencies (for a gi…
The existence of low frequency waveguide modes of ion acoustic waves is demonstrated in magnetized plasmas for electron temperature striated along the magnetic field lines. At higher frequencies, in a band between the ion cyclotron and the ion plasma frequency, radiative modes develop and propagate obliquely to the field away from the striation. Arguments for the subsequent formation and propagation of electrostatic shock are presented and demonstrated numerically. For such plasma conditions, the dissipation mechanism is the "leakage" of the harmonics generated by the wave steepening.
