Capacitively-coupled rf discharge with a large amount of microparticles: spatiotemporal emission pattern and microparticle arrangement

The effect of micron-sized particles on a low-pressure capacitively-coupled rf discharge is studied both experimentally and using numerical simulations. In the laboratory experiments, microparticle clouds occupying a considerable fraction of the discharge volume are supported against gravity with the help of the thermophoretic force. The spatiotemporally resolved optical emission measurements are performed with different arrangements of microparticles. The numerical simulations are carried out on the basis of a one-dimensional hybrid (fluid-kinetic) discharge model describing the interaction between plasma and microparticles in a self-consistent way. The study is focused on the role of microparticle arrangement in interpreting the spatiotemporal emission measurements. We show that it is not possible to reproduce simultaneously the observed microparticle arrangement and emission pattern in the framework of the considered one-dimensional model. This disagreement is discussed and attributed to two-dimensional effects, e.g., radial diffusion of the plasma components

Dim and bright void regimes in capacitively-coupled RF complex plasmas

We demonstrate experimentally that the void in capacitively-coupled RF complex plasmas can exist in two qualitative different regimes. The "bright" void is characterized by bright plasma emission associated with the void, whereas the "dim" void possesses no detectable emission feature. The transition from the dim to the bright regime occurs with an increase of the discharge power and has a discontinuous character. The discontinuity is manifested by a kink in the void size power dependencies. We reproduce the bright void (mechanically stabilized due to the balance of ion drag and electrostatic forces) by a simplified time-averaged 1D fluid model. To reproduce the dim void, we artificially include the radial ion diffusion into the continuity equation for ions, which allows to mechanically stabilize the void boundary due to very weak electrostatic forces. The electric field at the void boundary occurs to be so small that it, in accordance with the experimental observation, causes no void-related emission feature.Comment: 21 pages, 14 figure

Shear flow in a three-dimensional complex plasma in microgravity conditions

Shear flow in a three-dimensional complex plasma was experimentally studied in microgravity conditions using Plasmakristall-4 (PK-4) instrument on board the International Space Station (ISS). The shear flow was created in an extended suspension of microparticles by applying the radiation pressure force of the manipulation-laser beam. Individual particle trajectories in the flow were analyzed and from these, using the Navier-Stokes equation, an upper estimate of the complex plasma's kinematic viscosity was calculated in the range of $0.2$--$6.7~{\rm mm^2/s}$. This estimate is much lower than previously reported in ground-based experiments with 3D complex plasmas. Possible reasons of this difference are discussed.Comment: 5 pages, 4 figure

Dust density waves in a dc flowing complex plasma with discharge polarity reversal

We report on the observation of the self-excited dust density waves in the dc discharge complex plasma. The experiments were performed under microgravity conditions in the Plasmakristall-4 facility on board the International Space Station. In the experiment, the microparticle cloud was first trapped in an inductively coupled plasma, then released to drift for some seconds in a dc discharge with constant current. After that the discharge polarity was reversed. DC plasma containing a drifting microparticle cloud was found to be strongly non-uniform in terms of microparticle drift velocity and plasma emission in accord with [Zobnin et.al., Phys. Plasmas 25, 033702 (2018)]. In addition to that, non-uniformity in the self-excited wave pattern was observed: In the front edge of the microparticle cloud (defined as head), the waves had larger phase velocity than in the rear edge (defined as tail). Also, after the polarity reversal, the wave pattern exhibited several bifurcations: Between each of the two old wave crests, a new wave crest has formed. These bifurcations, however, occurred only in the head of the microparticle cloud. We show that spatial variations of electric field inside the drifting cloud play an important role in the formation of the wave pattern. Comparison of the theoretical estimations and measurements demonstrate the significant impact of the electric field on the phase velocity of the wave. The same theoretical approach applied to the instability growth rate, showed agreement between estimated and measured values.Comment: 7 pages, 4 figure

Quantum dot photoluminescence as charge probe for plasma exposed surfaces

Quantum dots (QDs) are used as nanometer-sized in situ charge probes for surfaces exposed to plasma. Excess charges residing on an electrically floating surface immersed in a low-pressure argon plasma are detected and investigated by analysis of variations in the photoluminescence spectrum of laser-excited QDs that were deposited on that surface. The experimentally demonstrated redshift of the PL spectrum peak is linked to electric fields associated with charges near the QDs’ surfaces, a phenomenon entitled the quantum-confined Stark effect. Variations in the surface charge as a function of plasma input power result in different values of the redshift of the peak position of the PL spectrum. The values of redshift are detected as 0.022 nm and 0.073 for 10 and 90 W plasma input powers, respectively; therefore indicating an increasing trend. From that, a higher microscopic electric field, 9.29 × 10 6 V m−1 for 90 W compared to 3.29 × 10 6 V m−1 for 10 W input power, which is coupled to an increased electric field in the plasma sheath, is sensed by the QDs when plasma input power is increased

Heat transport in a flowing complex plasma in microgravity conditions

Heat transport in a three-dimensional complex (dusty) plasma was experimentally studied in microgravity conditions using a Plasmakristall-4 (PK-4) instrument on board the International Space Station (ISS). An extended suspension of microparticles was locally heated by a shear flow created by applying the radiation pressure force of the manipulation-laser beam. Individual particle trajectories in the flow were analyzed, and from these, using a fluid heat transport equation that takes viscous heating and neutral gas drag into account, the complex plasma’s thermal diffusivity and kinematic viscosity were calculated. Their values are compared with previous results reported in ground-based experiments with complex plasmas

Physical aspects of dust–plasma interactions

Low-pressure gas discharge plasmas are known to be strongly affected by the presence of small dust particles. This issue plays a role in the investigations of dust particle-forming plasmas, where the dust-induced instabilities may affect the properties of synthesized dust particles. Also, gas discharges with large amounts of microparticles are used in microgravity experiments, where strongly coupled subsystems of charged microparticles represent particle-resolved models of liquids and solids. In this field, deep understanding of dust–plasma interactions is required to construct the discharge configurations which would be able to model the desired generic condensed matter physics as well as, in the interpretation of experiments, to distinguish the plasma phenomena from the generic condensed matter physics phenomena. In this review, we address only physical aspects of dust–plasma interactions, that is, we always imply constant chemical composition of the plasma as well as constant size of the dust particles. We also restrict the review to two discharge types: dc discharge and capacitively coupled rf discharge. We describe the experimental methods used in the investigations of dust–plasma interactions and show the approaches to numerical modelling of the gas discharge plasmas with large amounts of dust. Starting from the basic physical principles governing the dust–plasma interactions, we discuss the state-of-the-art understanding of such complicated, discharge-type-specific phenomena as dust-induced stratification and transverse instability in a dc discharge or void formation and heartbeat instability in an rf discharge

Towards a unified theory of Sobolev inequalities

We discuss our work on pointwise inequalities for the gradient which are connected with the isoperimetric profile associated to a given geometry. We show how they can be used to unify certain aspects of the theory of Sobolev inequalities. In particular, we discuss our recent papers on fractional order inequalities, Coulhon type inequalities, transference and dimensionless inequalities and our forthcoming work on sharp higher order Sobolev inequalities that can be obtained by iteration.Comment: 39 pages, made some changes to section 1

Doppler Shifts and Broadening and the Structure of the X-ray Emission from Algol

In a study of Chandra High Energy Transmission Grating spectra of Algol, we clearly detect Doppler shifts caused by the orbital motion of Algol B. These data provide the first definitive proof that the X-ray emission of Algol is dominated by the secondary, in concordance with expectations that Algol A (B8) is X-ray dark. The measured Doppler shifts are slightly smaller than expected, implying an effective orbital radius of about 10 Rsolar, instead of 11.5 Rsolar for the Algol B center of mass. This could be caused by a small contribution of X-ray flux from Algol A (10-15%), possibly through accretion. The more likely explanation is an asymmetric corona biased toward the system center of mass by the tidal distortion of the surface of Algol B. Analysis of the strongest lines indicates excess line broadening of ~150 km/s above that expected from thermal motion and surface rotation. Possible explanations include turbulence, flows or explosive events, or rotational broadening from a radially extended corona. We favor the latter scenario and infer that a significant component of the corona at temperatures <10^7 K has a scale height of order the stellar radius. This is supported by the shape of the X-ray lightcurve and the shallow dip at secondary eclipse. We also examine the O VII intercombination and forbidden lines in a Low Energy Transmission Grating Spectrograph observation and find no change in their relative line fluxes as the system goes from quadrature to primary eclipse. Since these lines are strongly affected by UV irradiation from Algol A, this supports the conjecture that the corona of Algol B at temperatures of several million K must be significantly extended and/or located toward the poles to avoid being shadowed from Algol A during primary eclipse.Comment: 36 pages, 10 figure