The correlation buildup and the formation dynamics of the shell structure in a spherically confined one-component plasma are studied. Using Langevin dynamics simulations the relaxation processes and characteristic time scales and their dependence on the pair interaction and dissipation in the plasma are investigated. While in systems with Coulomb interaction (e.g. trapped ions) in a harmonic confinement shell formation starts at the plasma edge and proceeds inward, this trend is significantly weakened for dusty plasmas with Yukawa interaction. With a suitable change of the confinement conditions the crystallization scenario can be externally controlled.
The stationary state of a spherically symmetric plasma configuration is investigated in the limit of immobile ions and weak collisions. Configurations with small radii are positively charged as a significant fraction of the electron population evaporates during the equilibration process, leaving behind an electron distribution function with an energy cutoff. Such charged plasma configurations are of interest for the study of Coulomb explosions and ion acceleration from small clusters irradiated by ultraintense laser pulses and for the investigation of ion bunches propagation in a plasma.
Tightly focused laser pulses as they diverge or converge in underdense plasma can generate wake waves, having local structures that are spherical waves. Here we report on theoretical study of relativistic spherical wake waves and their properties, including wave breaking. These waves may be suitable as particle injectors or as flying mirrors that both reflect and focus radiation, enabling unique X-ray sources and nonlinear QED phenomena.
The term Active Plasma Resonance Spectroscopy (APRS) denotes a class of related techniques which utilize, for diagnostic purposes, the natural ability of plasmas to resonate on or near the electron plasma frequency: A radio frequent signal (in the GHz range) is coupled into the plasma via an antenna or probe, the spectral response is recorded, and a mathematical model is used to determine plasma parameters like the electron density or the electron temperature. Based on the cold plasma model, this manuscript provides the general analytic expression of the electrical admittance of a spherical sh…
We describe an experiment to form and characterize a section of a spherically imploding plasma liner by merging six supersonic plasma jets that are launched by newly designed contoured-gap coaxial plasma guns. This experiment is a prelude to forming a fully spherical imploding plasma liner using many dozens of plasma guns, as a standoff driver for plasma-jet-driven magneto-inertial fusion. The objectives of the six-jet experiments are to assess the evolution and scalings of liner Mach number and uniformity, which are important metrics for spherically imploding plasma liners to compress magneti…
Three dimensional hydrodynamic simulations have been performed using smoothed particle hydrodynamics (SPH) in order to study the effects of discrete jets on the processes of plasma liner formation, implosion on vacuum, and expansion. The pressure history of the inner portion of the liner was qualitatively and quantitatively similar from peak compression through the complete stagnation of the liner among simulation results from two one dimensional radiationhydrodynamic codes, 3D SPH with a uniform liner, and 3D SPH with 30 discrete plasma jets. Two dimensional slices of the pressure show that t…
Dusty plasma crystals have traditionally been observed and studied in radio frequency (RF) discharge plasmas and their formation in a DC glow discharge plasma remains experimentally challenging. We report the first ever observation of a stable dusty plasma Coulomb crystal in the cathode sheath region of a DC glow discharge plasma. The observations are made in the DPEx device where crystals of mono-disperse Melamine Formaldehyde grains are produced in the background of an Argon plasma. The crystalline nature of the structure is confirmed through a host of measurements that includes the radial p…
Turbulence is a major factor limiting the achievement of better tokamak performance as it enhances the transport of particles, momentum and heat which hinders the foremost objective of tokamaks. Hence, understanding and possibly being able to control turbulence in tokamaks is of paramount importance, not to mention our intellectual curiosity of it.
A combined theoretical and experimental analysis of the normal modes of three-dimensional spherially confined Yukawa clusters is presented. Particular attention is paid to the breathing mode and the existence of multiple monopole oscillations in Yukawa systems. Finally, the influence of dissipation on the mode spectrum is investigated.
The space electron-ion-positive dust plasma system containing isothermal inertialess electron species, cold inertial ion species, and stationary positive (positivively charged) dust species is considered. The basic features of one dimensional (1D) planar and nonplanar subsonic solitary waves are investigated by the pseudo-potential and reductive perturbation methods, respectively. It is observed that the presence of the positive dust species reduces the phase speed of the ion-acoustic waves, and consequently supports the subsonic solitary waves with the positive wave potential in such a space …
Spatio-temporal evolution and breaking of relativistically intense cylindrical and spherical space charge oscillations in a homogeneous cold plasma is studied analytically and numerically using Dawson Sheet Model [J.M. Dawson, Phys. Rev.113, 383(1959)]. It is found that cylindrical and spherical space charge oscillations break via the process of phase mixing at an arbitrarily small amplitude due to anharmonicity introduced by geometry and relativistic mass variation effects. A general expression for phase mixing time (wave breaking time) has been derived and it is shown that for both cases, it…
A new type of quasi-two-dimensional complex plasma system was observed which consisted of monodisperse microspheres and their binary agglomerations (dimers). The particles and their dimers levitated in a plasma sheath at slightly different heights and formed two distinct sublayers. The sys- tem did not crystallize and may be characterized as disordered solid. The dimers were identified based on their characteristic appearance in defocused images, i.e., rotating interference fringe pat- terns. The in-plane and inter-plane particle separations exhibit nonmonotonic dependence on the discharge pre…
A spherical tokamak (ST) with a plasma center column (PCC) can be formed via driven magnetic relaxation of a screw pinch plasma. An ST-PCC could in principle eliminate many problems associated with a material center column, a key weakness of the ST reactor concept. This work summarizes the design space for an ST-PCC in terms of flux amplification, aspect ratio, and elongation, based on the zero-beta Taylor-relaxed analysis of Tang & Boozer [Phys. Plasmas 13, 042514 (2006)]. The paper will discuss (1) equilibrium and stability properties of the ST-PCC, (2) issues for an engineering design, and …
This work presents scaling relations for the peak thermal pressure and stagnation time (over which peak pressure is sustained) for an imploding spherical plasma liner formed by an array of merging plasma jets. Results were derived from three-dimensional (3D) ideal hydrodynamic simulation results obtained using the smoothed particle hydrodynamics code SPHC. The 3D results were compared to equivalent one-dimensional (1D) simulation results. It is found that peak thermal pressure scales linearly with the number of jets and initial jet density and Mach number, quadratically with initial jet radius…
Experiments with two-dimensional (2D) plasma crystals are usually carried out in rf plasma sheaths, where the interparticle interactions are modified due to the presence of plasma wakes. The wake-mediated interactions result in the coupling between wave modes in 2D crystals, which can trigger the mode-coupling instability and cause melting. The theory predicts a number of distinct fingerprints to be observed upon the instability onset, such as the emergence of a new hybrid mode, a critical angular dependence, a mixed polarization, and distinct thresholds. In this paper we summarize these key f…
The effects of viscosity and small-scale atomic-level mixing on plasmas in inertial confinement fusion (ICF) currently represent challenges in ICF research. Many current ICF hydrodynamic codes ignore the effects of viscosity though recent research indicates viscosity and mixing by classical transport processes may have a substantial impact on implosion dynamics. We have implemented a Lagrange hydrodynamic code in one-dimensional spherical geometry with plasma viscosity and mass transport and including a three temperature model for ions, electrons, and radiation treated in a gray radiation diff…
Dust-ion collisional effect in dust ion acoustic waves is investigated in the framework of spherical and cylindrical geometry. For such study the fluid equation are takes and collisional effect is consider in the equation of momentum balance. Using reductive perturbation technique the evolution equation is derived with additional damping term for non planner geometry. Using the conservation principle an analytical time dependent solitary wave solution is obtained for the evolution equation. It is seen that dust ion collisional frequency has an significant effect on the width and amplitude of t…
We report measurements of the time-averaged surface floating potential of magnetic and non-magnetic spherical probes (or large dust particles) immersed in a magnetized capacitively coupled discharge. In this study, the size of the spherical probes is taken greater than the Debye length. The surface potential of a spherical probe first increases, i.e. becomes more negative at low magnetic field (B $<$ 0.05 T), attains a maximum value and decreases with further increase of the magnetic field strength (B $>$ 0.05 T). The rate of change of the surface potential in the presence of a B-field mainly …
One-dimensional radiation-hydrodynamic simulations are performed to develop insight into the scaling of stagnation pressure with initial conditions of an imploding spherical plasma shell or "liner." Simulations reveal the evolution of high-Mach-number (M), annular, spherical plasma flows during convergence, stagnation, shock formation, and disassembly, and indicate that cm- and μs-scale plasmas with peak pressures near 1 Mbar can be generated by liners with initial kinetic energy of several hundred kilo-joules. It is shown that radiation transport and thermal conduction must be included to avo…
Spectra of phonons with out-of-plane polarization were studied experimentally in a 2D plasma crystal. The dispersion relation was directly measured for the first time using a novel method of particle imaging. The out-of-plane mode was proven to have negative optical dispersion, comparison with theory showed good agreement. The effect of the plasma wakes on the dispersion relation is briefly discussed.
We report an experimental observation of coupling of the transverse vertical and longitudinal in-plane dust-lattice wave modes in a two-dimensional complex plasma crystal in the absence of mode crossing. A new large diameter rf plasma chamber was used to suspend the plasma crystal. The observations are confirmed with molecular-dynamics simulations. The coupling manifests itself in traces of the transverse vertical mode appearing in the measured longitudinal spectra and vice versa. We calculate the expected ratio of the trace to the principal mode with a theoretical analysis of the modes in a c…
Analysis of helicon wave heating and current drive capability in EXL-50 spherical torus plasmas has been conducted. It is found that the driven current increases with the launched parallel refractive index $n_{||}$ and peaks around $n_{||} = 4.0$ when the frequency of the helicon wave is between 300~MHz and 380~MHz. The helicon wave current drive efficiency shows a relatively stable upward trend with increasing plasma temperature. Moreover, the driven current decreases as the plasma density increases. We also analyzed the current drive with helicon waves of 150~MHz and 170~MHz and found that t…
The formation of self-consistent dust crystal and its melting is a well known phenomenon in rf generated plasma but remains challenging in DC glow discharge plasma. Here, we report the melting of a two dimensional dusty plasma crystal, suspended in the cathode sheath of a DC glow discharge plasma. The experiments are carried out in a $Π-$shaped Dusty Plasma Experimental (DPEx) device where a stationary crystal of melamine formaldehyde particles is formed between the confining strips in a background of Argon plasma. The stable structure breaks and leads to a fluid state on reducing the neutral …
The creation of a spatially extended stable DC complex plasma crystal is a big experimental challenge and a topical area of research in the field of dusty plasmas. In this paper we describe a newly built and commissioned dusty plasma experimental device, DPEx-II, at the Institute for Plasma Research. The device can support the formation of large sized Coulomb crystals in a DC glow discharge plasma. The plasma in this L-shaped table-top glass chamber is produced between a circular anode and a long tray shaped cathode. It is characterized with the help of various electrostatic probes over a rang…
The standard Grad-Shafranov equation for axisymmetric toroidal plasma equilibrium is customary expressed in cylindrical coordinates with toroidal contours, and through which benchmark equilibria are solved. An alternative approach to cast the Grad-Shafranov equation in spherical coordinates is presented. This equation, in spherical coordinates, is examined for toroidal solutions to describe low $β$ Solovev and high $β$ plasma equilibria in terms of elementary functions.
A numerical model for a 2D-monolayer plasma crystal was established using the Box_tree code. Box_tree is a Barnes_Hut tree code which has proven effective in modeling systems composed of large numbers of particles. Thermally excited waves in this plasma crystal were numerically simulated and dispersion relations for both the longitudinal and transverse wave modes were found. These were compared with the dispersion relations extrapolated from experiment as well as a theory based on harmonic approximation. The results were found to agree with theoretical dispersion relations under different wave…
The start-up and sustainment of a stochastic wave non-inductive current on a spherical torus was experimentally demonstrated for the first time using only electron cyclotron waves. The plasma current is insensitive to the injection angle of ECWs and approximately linearly correlated with the slope of the X-ray spectrum. Its direction is determined by the vertical magnetic field (BV). The temporal development in the number of X-ray bremsstrahlung photons with a specified energy is consistent with the stochastic heating model. Moreover, the ratio of Amps to Watts of the ECW is generally >1 kA/kW…
Real dusty crystals are inhomogeneous due to the presence of external forces. We suggest approximations for calculations of different types of inhomogeneous DC (chain and DC with a few slabs) in the equilibrium state. The results are in a good agreement with experimental results and can be used as an effective diagnostic method for many dusty systems.
A two-dimensional dust crystal levitated in the sheath of a modified Gaseous Electronics Conference (GEC) reference cell is manipulated by heating or cooling the lower electrode. The dust charge is obtained by measuring global characteristics of the levitated crystal obtained from top-view pictures. From the force balance, the electric field in the sheath is reconstructed. From the Bohm criterion, we conclude that the dust crystal is levitated mainly above and just below the classical Bohm point.
It is shown that the wake-mediated interactions between microparticles in a two-dimensional plasma crystal affect the shape of the monolayer, making it non-flat. The equilibrium shape is calculated for various distributions of the particle number density in the monolayer. For typical experimental conditions, the levitation height of particles in the center of the crystal can be noticeably smaller than at the periphery. It is suggested that the effect of wake-induced bending can be utilized in experiments, to deduce important characteristics of the interparticle interaction.
The observation is presented of naturally occurring pairing of particles and their cooperative drift in a two-dimensional plasma crystal. A single layer of plastic microspheres was suspended in the plasma sheath of a capacitively coupled rf discharge in argon at a low pressure of 1 Pa. The particle dynamics were studied by combining the top-view and side-view imaging of the suspension. Cross analysis of the particle trajectories allowed us to identify naturally occurring metastable pairs of particles. The lifetime of pairs was long enough for their reliable identification.
I reply here to the comment of Dr Shmatov on my recent work and demonstrate the invalidity of his criticism of the classical physics description of the formation of bound states of electrons participating in spherically symmetric oscillations of plasma.
Dedicated experiments on melting of 2D plasma crystals were carried out. The melting was always accompanied by spontaneous growth of the particle kinetic energy, suggesting a universal plasma-driven mechanism underlying the process. By measuring three principal dust-lattice (DL) wave modes simultaneously, it is unambiguously demonstrated that the melting occurs due to the resonance coupling between two of the DL modes. The variation of the wave modes with the experimental conditions, including the emergence of the resonant (hybrid) branch, reveals exceptionally good agreement with the theory o…
Implications of recently discovered effect of channeling of upstream extra particles for transport phenomena in a two-dimensional plasma crystal are discussed. Upstream particles levitated above the lattice layer and tended to move between the rows of lattice particles. An example of heat transport is considered, where upstream particles act as moving heat sources, which may lead to anomalous heat transport. The average channeling length observed was 15 - 20 interparticle distances. New features of the channeling process are also reported.
The full melting of a two-dimensional plasma crystal was induced in a principally stable monolayer by localized laser stimulation. Two distinct behaviors of the crystal after laser stimulation were observed depending on the amount of injected energy: (i) below a well-defined threshold, the laser melted area recrystallized; (ii) above the threshold, it expanded outwards in a similar fashion to mode-coupling instability induced melting, rapidly destroying the crystalline order of the whole complex plasma monolayer. The reported experimental observations are due to the fluid mode-coupling instabi…
This work extends the one-dimensional radiation-hydrodynamic imploding spherical argon plasma liner simulations of T. J. Awe et al. [Phys. Plasmas 18, 072705 (2011)] by using a detailed tabular equation-of-state (EOS) model, whereas Awe et al. used a polytropic EOS model. Results using the tabular EOS model give lower stagnation pressures by a factor of 3.9-8.6 and lower peak ion temperatures compared to the polytropic EOS results. Both local thermodynamic equilibrium (LTE) and non-LTE EOS models were used in this work, giving similar results on stagnation pressure. The lower stagnation pressu…
The transition between linear and nonlinear regimes of the mode-coupling instability (MCI) operating in a monolayer plasma crystal is studied. The mode coupling is triggered at the centre of the crystal and a melting front is formed, which travels through the crystal. At the nonlinear stage, the mode coupling results in synchronisation of the particle motion and the kinetic temperature of the particles grows exponentially. After melting of the crystalline structure, the mean kinetic energy of the particles continued to grow further, preventing recrystallisation of the melted phase. The effect …
The formation and melting of a mono-layered charged dust particle crystal in a DC glow discharge Argon plasma is studied. The nature of the melting/formation process is established as a first order phase transition from the nature of the variations in the Coulomb coupling parameter, the dust temperature, the structural order parameter and from the existence of a hysteresis behavior. Our experimental results are distinctly different from existing theoretical predictions for 2D crystals based on the KTHNY mechanism or the Grain boundary induced melting and indicate a novel mechanism that is akin…
A Doppler backscattering diagnostic for the EXL-50U spherical tokamak: plasma considerations and preliminary quasioptical design
A*STAR Research Entities（新加坡科学研究局）；Imperial College London（帝国理工学院）；Nanyang Technological University（南洋理工大学）；UCLA（加州大学洛杉矶分校）；ENN Science & Technology Development Co., Ltd（新奥科技发展有限公司）
The ion temperature behavior in the plasma core of the spherical tokamak Globus-M (major radius 0.36 m, minor radius 0.24 m, torus aspect ratio 1.5, toroidal magnetic field near the plasma axis 0.4 T, plasma current up to 0.3 MA) was studied by means of 12-channels neutral particle analyzer (NPA) ACORD-12. The experiments were performed in ohmic regimes as well as in regimes with the ion cyclotron resonance heating (ICRH) in the vicinity of fundamental harmonic for hydrogen minority in deuterium bulk plasma and the neutral beam injection (NBI). The total auxiliary power exceeded the magnitude …
The collisional dynamics of test impurity ions in spherical tokamak plasmas with strongly-sheared radial electric fields is investigated by means of a test particle full orbit simulation code. The strength of the shear is such that the standard drift ordering can no longer be assumed and a full orbit approach is required. The effect of radial electric field shear on neoclassical particle transport is quantified for a range of test particle mass and charge numbers and electric field parameters. It is shown that the effect of a sheared electric field is to enhance the confinement of impurity spe…
The collective motion of dust particles during the mode-coupling induced melting of a two-dimensional plasma crystal is explored in molecular dynamics simulations. The crystal is compressed horizontally by an anisotropic confinement. This compression leads to an asymmetric triggering of the mode-coupling instability which is accompanied by alternating chains of in-phase and anti-phase oscillating particles. A new order parameter is proposed to quantify the synchronization with respect to different directions of the crystal. Depending on the orientation of the confinement anisotropy, mode-coupl…
A Novel Numerical Algorithms Optimization Method with Machine Learning Frameworks: Application on Real-time Plasmas Equilibrium Reconstruction in EXL-50U Spherical Torus
Nankai University（南开大学）；ENN Science and Technology Development Co., Ltd.（新奥科技发展有限公司）；Southwestern Institute of Physics（西南物理研究院）
The layered crystal formation in dusty plasma medium depicted by the Yukawa interaction amidst dust has been investigated using Molecular Dynamics simulations. The multilayer structures are shown to form in the presence of a combined gravitational and external electric field force (representing the sheath field in experiments) along the ^ z direction. A detailed study of the dependence of the number of crystal layer formation, their width etc., on various system parameters (viz., the external field profile and the screening length of Yukawa interaction) have been analyzed. The structural prope…
An interferometric imaging technique has been proposed to instantly measure the diameter of individual spherical dust particles suspended in a gas discharge plasma. The technique is based on the defocused image analysis of both spherical particles and their binary agglomerates. Above a critical diameter, the defocused images of spherical particles contain stationary interference fringe patterns and the fringe number increases with particle diameters. Below this critical diameter, the particle size has been measured using the rotational interference fringe patterns which appear only on the defo…
The spectral asymmetry of the wave energy distribution of dust particles during mode-coupling induced melting, observed for the first time in plasma crystals by Couëdel et al. [Phys. Rev. E 89, 053108 (2014)], is studied theoretically and by molecular-dynamics simulations. It is shown that an anisotropy of the well confining the microparticles selects the directions of preferred particle motion. The observed differences in intensity of waves of opposed directions is explained by a nonvanishing phonon flux. Anisotropic phonon scattering by defects and Umklapp scattering are proposed as possible…
The dissipative electron-ion-pcd (positively charged dust) plasma, which is observed in both space and laboratory plasmas, is considered. The basic features of nonplanar cylindrical and spherical ion-acoustic subsonic shock waves in such a medium are investigated by deriving a modified Burgers equation using the reductive perturbation method. It is found that the stationary pcd species reduces the phase speed of the ion-acoustic waves, and consequently supports the subsonic shock waves due to the kinematic viscosity (acting as a source of dissipation) of the ion species. It is observed that th…
The formation of self-consistent crystalline structure is a well-known phenomenon in complex plasmas. In most experiments the pressure and rf power are the main controlling parameters in determining the phase of the system. We have studied the effect of externally applied magnetic field on the configuration of plasma crystals, suspended in the sheath of a radio-frequency discharge using the Magnetized Dusty Plasma Experiment (MDPX) device. Experiments are performed at a fixed pressure and rf power where a crystalline structure is formed within a confining ring. The magnetic field is then incre…
Two-fluid flowing equilibrium configurations of a helicity-driven spherical torus (HD-ST) are numerically determined by using the combination of the finite difference and the boundary element methods. It is found from the numerical results that electron fluids near the central conductor are tied to an external toroidal field and ion fluids are not. The magnetic configurations change from the high-$q$ HD-ST ($q$>1) with paramagnetic toroidal field and low-$β$ (volume average $β$ value, ($<β>\approx$ 2 %) through the helicity-driven spheromak and RFP to the ultra low-$q$ HD-ST (0<q<1) with diagm…
Strong correlation effects in classical and quantum plasmas are discussed. In particular, Coulomb (Wigner) crystallization phenomena are reviewed focusing on one-component non-neutral plasmas in traps and on macroscopic two-component neutral plasmas. The conditions for crystal formation in terms of critical values of the coupling parameters and the distance fluctuations and the phase diagram of Coulomb crystals are discussed.
The impedance probe is a measurement device to measure plasma parameter like electron density. It consists of one electrode connected to a network analyzer via a coaxial cable and is immersed into a plasma. A bias potential superposed with an alternating potential is applied to the electrode and the response of the plasma is measured. Its dynamical interaction with the plasma in electrostatic, kinetic description can be modeled in an abstract notation based on functional analytic methods. These methods provide the opportunity to derive a general solution, which is given as the response functio…
We study spherically symmetric oscillations of electrons in plasma in the frame of classical electrodynamics. Firstly, we analyze the electromagnetic potentials for the system of radially oscillating charged particles. Secondly, we consider both free and forced spherically symmetric oscillations of electrons. Finally, we discuss the interaction between radially oscillating electrons through the exchange of ion acoustic waves. It is obtained that the effective potential of this interaction can be attractive and can transcend the Debye-Huckel potential. We suggest that oscillating electrons can …
