The standard equilibrium equation for magnetized plasma is extended to account for the magnetic polarization force. A factor of the pressure gradient arising from the magnetic decomposition of the Hall term survives the limit of vanishing magnetization and is canceled by a contribution from the magnetic polarization force, such that the proposed equation reduces to the standard form in the free current limit. Comparison of the solutions for an axially symmetric plasma column indicates agreement with the free current limit for vanishing magnetization and variation in the field and current profiles as the degree of magnetization increases.
Direct experimental evidence for the existence of axial magnetic field both in the radial implosion phase and the pinch phase of a plasma focus has raised many questions of fundamental importance. The most fundamental of these is the fact of its existence, which is incomprehensible in terms of a conventional view of plasma physics. The plasma is known to have an axis of symmetry in the radial implosion phase. The axial magnetic field has a defined polarity with respect to the axis. Since the equations of magnetohydrodynamics are unchanged by flipping the sign of the axial coordinate, the polar…
Using detailed spectroscopic measurements, highly-resolved in both time and space, a self-generated plasma rotation is demonstrated for the first time in a cylindrical Z-pinch implosion with a pre-embedded axial magnetic field. The plasma parameters and all three components of the magnetic field are resolved. The plasma is seen to rotate at a velocity comparable to the peak implosion velocity, considerably affecting the force and energy balance throughout the implosion. Moreover, the evolution of the rotation is consistent with magnetic flux surface isorotation, a novel observation in a Z-pinc…
Exact solutions to the static equilibrium magnetohydrodynamic equations are presented and discussed for both axially and helically reduced systems. For both symmetries, physical restrictions on the solutions are discussed and it is seen that there arise two different families of physical solutions corresponding to two distinct pressure profiles. One is suitable for atmospherically confined plasma whereas the other is suitable for plasma residing in a vacuum. For solutions in vacuum, the radial dependence is found to behave periodically for both axial and helical symmetries. For these physical …
The attainable transformer ratio in plasma accelerators is limited by instabilities. Using three-dimensional particle-in-cell simulations, we demonstrate that these can be controlled using a hollow plasma channel with a co-axial plasma filament. The driver scatters electrons from the filament, and the slow pinch of the ions leads to a strong chirp of the effective betatron frequency, preventing beam breakup. We demonstrate the monoenergetic acceleration of an electron bunch to 20 GeV over 4.4 m, achieving a transformer ratio of 10, an energy efficiency of 40% and an emittance of 1.8 um.
In this paper, the evolution of the induced axial magnetization due to the propagation of an electromagnetic (em) wave along the static background magnetic field in a two-component plasma has been investigated using the Block equation. The evolution process induces a strong magnetic anisotropy in the plasma medium, depending nonlinearly on the incident wave amplitude. This induced magnetic anisotropy can modify the dispersion relation of the incident em wave, which has been obtained in this paper. In the low frequency Alfven wave limit, this dispersion relation shows that the resulting phase v…
Magnetic field (B) distribution of the magnetron was measured and discussed its effect on plasma parameters and deposition rate. Plasma parameters such as electron temperature (Te), electron number density (ne) were estimated using electron flux (EF) and electron energy distribution function (EEDF) methods as function of axial, radial distances from the cathode. Te and ne decreased with increasing of axial, radial distances from the cathode. Dr was obtained for the same positions where the above plasma parameters were measured, and found that similar profile with Te and ne. Magnetron configura…
It is shown that electric current flowing along an axially non-uniform magnetic flux tube produces an associated non-linear, non-conservative axial MHD force which pumps plasma from regions where the flux tube diameter is small to regions where it is large. In particular, this force will ingest plasma into the ends of a fat, initially potential flux tube and then pump the ingested plasma towards the middle bulge, thereby causing mass accumulation at the bulge. The ingested plasma convects frozen-in toroidal magnetic flux which accumulates at the middle as well. Flux accumulation at the bulge h…
First experimental measurements are presented for the kink instability in a linear plasma column which is insulated from an axial boundary by finite sheath resistivity. Instability threshold below the classical Kruskal-Shafranov threshold, axially asymmetric mode structure and rotation are observed. These are accurately reproduced by a recent kink theory, which includes axial plasma flow and one end of the plasma column that is free to move due to a non-line-tied boundary condition.
Direct measurement of axial magnetic field in the PF-1000 dense plasma focus (DPF), and its reported correlation with neutron emission, call for a fresh look at previous reports of existence of axial magnetic field component in the DPF from other laboratories, and associated data suggesting toroidal directionality of fast ions participating in fusion reactions, with a view to understand the underlying physics. In this context, recent work dealing with application of the hyperbolic conservation law formalism to the DPF is extended in this paper to a curvilinear coordinate system, which reflects…
Recent experiments using 15 frame interferometry on PF-1000 facility in Warsaw confirm the association between neutron emission and spontaneously self-organized, relatively long lasting, finite plasma structures. A crucial aspect of this association is the simultaneous observation of an axial magnetic field, which can allow magnetic flux lines to densely cover closed surfaces creating "magnetic flux surfaces". Evolution of such 3-dimensional (3-D) magnetic field structures is necessarily accompanied by induced electric field that can provide a very long (theoretically infinite) acceleration pa…
Models of covariant linear electromagnetic constitutive relations are formulated that have wide applicability to the computation of susceptibility tensors for dispersive and inhomogeneous media. A perturbative framework is used to derive a linear constitutive relation for a globally neutral plasma enabling one to describe in this context a generalized Landau damping mechanism for non-stationary inhomogeneous plasma states.
Absorption of angular momentum from a high intensity laser pulse can lead to the generation of strong axial magnetic fields in plasma. The effect, known as the inverse Faraday effect can generate kilo-Tesla strength, multi-picosecond, axial magnetic fields extending over hundreds of microns in underdense plasma. In this paper we explore the effect with ultra-high intensity circularly polarized Gaussian beams and linearly polarized orbital angular momentum beams comparing analytic expressions with 3D particle-in-cell simulations. We develop a model for the transverse magnetic field profiles, in…
For a plasma in a stationary homogeneous turbulence, the Fokker-Planck equation is derived from the nonlinear Vlasov equation by introducing the entropy principle. The ensemble average in evaluating the kinetic diffusion tensor, whose symmetry has been proved, can be computed in a straightforward way when the fluctuating particle trajectories are provided. As an application, it has been shown that a mean electric filed can drive a particle flux through the Stokes-Einstein relation, independent of the details of turbulence.
Negative energy wave phenomena may appear in shear flows in the presence of a wave decay mechanism and external energy supply. We study the appearance of negative energy surface waves in a plasma cylinder in the incompressible limit. The cylinder is surrounded by an axial magnetic field and by a plasma of different density. Considering flow inside and viscosity outside the flux tube, we derive dispersion relations, and obtain analytical solutions for the phase speed and growth rate (increment) of the waves. It is found that the critical speed shear for the occurrence of the dissipative instabi…
A two-fluid model developed originally to describe wave oscillations in the vacuum arc centrifuge, a cylindrical, rapidly rotating, low temperature and confined plasma column, is applied to interpret plasma oscillations in a RF generated linear magnetised plasma (WOMBAT), with similar density and field strength. Compared to typical centrifuge plasmas, WOMBAT plasmas have slower normalised rotation frequency, lower temperature and lower axial velocity. Despite these differences, the two-fluid model provides a consistent description of the WOMBAT plasma configuration and yields qualitative agree…
We present results of twisted plasma waves driven by twisted ponderomotive force. With beating of two, co-propagating, Laguerre-Gaussian (LG) orbital angular momentum (OAM) laser pulses with different frequencies and also different twist indices, we can get twisted ponderomotive force. Three-dimensional particle-in-cell simulations are used to demonstrate the twisted plasma waves driven by lasers. The twisted plasma waves have an electron density perturbation with a helical rotating structure. Different from the predictions of the linear fluid theory, the simulation results show a nonlinear ro…
A nonlinear dispersion of a general stationary wave in collisionless plasma is obtained in a non-differential form from a single-particle oscillation-center Hamiltonian. For electrostatic oscillations in nonmagnetized plasma, considered as a paradigmatic example, the linear dielectric function is generalized, and the trapped particle contribution to the wave frequency shift $Δω$ is found analytically as a function of the wave amplitude $a$. Smooth distributions yield $Δω\sim a^{1/2}$, as usual. However, beam-like distributions of trapped electrons result in different power laws, or even a loga…
We show how an appropriate stationary crystalline structure of the magnetic field can induce a partial fragmentation of the accretion disk, generating an axial jet seed composed of hot plasma twisted in a funnel-like structure due to the rotation of the system. The most important feature we outline is the high degree of collimation, naturally following from the basic assumptions underlying the crystalline structure. The presence of non-zero dissipative effects allows the plasma ejection throughout the axial jet seed and the predicted values of the accretion rate are in agreement with observati…
The relaxation of a helical magnetic field ${\bf B}({\bf x}, t)$ in a high-conductivity plasma contained in the annulus between two perfectly conducting coaxial cylinders is considered. The plasma is of low density and its pressure is negligible compared with the magnetic pressure; the flow of the plasma is driven by the Lorentz force and and energy is dissipated primarily by the viscosity of the medium. The axial and toroidal fluxes of magnetic field are conserved in the perfect-conductivity limit, as is the mass per unit axial length. The magnetic field relaxes during a rapid initial stage t…
We report experimental results on the injection of a magnetized plasma jet into a transverse background magnetic field in the HelCat linear plasma device at the University of New Mexico [M. Gilmore et al., J. Plasma Phys. 81, 345810104 (2015)]. After the plasma jet leaves the plasma-gun muzzle, a tension force arising from an increasing curvature of the background magnetic field induces in the jet a sheared axial-flow gradient above the theoretical kink-stabilization threshold. We observe that this emergent sheared axial flow stabilizes the n=1 kink mode in the jet, whereas a kink instability …
It is shown that if a current-carrying magnetic flux tube is bulged at its axial midpoint z=0 and constricted at its axial endpoints z=+h,-h, then plasma will be accelerated from z=+h,-h towards z=0 resulting in a situation similar to two water jets pointed at each other. The ingested plasma convects embedded, frozen-in toroidal magnetic flux from z=+h,-h to z=0. The counter-directed flows collide and stagnate at z=0 and in so doing (i) convert their translational kinetic energy into heat, (ii) increase the plasma density at z~0, and (iii) increase the embedded toroidal flux density at z~0. Th…
The equations of motion for a fully ionized hydrogenic plasma in applied coaxial electric and magnetic fields are analyzed, where the term for the Hall effect in the generalized Ohm's law equation picks up a factor of 1/2 relative to its usual expression. Magnetization of the medium is incorporated through the decomposition of the Hall term and the inclusion of the magnetization force, which is found to equal or exceed the gradient of the scalar pressure. A limit on the kinetic pressure obtains which corresponds to the usual limit of unity for a certain selection of parameters. Solutions of th…
In this paper, we prove that the kappa distribution is the stationary solution of the Vlasov-Poisson system in an inhomogeneous plasma under the polytropic equation of state and an assumption restricting the local velocity distribution to a specific mathematical form. The profiles of density, temperature, and electric potential are obtained theoretically. The kappa index can be determined if the initial state is known. In order to verify the theory, particle-in-cell simulations are made and the results show excellent agreement with the theoretical predictions for density, temperature, and velo…
Effects of radio-frequency power and driven frequency on the two-dimensional (axial and radial) distributions of electron density and temperature were experimentally investigated in low pressure capacitively coupled argon plasmas. The intensity profiles of 696.5 nm and 750.4 nm emission lines were detected by employing a spatially resolved diagnostic system, which consists of a charge coupled device (CCD) and bandpass interference filters. The two-dimensional distributions of electron density and electron temperature were calculated from the spatial distributions of emission intensities via a …
We analyze a linear perturbation scheme for a two-dimensional background plasma, which is rotating with a differential frequency and is embedded in a poloidal magnetic field. The main two assumptions of the present study, which in turn are related, are that the plasma profile is axially symmetric, both in the background and the perturbation approximation, where the azimuthal magnetic field is requested to vanish identically and secondly the angular frequency on the magnetic surface function only still holds in the non-stationary regime, which, on the steady background equilibrium, is ensured b…
One dimensional high-order moment models with realistic collisions for nonequilibrium ion transport in weakly ionized plasmas
Laboratoire de Physique des Plasmas, Centre National de la Recherche Scientifique, Sorbonne Université, École polytechnique, Institut Polytechnique de Paris（等离子体物理实验室，法国国家科学研究中心，索邦大学，巴黎综合理工学院，巴黎理工学院）
We propose a new way of axial magnetic fields generation in a non-relativistic laser intensity regime by using a twisted light carrying orbital angular momentum (OAM) to stimulate two-plasmon decay (TPD) in a plasma. The growth of TPD driven by an OAM light in a Laguerre-Gauss (LG) mode is investigated through three dimensional fluid simulations and theory. A theory based on the assumption that the electron plasma waves (EPWs) are locally driven by a number of local plane-wave lasers predicts the maximum growth rate proportional to the peak amplitude of the pump laser field and is verified by …
We investigate distribution of magnetic fields around dense solid plasmas generated by intense p-polarized laser (~10^{16} W.cm^{-2}, 100 fs) irradiation of magnetic tapes, using high sensitivity magneto optical microscopy. We present evidence for giant axial magnetic fields and map out for the first time the spatial distribution of these fields. By using the axial magnetic field distribution as a diagnostic tool we uncover evidence for angular momentum associated with the plasma. We believe this study holds significance for investigating the process under which a magnetic material magnetizes …
Several simulations of turbulence in the Large Plasma Device (LAPD) [W. Gekelman et al., Rev. Sci. Inst. 62, 2875 (1991)] are energetically analyzed and compared with each other and with the experiment. The simulations use the same model, but different axial boundary conditions. They employ either periodic, zero-value, zero-derivative, or sheath axial boundaries. The linear stability physics is different between the scenarios because the various boundary conditions allow the drift wave instability to access different axial structures, and the sheath boundary simulation contains a conducting wa…
Enhancement of axial magnetic field generation during relativistic self-channeling of laser radiation propagating along thin films
Lomonosov Moscow State University（莫斯科国立大学）；Gaponov–Grekhov Institute of Applied Physics of the Russian Academy of Sciences（俄罗斯科学院应用物理加波诺夫-格列霍夫研究所）；Lobachevsky State University of Nizhny Novgorod（下诺夫哥罗德洛巴切夫斯基国立大学）
The creation and design of a plasma thruster are considered using a rotating cylindrical plasma flow in crossed magnetic fields. The thruster scheme uses this plasma guided by a permanent, radial and a time-dependent axial magnetic field. Namely, the acceleration effect is formed by the azimuthal electric field which comes about as a variation of an external, axial magnetic flux. Besides, it is possible to go beyond the approach of quasi-neutrality. These processes can lead to the generation of a local azimuthal time-dependent electric field which may also accelerate the rotation of the electr…
The derivation of the helicon dispersion relation for a uniform plasma with stationary ions subject to a constant background magnetic field is reexamined in terms of the potential formulation of electrodynamics. Under the same conditions considered by the standard derivation, the nonlinear self-coupling between the perturbed electron flow and the potential it generates is addressed. The plane wave solution for general propagation vector is determined for all frequencies and expressed in terms of a vector phasor. The behavior of the solution as described in vacuum units depends upon the ratio o…
A new plasma state has been investigated [C.~Akcay, J.~Finn, R.~Nebel and D.~Barnes, Phys.~Plasmas $\textbf{24}$, 052503 (2017)], with a uniform applied axial magnetic field in a periodic cylinder of length $L=2πR$, driven by helical electrodes. The drive is single helicity, depending on $mθ+kz=mθ-nζ$, where $ζ=z/R$ and $k=-n/R$. For strong $(m,n)=(1,1)$ drive the state was found to have a strong axial mean current density, with a mean-field safety factor $q_0(r)$ just above the pitch of the electrodes $m/n=1$ in the interior. This state has possible applications to DC electrical transformers …
Using high resolution kinetic (VPPM-OMP 1.0) and fluid (BOUT++) solvers, evolution of long-wavelength electron plasma wave (EPW) in the presence of stationary periodic ion background non-uniformity is investigated. Mode coupling dynamics between long-wavelength EPW mode of scale k and ion inhomogeneity of scale $k_{0}$ is illustrated. Validity of well known Bessel function $J_{n}(x)$ scaling in the cold plasma approximation (i.e., when phase velocity $ω/k >> v_{thermal}$) along-with the effect of ion inhomogeneity amplitude (A) on temporal evolution of energy density in the long-wavelength EPW…
Within the kinetic approach velocity and charge distributions of grains in stationary dusty plasmas are calculated and the relations between the effective temperatures of such distributions and plasma parameters are established. It is found that the effective temperature which determines the velocity grain distribution could be anomalously large due to the action of accelerating ionic bombarding force. The possibility to apply the results obtained to the explanation of the increasing grain temperature in the course of the Coulomb-crystal melting by reduction of the gas pressure is discussed. T…
Starting from the given passive particle equilibrium particle cylindrical profiles, we built self-consistent stationary conditions of the Maxwell-Vlasov equation at thermodynamic equilibrium with non-flat density profiles. The solutions to the obtained equations are then discussed. It appears that the presence of an azimuthal (poloidal) flow in the plasma can insure radial confinement, while the presence of a longitudinal (toroidal) flow can enhance greatly the confinement. Moreover in the global physically reasonable situation, we find that no unstable point can emerge in the effective integr…
In this paper, we address the theoretical resolution of the Vlasov-Gauss system from the linear regime to the strongly nonlinear one, when significant trapping has occurred. The electric field is that of a sinusoidal electron plasma wave (EPW) which is assumed to grow from the noise level, and to keep growing at least up to the amplitude when linear theory in no longer valid (while the wave evolution in the nonlinear regime may be arbitrary). The ions are considered as a neutralizing fluid, while the electron response to the wave is derived by matching two different techniques. We make use of …
The existence of axial (poloidal) magnetic field in a plasma focus and its significance in plasma focus phenomenology has been extensively discussed in a recent review paper. The poloidal magnetic field is a part of the transient 3-dimensional magnetic field structures which arise spontaneously, accelerate ions and keep them moving in trajectories that repeatedly cross a dense and warm plasma target. This is the origin of the abnormally high fusion reaction rate of the plasma focus, which has been known since the 1960s but has begun to be understood quite recently. Further progress now depends…
Nonlinear stationary structures formed in a cold plasma with immobile ions in the presence of a relativistic electron current beam have been investigated analytically in the collisionless limit. These are cold plasma version of the relativistic Berstein-Greene-Kruskal (BGK) waves. The structure profile is governed by the ratio of maximum electrostatic field energy density to the relativistic kinetic energy density of the electron beam, {\it i.e.}, $κ_{R} = E_{m}/ (8 πn_{0} (γ_{0}-1)m_{0} c^{2})^{1/2}$, where $E_{m}$ is the maximum electric field associated with the nonlinear structure and $γ_{…
The ionization efficiency of helicon plasma discharge is explored by changing the low axial magnetic field gradients near the helicon antenna. The highest plasma density is found for a most possible diverging field near the antenna by keeping the other operating condition constant. Measurement of axial wave number together with estimated radial wavenumber suggests the oblique mode propagation of helicon wave along the resonance cone boundary. Propagation of helicon wave near the resonance cone angle boundary can excite electrostatic fluctuations which subsequently can deposit energy in the pla…
It is demonstrated that targets with a broken rotational symmetry may facilitate generation of a strong axial (poloidal) magnetic field. An intense laser beam irradiating such a target creates intense electron currents carrying vorticity and producing strong spontaneous magnetic fields. Combined with a laser electron acceleration, such targets may be used for generation and guiding of magnetized, collimated particle or plasma beams.
The electron cross-field transport by the induced azimuthal electric field in a Hall thruster exhibits the mobility scaled by $1/B$. This study investigates parameters affecting this transport over a Hall thruster's distinct regions, such as the ionization, acceleration, and plume region. The main focus is on the nonzero equilibrium azimuthal electric field induced by an azimuthally inhomogeneous neutral supply. A fast Fourier transform analysis of the plasma structure reveals that the wavenumber $k$ of the azimuthal plasma structure increases from $k=2$, which is the input condition, to $k=4$…
Experimental investigation of an electronegative cylindrical capacitively coupled geometrically asymmetric plasma discharge with an axisymmetric magnetic field
Observations and numerical simulations of laboratory and space plasmas in almost collisionless regimes reveal anisotropic and non-gyrotropic particle distribution functions. We investigate how such states can persist in the presence of a sheared flow. We focus our attention on the pressure tensor equation in a magnetized plasma and derive analytical self-consistent plasma equilibria which exhibit a novel asymmetry with respect to the magnetic field direction. These results are relevant for investigating, within fluid models that retain the full pressure tensor dynamics, plasma configurations w…
We investigate in stationary regime on the linear plasma device OMT-2 the methods of plasma heating by electromagnetic waves, interaction of electromagnetic waves with magnetoactive plasma and plasma turbulence and transport processes in the trap. We use ultra-high frequency (UHF) contactless method to fill the open magnetic trap by plasma. We have proposed new method of open magnetic trap filling with plasma. Namely, plasma is injected in the trap along the magnetic field from independent stationary UHF source where plasma is formed in ECR regime. In this paper we present the results of inves…
Coagulation growth kinetics of nanoparticles in plasma is affected by inter-particle electrostatic forces due to charging phenomenon. In stationary plasmas, unipolar charging of particles results in retardation of particles growth and may result in limitation on a particle size. We demonstrate opposite effect of enhanced particles growth in atmospheric pressure non-stationary arc discharge. Modeling of the nanoparticles growth kinetics revealed the formation of bipolar charge distribution. As a result, reversed (attractive) Coulomb forces promote formation of micrometer size particles in a mil…
Under certain conditions an intense kinetic plasma jet is observed to emerge from the apex of laboratory simulations of coronal plasma loops. Analytic and numerical models show that these jets result from a particle orbit instability in a helical magnetic field whereby magnetic forces radially eject rather than confine ions with sufficiently large counter-current axial velocity.
A kinetic treatment is developed for collisionless magnetized plasmas occurring in high-temperature, low-density astrophysical accretion disks, such as are thought to be present in some radiatively-inefficient accretion flows onto black holes. Quasi-stationary configurations are investigated, within the framework of a Vlasov-Maxwell description. The plasma is taken to be axisymmetric and subject to the action of slowly time-varying gravitational and electromagnetic fields. The magnetic field is assumed to be characterized by a family of locally nested but open magnetic surfaces. The slow colli…
We derive the differential equation governing the asymptotic quasi-stationary states of the two dimensional plasma immersed in a strong confining magnetic field and of the planetary atmosphere. These two systems are related by the property that there is an intrinsic constant length: the Larmor radius and respectively the Rossby radius and a condensate of the vorticity field in the unperturbed state related to the cyclotronic gyration and respectively to the Coriolis frequency. Although the closest physical model is the Charney-Hasegawa-Mima (CHM) equation, our model is more general and is rela…
Fluctuations of electric and magnetic fields in the collisionless plasma are found as a solution of the initial value linearized problem. The plasma initial state is on average stationary and homogeneous. When the state is stable, the initial fluctuations decay exponentially and in the long time limit a stationary spectrum of fluctuations is established. For the equilibrium plasma it reproduces the spectrum obtained from the fluctuation-dissipation relation. Fluctuations in the unstable two-stream system are also discussed.
