Sheath Impedance Research Articles

Using the Stix finite element RF code to investigate operation optimization of the ICRF antenna on Alcator C-Mod

As the Ion Cyclotron Radio Frequency range (ICRF) heating becomes more favorable in fusion devices, the urgency of predicting and mitigating impurity generation that arises from it becomes more pressing. In the ICRF regime, rectified Radio Frequency (RF) sheaths are known to form at antenna and material edges that influence negative effects like sputtering and a decrease in heating efficiency. Methods to mitigate the formation of these RF sheaths through RF image currents cancellation have been experimentally studied. A power-phasing scan done on Alcator C-Mod in which the amount of power on the two inner straps (P in) versus the total 4 straps (P tot) was varied showed a minimization of enhanced potentials between Pin/Ptot∼ 0.7–0.9 while impurities were minimized for Pin/Ptot∼ 0.5–0.8. New capabilities in the realm of representing the RF sheath numerically now allow for these experiments to be simulated. Given the size of the sheath relative to the scale of the device, it can be approximated as a Boundary Condition (BC). A new parallelized cold-plasma wave equation solver called Stix implements a non-linear sheath impedance model BC formulated by Myra et al (2015 Phys. Plasmas 22 062507) through the method of finite elements using the MFEM library [http://mfem.org]. It is seen that Stix shows qualitative agreement with the measured C-Mod enhanced potentials.

Chorus Wave Properties From Van Allen Probes: Quantifying the Impact of the Sheath Corrected Electric Field

AbstractA sheath impedance model has recently been developed to describe how the variable coupling impedance between the Van Allen Probes instrumentation and the ambient plasma affects both the amplitude and phase of electric field wave measurements. Here, the impact of this sheath correction on measured chorus wave properties, including electric field wave power and the Poynting vector, is directly quantified. It is found that the sheath‐corrected electric field wave power is typically between two and nine times larger than the uncorrected measurement, depending on wave frequency. The sheath correction typically increases the Poynting flux by a factor of ∼2, and causes the polar angle of the Poynting vector to switch hemisphere from parallel to anti‐parallel propagation in ∼2% of cases. The uncorrected data exhibit significant deviations from the theoretically predicted relationship between the wave vector and the Poynting vector whereas this relationship is well‐reproduced with the sheath‐corrected observations.

Magnetic potential based formulation for linear and non-linear 3D RF sheath simulation

This paper reports a new numerical scheme to simulate the radio-frequency (RF) induced RF sheath, which is suitable for a large 3D simulation. In the RF sheath boundary model, the tangential component of the electric field () is given by the gradient of a scalar electric field potential. We introduce two additional scalar potentials for the tangential components of the magnetic field, which effectively impose the normal electric displacement (D n ) on the plasma sheath boundary condition via in-homogeneous Neumann boundary condition and constrain the tangential electric field on the surface as curl-free (). In our approach, the non-linear sheath impedance is formulated as a natural extension of the large thickness (or asymptotic) sheath limit (), allowing for handling both asymptotic and non-linear regimes seamlessly. The new scheme is implemented using the Petra-M finite element method analysis framework and is verified with simulations in the literature. The significance of non-linearity is discussed in various plasma conditions. An application of this scheme to asymptotic RF sheath simulation on the WEST ICRF antenna side limiters is also discussed.

Identification of defects in HV cable sheath based on equivalent impedance spectrum characteristic coding

In recent years, on-line monitoring and condition-based maintenance of HV cable systems have been extensively investigated to prevent cable fault. By analyzing cable sheath current, sheath defects can be identified. A new method of cable sheath defect identification is proposed in this study on the basis of the coding of the equivalent sheath impedance spectrum characteristics. In the proposed method, the sheath defects are identified by calculating the equivalent sheath impedance spectrum on the basis of the detected currents of the on-line sheath monitoring system. The equivalent circuit model of cross-bonded (CB) HV cable for sheath defect identification is constructed. The three-phase circuit model is decoupled to solve each phase independently in accordance with the CB scheme of the cable sheath. The equations of solving the equivalent sheath impedance are deduced. The criteria of sheath defect identification are proposed using the coding of characteristic parameters of the equivalent sheath impedance spectrum. Finally, a simulation model of the HV cable is built in the Simulink software to simulate 12 types of sheath defects. The simulation results have proven the correctness and efficiency of the proposed method.

Measurement and modeling of the radio frequency sheath impedance in a large magnetized plasma

The DC and radio frequency (RF) properties of RF driven sheaths were studied in the Large Plasma Device (LAPD) at the University of California, Los Angeles. The experiments diagnosed RF sheaths on field lines connected to a grounded plate at one end and an ion cyclotron range of frequencies antenna at the other end. The experimental setup permitted measurement of the RF sheath impedance at the plate as a function of DC sheath voltage, with the latter controlled by varying the RF current applied to the antenna. The DC–voltage characteristics of these sheaths and the RF sheath impedance measurements were compared with modeling. Hot electrons, present in the LAPD plasma, were inferred to contribute significantly to both the DC and RF currents and hence the RF impedance. It was postulated that at very low power, hot electrons could not access the region of the plasma subject to RF waves resulting in an increased RF impedance. Within some experimental limitations and significant assumptions, an RF sheath impedance model was verified by the experimental data.

Modified high frequency probe approach for diagnostics of highly reactive plasma

The paper introduces a modified approach of time resolved in situ diagnostics of highly reactive discharges (C2H2 in our case) usually used for a deposition process of various non-conductive thin films. Reactive plasma could create an insulating film onto inserted diagnostic tools, which distorts measured data and makes their processing unreliable; a typical problem of Langmuir probe measurements. The proposed approach utilizes a so-called radiofrequency (rf) Sobolewski probe for ion flux measurement which is further modified to also obtain the electron temperature in some cases and the ion density. In this work, we introduce the procedure where measured rf probe characteristics are transformed towards I–V curves of the plasma sheath with subtracted capacitive current. This processing enables not only the monitoring of plasma sheath impedance and the ion flux towards the substrate but also allows for an estimation of other parameters as the plasma density or electron temperature, respectively. We demonstrate that the substrate used for thin film deposition can act as an active probe itself. The relevance of the proposed method was verified in pure Ar discharge where the results correspond with conventional Langmuir probe diagnostics. Furthermore, internal plasma parameters of highly reactive Ar/C2H2 plasma, formed from acetylene, were evaluated, too.

Radio frequency wave interactions with a plasma sheath: The role of wave and plasma sheath impedances

Radio frequency (RF) sheaths form near surfaces where plasma and strong RF fields coexist. The effect of these RF sheaths on wave propagation near the boundary can be characterized by an effective sheath impedance that includes both resistive and capacitive contributions describing RF sheath rectification and RF power absorption in the sheath [J. R. Myra and D. A. D'Ippolito, Phys. Plasmas 22, 062507 (2015)]. Here, we define a dimensionless parameter, the ratio of incoming wave impedance to the sheath impedance, which determines the characteristics of the interaction, ranging from quasi-conducting to quasi-insulating, or in the case of matched impedances, to either perfect absorption or a sheath-plasma resonance. A semi-analytical analysis is carried out for electrostatic slow waves in the ion cyclotron range of frequencies. For the propagating slow wave case, where the incident wave is partially reflected, the fraction of power dissipated in the sheath is calculated. For the evanescent slow wave case, which admits a sheath-plasma resonance, an amplification factor is calculated. Using the impedance ratio approach, RF sheath interactions are characterized for a range of RF wave and plasma parameters including plasma density, magnetic field angle with respect to the surface, wave frequency, and wave-vector components tangent to the surface. For a particularly interesting example case, results are compared with the rfSOL code [H. Kohno and J. R. Myra, Comput. Phys. Commun. 220, 129 (2017)]. Finally, electromagnetic effects, absent from the semi-analytical analysis, are assessed.

Radio-frequency wave interactions with a plasma sheath in oblique-angle magnetic fields using a sheath impedance model

The physics of interactions between waves in plasmas and sheaths for background magnetic fields which make oblique angles with sheath surfaces is studied with the use of the self-consistent finite element code rfSOL incorporating the recently developed sheath impedance model [J. R. Myra, Phys. Plasmas 24, 072507 (2017)]. The calculation based on this model employs the generalized sheath boundary condition (sheath BC), which surpasses the previously used capacitive sheath BC in reliability by taking into account the contributions of the ion and electron currents in the sheath and the displacement current. A series of numerical simulations is carried out in two-dimensional slab geometry with a flat or curved sheath surface as part of the boundary. It is shown that the sheath–plasma wave appears when the equilibrium magnetic field line angle with respect to the sheath surface is small, the absolute value of the radio-frequency (RF) sheath voltage is large, and the plasma density is slightly higher than the lower hybrid resonance density (LHR density), all of which bring the sheath property closer to being capacitive. It is also shown that the sharp variation of the magnetic field line angle along the sheath surface can sensitively affect the maximum absolute value of the RF sheath voltage at a plasma density slightly lower than the LHR density.

Radio frequency wave interactions with a plasma sheath: the role of wave and plasma sheath impedances

Radio frequency wave interactions with a plasma sheath: the role of wave and plasma sheath impedances

Radio-frequency wave interactions with a plasma sheath in oblique-angle magnetic fields using a sheath impedance model

Radio-frequency wave interactions with a plasma sheath in oblique-angle magnetic fields using a sheath impedance model

A finite element procedure for radio-frequency sheath–plasma interactions based on a sheath impedance model

A finite element code that solves self-consistent radio-frequency (RF) sheath–plasma interaction problems is improved by incorporating a generalized sheath boundary condition in the macroscopic solution scheme. This sheath boundary condition makes use of a complex sheath impedance including both the sheath capacitance and resistance, which enables evaluation of not only the RF voltage across the sheath but also the power dissipation in the sheath. The newly developed finite element procedure is applied to cases where the background magnetic field is perpendicular to the sheath surface in one- and two-dimensional domains filled by uniform low- and high-density plasmas. The numerical results are compared with those obtained by employing the previous capacitive sheath model at a typical frequency for ion cyclotron heating used in fusion experiments. It is shown that for sheaths on the order of 100 V in a high-density plasma, localized RF power deposition can reach a level which causes material damage. It is also shown that the sheath–plasma wave resonances predicted by the capacitive sheath model do not occur when parameters are such that the generalized sheath impedance model substantially modifies the capacitive character of the sheath. Possible explanations for the difference in the maximum RF sheath voltage depending on the plasma density are also discussed.

An improved sheath impedance model for the Van Allen Probes EFW instrument: Effects of the spin axis antenna

AbstractA technique to quantitatively determine the sheath impedance of the Van Allen Probes Electric Field and Waves (EFW) instrument is presented. This is achieved, for whistler mode waves, through a comparison between the total electric field wave power spectra calculated from magnetic field observations and cold plasma theory and the total electric field wave power measured by the EFW spherical double probes instrument. In a previous study, a simple density‐dependent sheath impedance model was developed in order to account for the differences between the observed and calculated wave electric field. The current study builds on this previous work by investigating the remaining discrepancies, identifying their cause, and developing an improved sheath impedance correction. Analysis reveals that anomalous gains are caused by the spin axis antennas measuring too much electric field at specific densities and frequencies. This is accounted for in an improved sheath impedance model by introducing a density‐dependent function describing the relative effective length of the probe separation, Leff, in addition to the sheath capacitance and resistance values previously calculated. Leff values vary between between 0.5 and 1.2, with values >1 accounting for the anomalous gains and values <1 accounting for the shorting effect at low densities. Applying this improved sheath impedance model results in a significant increase in the agreement level between observed and calculated electric field power spectra and wave powers over the previous model.

Time-resolved ion flux and impedance measurements for process characterization in reactive high-power impulse magnetron sputtering

A new planar ion flux probe, based on the Sobolewski method for time-resolved plasma characterization in inherently noisy pulsed plasma discharges, has been developed. The probe was evaluated in a high-power impulse magnetron sputtering (HiPIMS) process, which is a promising ionized physical vapor deposition technique based on pulsed plasma discharges used to engineer thin films with improved properties. Both nonreactive (pure Ar) and reactive (Ar/O2) deposition processes were investigated using a Ti sputtering target. It was found that the process exhibited a nearly hysteresis-free and stable transition region at the chosen deposition conditions. Time-resolved measurements of the absolute ion flux impinging on the probe placed at the substrate position, as well as of the probe sheath impedance, were recorded in the metal, transition, and compound modes during the HiPIMS pulse. Gradual changes in the measured ion flux, as well as the impedance, were seen when transiting from the metal mode to the compound (poisoned) mode. It is therefore suggested that this type of robust plasma probe can potentially be used for reactive process control, where the user would like to stably operate in the transition region over long periods of time.

RF compensation of single Langmuir probe in low density helicon plasma

Interpretations of Single Langmuir probe measurements in electrode-less radio frequency (RF) plasmas are noteworthy tricky and require adequate compensation of RF. Conventional RF compensation technique is limited only at high density (>1017m−3) RF plasmas. RF compensation of single Langmuir probe at low density RF plasmas (∼1016m−3) is presented in this paper. In RF driven plasmas, where the RF voltage is high (∼50V) and density is in the range (∼1016m−3), the primary RF compensation condition (Zck>>Zsh) is very difficult to fulfill, because of high sheath impedance (Zsh) at 13.56MHz and the construction limitation of a self-resonant tiny chock (Zck) with very high impedance. Introducing a large auxiliary electrode (Ax), (Ax>>>Ap), close to the small Langmuir probe (Ap) tip, connected in parallel with probe via a coupling capacitor (Ccp), significantly reduces the effective sheath impedance (Zsh) and allows probe bias to follow the RF oscillation. Dimensional requirements of the auxiliary electrode and the role of suitable coupling capacitor are discussed in this paper. Observations show proper compensation leads to estimation of more positive floating potentials and lower electron temperatures compared to uncompensated probe. The electron energy probability function (EEPF) is also obtained by double differentiating the collected current with respect to the applied bias voltage using an active analog circuit.

Using the cold plasma dispersion relation and whistler mode waves to quantify the antenna sheath impedance of the Van Allen Probes EFW instrument

AbstractCold plasma theory and parallel wave propagation are often assumed when approximating the whistler mode magnetic field wave power from electric field observations. The current study is the first to include the wave normal angle from the Electric and Magnetic Field Instrument Suite and Integrated Science package on board the Van Allen Probes in the conversion factor, thus allowing for the accuracy of these assumptions to be quantified. Results indicate that removing the assumption of parallel propagation does not significantly affect calculated plasmaspheric hiss wave powers. Hence, the assumption of parallel propagation is valid. For chorus waves, inclusion of the wave normal angle in the conversion factor leads to significant alterations in the distribution of wave power ratios (observed/ calculated); the percentage of overestimates decreases, the percentage of underestimates increases, and the spread of values is significantly reduced. Calculated plasmaspheric hiss wave powers are, on average, a good estimate of those observed, whereas calculated chorus wave powers are persistently and systematically underestimated. Investigation of wave power ratios (observed/calculated), as a function of frequency and plasma density, reveals a structure consistent with signal attenuation via the formation of a plasma sheath around the Electric Field and Waves spherical double probes instrument. A simple, density‐dependent model is developed in order to quantify this effect of variable impedance between the electric field antenna and the plasma interface. This sheath impedance model is then demonstrated to be successful in significantly improving agreement between calculated and observed power spectra and wave powers.

Gas breakdown and plasma impedance in split-ring resonators

The appearance of resonant structures in metamaterials coupled to plasmas motivates the systematic investigation of gas breakdown and plasma impedance in split-ring resonators over a frequency range of 0.5−9 GHz. In co-planar electrode gaps of 100 μm, the breakdown voltage amplitude decreases from 280 V to 225 V over this frequency range in atmospheric argon. At the highest frequency, a microplasma can be sustained using only 2 mW of power. At 20 mW, we measure a central electron density of 2 × 1020 m-3. The plasma-electrode overlap plays a key role in the microplasma impedance and causes the sheath impedance to dominate the plasma resistance at very low power levels.

Radio frequency sheaths in an oblique magnetic field

The physics of radio-frequency (rf) sheaths near a conducting surface is studied for plasmas immersed in a magnetic field that makes an oblique angle θ with the surface. A set of one-dimensional equations is developed that describes the dynamics of the time-dependent magnetic presheath and non-neutral Debye sheath. The model employs Maxwell-Boltzmann electrons, and the magnetization and mobility of the ions is determined by the magnetic field strength, and wave frequency, respectively. The angle θ, assumed to be large enough to insure an electron-poor sheath, is otherwise arbitrary. Concentrating on the ion-cyclotron range of frequencies, the equations are solved numerically to obtain the rectified (dc) voltage, the rf voltage across the sheath, and the rf current flowing through the sheath. As an application of this model, the sheath voltage-current relation is used to obtain the rf sheath impedance, which in turn gives an rf sheath boundary condition for the electric field at the sheath-plasma interface that can be used in rf wave codes. In general, the impedance has both resistive and capacitive contributions, and generalizes previous sheath boundary condition models. The resistive part contributes to parasitic power dissipation at the wall.

Resilient Batch-Fabricated Planar Arrays of Miniaturized Langmuir Probes for Real-Time Measurement of Plasma Potential Fluctuations in the HF to Microwave Frequency Range

We report the design, fabrication, and characterization of miniaturized, flush-mounted Langmuir probe arrays for RF diagnosis of plasmas in the HF to microwave range of frequencies. We developed probes of radii ≥125 μm by electroless nickel metallization of ultrasonically drilled through-substrate vias. Planar arrays with as many as 25 probes spaced 1.6 mm apart (39 probes/cm2) in Pyrex, silicon carbide, and alumina substrates were produced. The sensor system was built to have a frequency response between 2 MHz and 3 GHz, and a probe impedance greater than or within close range of the plasma sheath impedance for plasma densities ≥1016 m -3 . We characterized a self-biasing nickel probe part of a 2×2 array with alumina substrate using a high-density magnetized helicon plasma source; we found that the measurement of the plasma potential from the MEMS probe compares well with independent measurements using a hot emissive probe and an ion sensitive probe. The sensor technology can be used to monitor plasma-based manufacturing systems, plasma-based energy generation systems, and as on-board plasma diagnostics in spacecraft including nanosatellites.

Wall current closure effects on plasma and sheath fluctuations in Hall thrusters

The excitation of negative energy, ion sound type modes driven by the E × B drift and the reactive/dissipative response of the wall sheath interface is analyzed for conditions typical in a Hall thruster. Such sheath impedance modes are sensitive to the dielectric properties of the thruster wall material, which therefore may have direct influence (other than via the secondary electron emission) on fluctuations and transport. Our results predict mode frequencies consistent with the frequencies of fluctuations observed experimentally.

Proximity effect in fast transient simulations of an underground transmission cable

It has been discussed in various papers, how lack of proximity effect in modelling affects simulations and gives inaccurate results at high frequencies. This paper describes a method for how to include the proximity effect calculations in EMT11EMT: electromagnetic transients.-based simulations. A subdivision of conductors method is used to calculate conductor (core and sheath) impedances. A full phase impedance matrix is then constructed, including semiconductive layers, insulation layers and a special screen of two conducting materials. Finally the method is tested using the universal line model and is verified against field measurements. It is shown in the paper how including the proximity effect, it is possible to obtain good comparison between measurements and simulations, even for the intersheath mode.