A. M. Ignatov, P. P. J. M. Schram, S. A. Trigger
The inhomogeneity of the plasma pressure near a conducting electrode is a cause for introducing the surface tension associated with the plasma-electrode interface. We evaluate the dependence of the surface tension on the density of the charged dust immersed in the plasma sheath. In a wide range of parameters, the surface tension turns out to be an increasing function of the dust density.
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We wish to transmit messages to and from a hypersonic vehicle around which a plasma sheath has formed. For long distance transmission, the signal carrying these messages must be necessarily low frequency, typically 2 GHz, to which the plasma sheath is opaque. The idea is to use the plasma properties to make the plasma sheath appear transparent.
Most plasmas have a very thin sheath compared with the plasma dimension. This necessitates separate calculations of the plasma and sheath. The Bohm criterion provides the boundary condition for calculation of plasma profiles. To calculate sheath properties a value of electric field at the plasma-sheath interface has to be specified in addition to the Bohm criterion. The value of the boundary electric field and robust procedure to approximately patch plasma and collisionless sheath with a very good accuracy are reported.
We numerically investigate the dust charging in the sheath, by using the usual fluid approximation, it is extended to include self consistently the dust charge variation. The grain charge becomes a new self consistent dynamic variable, it is found that dust grains are first charged negatively at the sheath edge and then begin to be charged positively in the sheath. The numerical results show that the initial velocity of dust charged grains, sized grains and the density ratio of ion to electron at the sheath edge have affected the neutral point of dust charge. Moreover, the neutral point of dus…
Plasma sheath is the non-neutral space charge region that isolates bulk plasma from boundary. Radio-frequency (RF) sheathes are formed when applying RF voltage to electrodes. Generally, applied bias is mainly consumed by RF sheath which shields external field. Here we report first evidence that intense boundary emission destroys normal RF sheath and establishes a novel type of RF plasma where external bias is consumed by bulk plasma instead of sheath. Ions are naturally confined while plasma electrons are unobstructed, generating strong RF current in entire plasma, combined with unique particl…
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.
An electric circuital analysis of laboratory plasma sheath fluctuations and propagations
本文通过将等离子体鞘层建模为串联谐振LCR电路，理论解释了鞘层振荡、电流扰动及鞘层波，并揭示其触发离子声波的机制，可用于天线与探针诊断。
Driven dust-charge fluctuation and chaotic ion dynamics in the plasma sheath and pre-sheath regions
本文利用h-PIC-MCC模拟研究尘埃等离子体鞘层与预鞘层中由紫外辐射驱动的尘埃电荷涨落，证明其可诱发离子动力学的混沌振荡。
Equilibrating gravitation by electric forces, microparticles can be confined in the plasma sheath above suitably biased local electrodes.Their position depends on the detailed structure of the plasma sheath and on the charge that the particles acquire in the surrounding plasma, that is by the electron and ion currents towards it. Bias switching experiments reveal how the charge and equilibrium position of the microparticle change upon altered sheath conditions. We observe similar particle behaviors also in the afterglow of the discharge for a persisting bias voltage on the electrode: damped os…
The electron sheath is a particular electron-rich sheath with negative net charges where plasma potential is lower than the biased electrode. Here an improved understanding of electron sheath theory is provided using both fluid and kinetic approaches while elaborating on its implications for plasma-surface interaction. A fluid model is first proposed considering the electron presheath structure, avoiding the singularity in electron sheath Child-Langmuir law. The latter is proved to underestimate the sheath potential. Subsequently, the kinetic model of electron sheath is established, showing co…
New class instabilities is identified in Hall plasmas in configurations with open magnetic field lines. It is shown that sheath resistivity results in a robust instability driven by the equilibrium electric field. It is conjectured that these instabilities play a crucial role in anomalous transport in Hall plasmas devices.
Biased electrodes are common components of plasma sources and diagnostics. The plasma-electrode interaction is mediated by an intervening sheath structure that influences properties of the electrons and ions contacting the electrode surface, as well as how the electrode influences properties of the bulk plasma. A rich variety of sheath structures have been observed, including ion sheaths, electron sheaths, double sheaths, double layers, anode glow, and fireballs. These represent complex self-organized responses of the plasma that depend not only on the local influence of the electrode, but als…
In this work, we have considered the formation of warm plasma sheath in the vicinity of a wall in a plasma with considerable presence of dust particles. As an example, we have used the parameters relevant in case of lunar plasma sheath, though the results obtained in this work could be applied to any other physical situation such as laboratory plasma. In the ion-acoustic time scale, we neglect the dust dynamics. The dust particles affect the sheath dynamics by affecting the Poisson equation which determines the plasma potential in the sheath region. We have assumed the current to a dust partic…
A large family of plasmas has collisional mean-free-path much longer than the non-neutral sheath width, which scales with the plasma Debye length. The plasmas, particularly the electrons, assume strong temperature anisotropy in the sheath. The temperature in the sheath flow direction ($T_{e\parallel}$) is lower and drops towards the wall as a result of the decompressional cooling by the accelerating sheath flow. The electron temperature in the transverse direction of the flow field ($T_{e\perp}$) not only is higher but also spikes up in the sheath. This abnormal behavior of $T_{e\perp}$ spike …
Plasma sheath physics: A circuital description, amelioration, and application
本文综述了等离子体鞘层的电路模型分析方法，阐释其电感、电容和电阻特性的物理机制，并讨论了该模型在多个研究领域的应用及相对非电路方法的优势。
Employing an attenuated oscillation method, the anisotropic interaction force between two vertically aligned dust particles located in the sheath of a complex plasma was measured experimentally based on a linear approximation to the interaction force. Experimental data shows that although both particles experience a repulsive interaction force, the upper particle experiences a stronger magnitude force than does the lower. This result can be explained by the ion wakefield since the lower particle resides within the ion wakefield generated by the streaming ions passing through the sheath and aro…
The plasma exit flow speed at the sheath entrance is constrained by the Bohm criterion. The so-called Bohm speed regulates the plasma particle and power exhaust fluxes to the wall, and it is commonly deployed as a boundary condition to exclude the sheath region in quasi-neutral plasma modeling. Here the Bohm criterion analysis is performed in the intermediate plasma regime away from the previously known limiting cases of adiabatic laws and the asymptotic limit of infinitesimal Debye length in a finite-size system, using the transport equations of an anisotropic plasma. The resulting Bohm speed…
The classical Debye-Hückel screening effect of the electrostatic field generated by isolated charged particles immersed in a plasma is reviewed. The validity of the underlying mathematical model, and particularly of the weak-field approximation, are analyzed. It is shown that the presence of the plasma sheath around test particles and the resulting effect of charge screening are essential for the description of plasmas which are strongly coupled.
A Nonlinear Two-Sheath Circuit Model for Low-Pressure Symmetric and Asymmetric Capacitively Coupled Radio-Frequency Plasmas
本文提出非线性双鞘层电路模型，统一描述对称与不对称低压电容耦合射频等离子体，揭示不对称性增强谐波与串联共振振荡的机理。
Due to the complicated environment of the plasma sheath, it is difficult to experimentally measure plasma characteristics in the narrow geometry where sheaths from opposite boundaries overlap. Since such geometries are often found in industrial plasma applications, accurate measurements of this type are of significant interests. In this paper, we employ micron-sized dust grains as non-perturbative probes of the plasma environment. A particle-freefall technique is then used to measure the sheath profiles produced by a rf plasma within a glass box. The results show that this technique can identi…
A collisional magnetized plasma consisting of two temperature electrons has been investigated numerically to study the sheath structure and the ion energy flux to the wall. The low-temperature electrons are described by Maxwellian distribution, and the high-temperature electrons are described by truncated Maxwellian distribution. It has been observed that high-temperature electrons play a major role in the sheath potential as well as the ion energy flux to the wall. The presence of collision in the sheath has a significant effect on the properties of the sheath. The study of such a system can …
A Deep Learning Approach to Describing the Plasma Sheath
本文提出利用物理信息神经网络PINN，无需实验或模拟数据，高效预测等离子体鞘层在不同物理保真度下的参数解，提供有效的替代模型。
Experiments are performed in which dust particles are levitated at varying heights above the powered electrode in a RF plasma discharge by changing the discharge power. The trajectories of particles dropped from the top of the discharge chamber are used to reconstruct the vertical electric force acting on the particles. The resulting data, together with the results from a selfconsistent fluid model, are used to determine the lower levitation limit for dust particles in the discharge and the approximate height above the lower electrode where quasineutrality is attained, locating the sheath edge…
A one dimensional Vlasov Poisson simulation code is employed to investigate the plasma sheath considering electron induced secondary electron emission (SEE) and backscattering. The SEE coefficient is commonly treated as constant in a range of plasma simulations, here improved SEE model of a charged dielectric wall is constructed which includes the wall charging effect on SEE coefficient and the energy dependency of SEE coefficient. Pertinent algorithms to implement above SEE model in plasma simulation are studied in detail. It is found that the SEE coefficient increases with the amount of nega…
The results of an analysis of the physics of levitation of negatively charged dust particles over a surface (wall) in an inverse sheath are reported. It is shown that under suitable parameter regime, the ion-drag force may balance the combined electrostatic and gravitational force on the dust particles owing to its hollow profile as one moves away from the surface. Our analysis shows that the parameter regimes in which such a situation may result is realizable in laboratory and space plasma environments, particularly the near-surface dayside lunar plasma. The lunar surface and dust grains are …
A review of the theoretical and computational aspects of plasma-wall transition is presented. The conditions for the existence of plasma sheaths in front of a solid surface are established. Various regimes are analyzed -collisionless and collisional. fluid and kinetic, with and without ionization. The partition of the plasma-wall transition into distinct regions (Debye sheath, quasineutral presheath. magnetic presheath, etc...) is also discussed. Applications to the theory of electrostatic probes are illustrated by means of a recently developed kinetic model. The influence of the probe on ion …
The properties of plasma sheath containing the primary electrons with a Cairns-distribution
研究含冷正离子、二次电子和初级电子的等离子体鞘层性质，推导广义Bohm准则和Bohm速度，新壁面浮势及新临界二次电子发射系数，揭示非热Cairns分布参数对鞘层性质的显著影响。
Two in-situ experimental methods are presented in which dust particles are used to determine the extent of the sheath and gain information about the time-averaged electric force profile within a RF plasma sheath. These methods are advantageous because they are not only simple and quick to carry out, but they also can be performed using standard dusty plasma experimental equipment. In the first method, dust particles are tracked as they fall through the plasma toward the lower electrode. These trajectories are then used to determine the electric force on the particle as a function of height as …
The plasma force on grains of specified charge and height in a collisional DC plasma sheath are calculated using the multidimensional particle in cell code COPTIC. The background ion velocity distribution functions for the unperturbed sheath vary substantially with collisionality. The grain force is found to agree quite well with a combination of background electric field force plus ion drag force. However, the drag force must take account of the non-Maxwellian (and spatially varying) ion distribution function, and the collisional drag enhancement. It is shown how to translate the dimensionles…
By combining the results from a self-consistent 2D dusty plasma fluid model and a 3D N-body code, the equilibrium position and crystal structure were determined for dust particles levitated in the sheath in a modified Gaseous Electronics Conference (GEC) reference cell, in which the lower electrode was heated or cooled. The Debye length, charge and electric field were reconstructed on a sub-millimeter scale by applying a previously developed, independent method. However, this method seems to overestimate the charge, and hence underestimate the electric field. Even corrected for this fact, the …
Plasma sheath tailoring by a magnetic field for three-dimensional plasma etching
提出利用磁场结合掩模调控等离子体鞘层，通过E×B漂移实现三维方向性刻蚀，并经实验和2d3v PIC/MCC模拟验证。
Experimental data compiled over five decades of dense plasma focus research is consistent with the snowplow model of sheath propagation, based on the hypothetical balance between magnetic pressure driving the plasma into neutral gas ahead and wind pressure resisting its motion. The resulting sheath velocity, or the numerically proportional drive parameter, is known to be approximately constant for devices optimized for neutron production over 8 decades of capacitor bank energy. This paper shows that the validity of the snowplow hypothesis, with some correction, as well as the non-dependence of…
The plasma sheath sets a stage for a strongly nonlinear coupling of the thermal, kinetic, and electric energies of plasma in a non-equilibrium, open environment. The pressure, velocity, and electrostatic potential profiles depend strongly on the boundary condition given on the internal side (pre-sheath). By controlling the boundary values of the heat flux and the ion Mach number, we solve a set of equations for the ion temperature and the electrostatic potential. The boundary values of the ion velocity and the electrostatic potential vary due to the change of the boundary ion temperature. When…
It is well known that oscillations at the electron plasma frequency may appear due to instability of the plasma sheath near a positively biased electrode immersed in plasma. This instability is caused by transit-time effects when electrons, collected by this electrode, pass through the sheath. Such oscillations appear as low-power short spikes due to additional ionization of a neutral gas in the electrode vicinity. Herein we present first results obtained when the additional ionization was eliminated. We succeeded to prolong the oscillations during the whole time a positive bias was applied to…
We propose a theoretical ground for emissive capacitively coupled radio-frequency plasma sheath under low pressure. The rf sheath is assumed to be collisionless, and oscillates with external source. A known sinusoidal voltage instead of current is taken as prerequisite to derive sheath dynamics. Kinetic studies are performed to determine mean wall potential as a function of secondary emission coefficient and applied voltage amplitude, with which the complete mean DC sheath is resolved. Analytical analyses under homogeneous model and numerical analyses under inhomogeneous model are conducted to…
The electron sheath formation in a DC magnetised plasma of modified hollow cathode source is studied. The discharge consists of two plane parallel cathodes and a small cubical anode placed off axis at the center. The argon plasma is produced and the properties of the plasma in response to the sheath formation near the anode are studied using electrical and optical diagnostics. In particular, the effect of pressure, magnetic field on discharge parameters such as discharge current, plasma potential, plasma density and electron temperature is studied. The discharge showed an onset of anode glow a…
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…
Dependencies of levitation position of positively charged fine-particles on plasma parameters are investigated. The charges on the particles become positive in a cross-field sheath between magnetized double plasmas with different potentials separated vertically by horizontal magnetic field, because ion current flowing from a lower high-potential plasma surpasses electron current coming across the magnetic field from an upper low-potential plasma. From measurement of the resonance frequency of the particles driven by external oscillating electric field, the charge on particle is estimated to be…
Adiabatic sheath model for beam-driven blowout plasma channels
针对等离子体尾场加速器中吹出鞘层分布函数不准确或依赖先验参数的问题，本文基于力平衡提出绝热鞘层模型，实现了鞘层分布的自洽描述，并更准确地估计了吹出通道平衡半径。
Impact of plasma potential and plasma sheath composition on the InN PAMOCVD growth kinetics and structural properties
该研究探讨PA-MOCVD生长参数对等离子体电势的影响，分析电势变化及外加直流偏置扰动对InN薄膜生长过程与结构特性的作用，为InN薄膜的可控制备提供参考。
This paper describes in detail the construction of a local right-handed, orthogonal curvilinear coordinate system whose axes are along the local tangent, the local azimuth and the local normal of an analytically defined 3D surface of rotation, whose shape mimics the shape of a plasma focus current sheath. Expressions for various differential operators are derived in a tutorial format for the benefit of young researchers and non-specialists. Physical problems expressed in this coordinate system would benefit from the natural symmetry properties of the plasma focus sheath. For example, the norma…
The sheath formation in a weakly magnetized collisionless electronegative plasma consisting of electrons, negative and positive ions has been numerically investigated using the hydrodynamic equations. The electrons and negative ions are assumed to follow Boltzmann relation. A sheath formation criterion has been analytically derived. The paper focuses on studying the sheath structure by varying the electronegativity. It has been observed that the presence of negative ions has a substantial effect on the sheath structure. The observations made in the present work have profound significance on pr…
Space resolved concentrations of helium He metastable atoms in an atmospheric pressure radio-frequency micro-plasma jet were measured using tunable diode laser absorption spectroscopy. The spatial profile of metastable atoms in the volume between the electrodes was deduced for various electrode gap distances. Density profiles reveal the sheath structure and reflect the plasma excitation distribution, as well as the dominance of the alpha-mode discharge. Gap width variations show the transition from a normal glow plasma to a pure sheath discharge. In order to analyze and verify the experimental…
This paper describes the surface environment of the dense plasma arcs that damage rf accelerators, tokamaks and other high gradient structures. We simulate the dense, non-ideal plasma sheath near a metallic surface using Molecular Dynamics (MD) to evaluate sheaths in the non-Debye region for high density, low temperature plasmas. We use direct two-component MD simulations where the interactions between all electrons and ions are computed explicitly. We find that the non-Debye sheath can be extrapolated from the Debye sheath parameters with small corrections. We find that these parameters are r…
Sheath Analysis of Conducting Channel Walls in Anode-Layer Hall Thruster with Acceleration Zone Shifted Downstream
本研究针对阳极层霍尔推力器RAIJIN66的通道壁鞘层，结合二维混合模拟与一维鞘层模型开展研究，得到了通道出口的离子壁面电流密度与鞘层厚度，并明确了电流密度降低对鞘层覆盖范围的影响规律。
Plasma fireball sheath dynamics: A brief review and meta-analysis
本文综述了等离子体火球鞘层的形成机制、相关不稳定性及触发条件，比较了规则与反向火球的实验差异，并展望了理论与应用前景。
In this paper, the central concern is to analyze the influence of the forces that controls the ion dynamics inside a magnetized plasma sheath under collisionless conditions. The ionization effects are considered within the sheath. The magnetic field is tilted in x-z plane and makes an angle with the x-axis. The motivation of the paper is to see the effect of both field strength variation and the variation of the inclination angle on the force fields inside the sheath. The pitch length and pitch angle for the particle velocity field is also calculated and has been found to vary widely with the …
This letter provides the first prediction of the probability density function (PDF) of flux $R$ in plasma sheath sheath region in magnetic fusion devices which is characterized by dynamical equations with exponential non-linearities. By using a non-perturbative statistical theory (instantons), the PDF tails of first moment are shown to be modified Gumbel distribution which represents a frequency distribution of the extreme values of the ensemble. The non-Gaussian PDF tails that are enhanced over Gaussian predictions are the result of intermittency caused by short lived coherent structures (ins…
A particle-in-cell (PIC) simulation study is performed to investigate the discharge asymmetry, higher harmonic generations and electron heating mechanism in a low pressure very high frequency capacitively coupled plasma (CCP) excited by a saw-tooth like current waveform. Two current densities, 50 A/m2 and 100 A/m2 are chosen for a constant gas pressure of 5 mTorr in argon plasma. The driving frequency is varied from 13.56 MHz to 54.24 MHz. At a lower driving frequency, high frequency modulations on the instantaneous sheath edge position at the grounded electrode are observed. These high freque…
Multifluid simulations of plasma sheaths are increasingly used to model a wide variety of problems in plasma physics ranging from global magnetospheric flows around celestial bodies to plasma-wall interactions in thrusters and fusion devices. For multifluid problems, accurate boundary conditions to model an absorbing wall that resolves a classical sheath remains an open research area. This work justifies the use of vacuum boundary conditions for absorbing walls to show comparable accuracy between a multifluid sheath and lower moments of a continuum-kinetic sheath.
A careful study of plasma-material interactions is essential to understand and improve the operation of devices where plasma contacts a wall. Key contributions of this work include (i) novel continuum kinetic algorithms with novel boundary conditions that directly discretize the Vlasov/Boltzmann equation using the discontinuous Galerkin method, (ii) fundamental studies of a plasma sheath physics with collisions, ionization, and physics-based wall emission, and (iii) theoretical and numerical studies of the linear growth and nonlinear saturation of the kinetic Weibel instability, including its …
We investigate the electron heating dynamics in electropositive argon and helium capacitively coupled RF discharges driven at 13.56 MHz by Particle in Cell simulations and by an analytical model. The model allows to calculate the electric field outside the electrode sheaths, space and time resolved within the RF period. Electrons are found to be heated by strong ambipolar electric fields outside the sheath during the phase of sheath expansion in addition to classical sheath expansion heating. By tracing individual electrons we also show that ionization is primarily caused by electrons that col…
The control of the spatial distribution of micrometer-sized dust particles in capacitively coupled radio frequency discharges is relevant for research and applications. Typically, dust particles in plasmas form a layer located at the sheath edge adjacent to the bottom electrode. Here, a method of manipulating this distribution by the application of a specific excitation waveform, i.e. two consecutive harmonics, is discussed. Tuning the phase angle θbetween the two harmonics allows to adjust the discharge symmetry via the Electrical Asymmetry Effect (EAE). An adiabatic (continuous) phase shift …
Plasma sheath studies using a physical treatment of electron emission from a dielectric wall
本研究针对介电壁附近等离子体鞘层模拟中低能电子相互作用未被严格考量的问题，将低能电子反射作为边界条件纳入连续动力学框架开展模拟，发现材料参数对鞘层特性有显著影响，高反射率表面会形成空间电荷限制鞘层。
The potential difference between a floating emitting surface and the plasma surrounding it has been described by several sheath models, including the space-charge-limited sheath, the electron sheath with high emission current, and the inverse sheath produced by charge-exchange ion trapping. Our measurements reveal that each of these models has its own regime of validity. We determine the potential of an emissive filament relative to the plasma potential, emphasizing variations in emitted current density and neutral particle density. The potential of a filament in a diffuse plasma is first show…
We have investigated magnetic field generation in velocity shears via the kinetic Kelvin-Helmholtz instability (kKHI) using a relativistic plasma jet core and stationary plasma sheath. Our three-dimensional particle-in-cell simulations consider plasma jet cores with Lorentz factors of 1.5, 5, and 15 for both electron-proton and electron-positron plasmas. For electron-proton plasmas we find generation of strong large-scale DC currents and magnetic fields which extend over the entire shear-surface and reach thicknesses of a few tens of electron skin depths. For electron-positron plasmas we find …
A low-pressure magnetized plasma is studied to find the dependency of sheath properties on ion-neutral collisions in presence of an inhomogeneous magnetic field. A self-consistent one-dimensional two-fluid hydrodynamic model is considered, and the system of equations is solved numerically. The study reveals that the width of the plasma sheath expands and space charge increases with collisions. The ion-neutral collisions and the inhomogeneous magnetic field restrict the ions to move towards the surface. The movement of the ions towards the wall can be controlled by choosing a suitable configura…
Plasma sheaths driven by radio-frequency voltages occur frequently, in contexts ranging from plasma processing applications to magnetically confined fusion experiments. These sheaths are crucial because they dominantly affect impedance, power absorption, ion acceleration and sometimes the stability of the nearby plasma. An analytical understanding of sheath behavior is therefore important, both intrinsically and as an element in more elaborate theoretical structures. In practice, these radio-frequency sheaths are commonly excited by highly anharmonic waveforms, but no analytical model exists f…
The Debye sheath is known to vanish completely in magnetised plasmas for a sufficiently small electron gyroradius and small angle between the magnetic field and the wall. This angle depends on the current onto the wall. When the Debye sheath vanishes, there is still a potential drop between the wall and the plasma across the magnetic presheath. The magnetic field angle corresponding to the predicted sheath collapse is shown to be much smaller than previous estimates, scaling with the electron-ion mass ratio and not with the square root of the mass ratio. This is shown to be a consequence of th…
The survivability of dust being transported in the magnetized sheath near the divertor plate of a tokamak and its impact on the desired balance of erosion and redeposition for a steady-state reactor are investigated. Two different divertor scenarios are considered. The first is characterized by an energy flux perpendicular to the plate $q_0\simeq 1$ MW/m$^2$ typical of current short-pulse tokamaks. The second has $q_0\simeq 10$ MW/m$^2$ and is relevant to long-pulse machines like ITER or DEMO. It is shown that micrometer dust particles can survive rather easily near the plates of a divertor pl…
Micron-size charged particles can be easily levitated in low-density plasma environments. At low pressures, suspended particles have been observed to spontaneously oscillate around an equilibrium position. In systems of many particles, these oscillations can catalyze a variety of nonequilibrium, collective behaviors. Here, we report spontaneous oscillations of single particles that remain stable for minutes with striking regularity in amplitude and frequency. The oscillation amplitude can also exceed 1 cm, nearly an order of magnitude larger than previously observed. Using an integrated experi…
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