Rf Sheath Research Articles

Measurements of electric charge and screening length of microparticles in a plasma sheath

An experiment is described in which microparticles are levitated within a rf sheath above a conducting plate in argon plasma. The microparticles forming a two-dimensional crystal structure are considered to possess Debye screening Coulomb potential ϕ(r)=(Q/4πε0r)exp(−r/λ), where Q is the electric charge, r is distance, and λ is the screening length. When the crystal structure is slanted with an angle θ, a particle experiences a force Mg sin θ, where M is the mass of the particle and g is acceleration due to gravity, which must be equal to the Debye screened Coulomb force from other particles. By changing θ, relations for λ(Q) are measured. The screening length λ and Q are determined uniquely from the crossing points of several relations. The electric charge Q is also estimated from a floating potential measured with a probe. The measured λ is nearly equal to an ion Debye length.

Effects of ICRF induced density modifications on LH wave coupling at JET

Lower hybrid (LH) wave coupling is modified and usually degraded when the system is powered simultaneously with the ion cyclotron range of frequency (ICRF) antennas magnetically connected to the launcher. This has been attributed to scrape-off layer density modifications by the RF sheaths. LH reflection coefficients dependences on various parameters are investigated and shown to be consistent with RF sheath physics. Gas puffing near the launcher has been used to improve the coupling of LH waves.

ICRF specific impurity sources and plasma sheaths in Alcator C-Mod

In Alcator C-Mod, we have sought to identify ICRF specific impurity sources and estimate the lifetime of thin, low-Z films in the presence of high power ICRF heating. With ICRF, the erosion rate of low-Z films is estimated to be 15–20 nm/s indicating the eroding species energy is much higher than that normally found in the SOL. Using emissive probes, plasma potential measurements confirm the presence of an enhanced sheath with ICRF when the probe is magnetically linked to the active antenna. Plasma potentials were typically 100–200 V for ∼1.25 MW injected ICRF power. Furthermore, an RF sheath was unexpectedly present with insulating limiters and was dependent on the wall conditions and plasma confinement. These dependencies suggest that other scrape-off layer and plasma-surface characteristics are influencing the resulting RF sheaths.

Estimated RF sheath power fluxes on ITER plasma facing components

Using numerical simulation, a first estimate is made of power fluxes caused by radio-frequency sheaths on plasma facing components surrounding the ITER Ion Cyclotron Range of Frequencies wave launcher. Three toroidal strap phasings were considered, and four plasma scenarios covering a broad range of Scrape-Off Layer densities. Parallel heat fluxes up to ∼16 MW/m 2 are obtained, localized in poloidal peaks whose radial extension (initially 4–35 mm) increases when nearby flux tubes are coupled by exchanging RF currents. Quantitative results strongly depend on the local density, both via the unperturbed input profiles and via subsequent RF-induced modifications by E × B 0 convection. Sources of uncertainty and aspects requiring further validation are identified.

Far-field sheaths due to fast waves incident on material boundaries

The problem of “far-field” sheath formation is studied with a new quantitative one-dimensional model. These radio-frequency (rf) sheaths occur when unabsorbed fast waves in the ion cyclotron range of frequencies are incident on a conducting surface not aligned with a flux surface. Use of a nonlinear sheath boundary condition gives self-consistent solutions for the wave fields and sheath characteristics, and it introduces a sheath-plasma-wave resonance which can enhance the sheath potential. The model is used to compute the parametric dependence of the far-field sheath potential. Its application to post-process the rf fields computed by a full-wave code for a typical D(H) minority heating scenario is also discussed. This work shows that two-dimensional effects (included heuristically) are essential in determining whether far-field sheath potentials are strong enough to cause significant edge interactions, such as impurity generation and reduced heating efficiency.

Secondary electrons in rf and dc/rf capacitive discharges

We extend an analytic model of the effects of secondary electrons on symmetric (equal area) capacitive discharges to include a combination of rf and dc voltage sources. A ‘dc/rf sheath’ develops on the negatively biased dc electrode while a typical rf sheath develops on the other electrode. The analytical results for rf-only and dc/rf cases, including secondaries, are compared with the results of numerical simulations using a one-dimensional (1D) plane-parallel particle-in-cell (PIC) code, confirming the pressure and density regimes for which adding dc improves the overall discharge efficiency and can control the fluxes and energy distributions of the secondary electrons incident on the electrodes. From a 2D PIC simulation, the effects of secondaries and dc voltage on the uniformity of the ions and secondary electrons are investigated, with the dc adding an additional element of uniformity control. The uniformity of the secondary electron energy and angular distributions on the substrate electrode are determined from the 2D simulations.

Plasma Ionization in Low-Pressure Radio-Frequency Discharges. Part I: Optical Measurements

The electron dynamics in the low-pressure operation regime (<5 Pa) of a neon capacitively coupled plasma is investigated using phase-resolved optical emission spectroscopy. Plasma ionization and sustainment mechanisms are governed by the expanding and contracting sheath and complex wave-particle interactions. Electrons are energized through the advancing and retreating electric field of the RF sheath. The associated interaction of energetic sheath electrons with thermal bulk plasma electrons drives a two-stream instability also dissipating power in the plasma.

A new structure for RF-compensated Langmuir probes with external filters tunable in the absence of plasma

A new Langmuir probe structure using externally placed filters that can be tuned in the absence of plasma is proposed. The probe design and tuning procedure take into account especially the change in the probe's environment when plasma is turned on, thereby ensuring that the filters do not become detuned in the presence of plasma. Measurement of the RF voltage amplitudes in RF plasma using a calibrated capacitive probe gave, respectively, ≈15.7 V, ≈4.1 V, ≈2.1 V and ≈0.5 V at the fundamental frequency (≈13.56 MHz), the second, third and the fourth harmonics; based on these values a three-stage filter was built at the fundamental and the second and third harmonics. A complete analysis of the probe including its stray capacitance, RF equivalent circuit, filter and plasma impedance has been carried out, from which the maximum RF sheath voltage drop could be estimated as ≈0.27 V, ≈0.34 V and ≈1.30 V at the fundamental, the second harmonic and the third harmonic, respectively; the drop for the latter is somewhat large because of unexpectedly high loss in the filter components at the higher frequencies. I–V characteristics presented show that the floating potential of the probe decreases by ≈60 V, as the probe is detuned progressively from its tuned condition; also, the electron temperature increases from ≈1.7 to 3.5 eV with progressive detuning. It is worth noting here that although the method of calibrating the capacitive probe in this work is accurate for moderately high plasma densities (RF skin depth in plasma (= δs) small in comparison with the plasma dimension, L) its accuracy for lower densities (δs ∼ L) is not too certain. Therefore, although the probe itself can be used at low plasma densities, verifying its efficacy for such cases could be difficult.

Radio-frequency discharges in oxygen: II. Spatio-temporally resolved optical emission pattern

Axially and temporally resolved optical emission structures were investigated in the rf sheath region of a parallel plate capacitively coupled rf discharge (13.56 MHz) in pure oxygen and tetrafluoromethane. The rf discharge was driven at total pressures of between 10 and 100 Pa, gas flow rate of 3 sccm and rf power in the range 5–100 W. In particular, the emission of the atomic oxygen at 844.6 nm (3p3P → 3s3S0) and the atomic carbon at 193 nm (3s1P0 → 2p1D) were imaged with a lens onto the entrance slit of a spectrometer and detected by a fast ICCD-camera. The spatio-temporally resolved analysis of the emission intensity during the rf cycle (73.75 ns) provides two significant excitation processes inside the rf sheath: the electron impact excitation at the sheath edge, and heavy particle impact excitation in front of the powered electrode. In oxygen plasma the emission of atomic oxygen was found in both regions whereas in tetrafluoromethane the emission of atomic carbon was observed only in front of the powered electrode. The experimental results reveal characteristic dependence of the emission pattern in front of the powered electrode on plasma process parameters (self-bias voltage, pressure) and allow an estimation of the excitation threshold energy and effective cross section of energetic heavy particle loss.

Overview of the Alcator C-MOD research programme

Alcator C-MOD has compared plasma performance with plasma-facing components (PFCs) coated with boron to all-metal PFCs to assess projections of energy confinement from current experiments to next-generation burning tokamak plasmas. Low-Z coatings reduce metallic impurity influx and diminish radiative losses leading to higher H-mode pedestal pressure that improves global energy confinement through profile stiffness. RF sheath rectification along flux tubes that intersect the RF antenna is found to be a major cause of localized boron erosion and impurity generation. Initial lower hybrid current drive (LHCD) experiments (PLH < 900 kW) in preparation for future advanced-tokamak studies have demonstrated fully non-inductive current drive at Ip ∼ 1.0 MA with good efficiency, Idrive = 0.4 PLH/neoR (MA, MW, 1020 m−3,m). The potential to mitigate disruptions in ITER through massive gas-jet impurity puffing has been extended to significantly higher plasma pressures and shorter disruption times. The fraction of total plasma energy radiated increases with the Z of the impurity gas, reaching 90% for krypton. A positive major-radius scaling of the error field threshold for locked modes (Bth/B ∝ R0.68±0.19) is inferred from its measured variation with BT that implies a favourable threshold value for ITER. A phase contrast imaging diagnostic has been used to study the structure of Alfvén cascades and turbulent density fluctuations in plasmas with an internal transport barrier. Understanding the mechanisms responsible for regulating the H-mode pedestal height is also crucial for projecting performance in ITER. Modelling of H-mode edge fuelling indicates high self-screening to neutrals in the pedestal and scrape-off layer (SOL), and reproduces experimental density pedestal response to changes in neutral source, including a weak variation of pedestal height and constant width. Pressure gradients in the near SOL of Ohmic L-mode plasmas are observed to scale consistently as , and show a significant dependence on X-point topology. Fast camera images of intermittent turbulent structures at the plasma edge show they travel coherently through the SOL with a broad radial velocity distribution having a peak at about 1% of the ion sound speed, in qualitative agreement with theoretical models. Fast Dα diagnostics during gas puff imaging show a complex behaviour of discrete ELMs, starting with an n ≈ 10 precursor oscillation followed by a rapid primary ejection as the pedestal crashes and then multiple, slower secondary ejections.

Comparative experimental analysis of the a-C:H deposition processes using CH4 and C2H2 as precursors

The plasma enhanced chemical vapor deposition of a-C:H films using methane and acetylene as precursors was studied. Noninvasive in situ techniques were used to analyze the plasma processes with respect to the self-bias voltage, the displacement currents to the grounded electrode, the neutral gas composition, the optical sheath thickness as well as current and energy of the ions hitting the powered electrode. The a-C:H films were characterized for their deposition rate, surface roughness, hardness, mass density, and hydrogen content. Ion mean free paths, suitable for low-pressure rf sheaths, have been quantified for both precursors. The film with the highest hardness of 25GPa was formed in the C2H2 discharge when the mean energy per deposited carbon atom was approximately 50eV. The hardness obtained with the CH4 discharge was lower at 17GPa and less sensitive to changes in the process parameters. It was found that the creation of hard (hardness &amp;gt;15GPa) a-C:H films from both precursors is possible if the mean energy per deposited carbon atom exceeds only ∼15eV. Further film characteristics such as surface roughness and hydrogen content show the interplay of ion flux and deposition from radicals to form the a-C:H structure and properties.

Capacitive discharges driven by combined dc/rf sources

We have obtained analytic expressions for the sheath voltages and sheath widths for both collisional and collisionless sheaths driven by a combination of dc and rf voltage sources. A “dc/rf sheath” develops on the negatively biased electrode while a typical rf sheath develops on the other electrode. The dc/rf sheath has a dc region with negligible electron density near the negatively biased electrode. Furthermore, if the rf power is held constant (typical for industrial plasmas driven by rf power sources), the sheath voltage drop of the rf sheath is nearly independent of the dc voltage provided the discharge configuration does not lead to a significant increase in the ionization efficiency of the secondary electrons. The analysis is done for both symmetric (equal area) and asymmetric diode discharges, as well as a triode configuration. The analytical results for the symmetric and asymmetric diode discharges are compared to the results of numerical simulations using plane-parallel and cylindrical particle-in-cell (PIC) codes over a wide range of pressures and rf frequencies, finding good agreement. The effect of secondary electrons is also examined with the PIC codes, finding increased discharge efficiency.

Collisional Sheath in the Electronegative Radio-Frequency Plasma

A model of collisional RF sheath with negative ions is discussed inthis paper. The influences of collision and negative ions on theparameters of the sheath are studied through numerical simulation.It is found that when the collision coefficient increases and the RFpower is fixed, the electrode potential and sheath electric fieldpotential increase, the electrode current and thickness of thesheath decrease. When the negative ion content changes, the samephenomenon occurs.

Evolution of nonthermal particle distributions in radio frequency heating of fusion plasmas

Progress is reviewed on the simulation of wave-particle interactions in the ion cyclotron range of frequencies (ICRF). Two important aspects of this problem are described. First, mode conversion from a long wavelength fast magnetosonic wave to short wavelength ion Bernstein waves (IBW) and ion cyclotron waves (ICW) is simulated and validation tests of the simulations against experiment are presented. Second, simulations of the quasilinear evolution of nonthermal ion tails during the minority heating are reviewed and experimental validation tests are also discussed. In this paper we describe how access to teraflop computing capability has made it possible to advance the state of the art in this area. We also discuss two aspects of the wave-particle interaction where future work is needed and where in particular access to sub-petaflop and petaflop computing capability would be highly desirable. This work involves the interaction of ICRF waves with energetic neutral beam ions at high ion cyclotron harmonic number and addresses the inclusion of finite ion drift orbit effects in the nonthermal ion tail evolution and the inclusion of nonlinear effects such as RF sheaths in the antenna – edge plasma coupling.

Time domain modeling of plasmas at RF time-scales

Results from tokamak experiments such as PPPL's NSTX indicate that significant anomalous power absorption can occur in the edge of the fusion plasma. Understanding of this phenomenon is a critical issue for analysis of RF heating scenarios on the ITER fusion experiment. Two probable edge absorption candidates, rf sheath losses and parametric decay instability, are both inherently non-linear, and likely to depend significantly on non-axi-symmetric geometric detail in the vicinity of the antenna structures. Analysis of these phenomenon is beyond the capabilities of existing axi-symmetric frequency-domain linear-solvers used for analysis of heating and current drive in core fusion plasma, and so we are augmenting our analysis capability with the time-domain 3-D general-geometry electromagnetic and particle-in-cell simulation framework, Vorpal [1]. This framework is a modern object-oriented software package, which has demonstrated fast scalable operation on clusters of over 1000 cpu's, a necessity for this type of calculation. We have successfully introduced into this framework an implicit plasma solver [2], in order to accurately treat electromagnetic plasma wave characteristics in the wide range of plasma conditions occurring from edge plasma to core plasma, including situations where the plasma frequency is not resolvable at the rf time-scales of interest, and including sharp plasma resonances and cutoff behaviours common in the rf regime. We present benchmarking of this new plasma solver for 1-D, 2-D, and 3-D scenarios. We also discuss implementation plans for non-linear sheath boundary models, non-linear edge-plasma conditions leading to parametric decay, and also tracking of high-energy particles in core-heating scenarios, where issues of finite-banana-width effects and superadiabaticity remain outside the scope of the existing frequency-domain solvers.

Plasma ionization through wave-particle interaction in a capacitively coupled radio-frequency discharge

Phase resolved optical emission spectroscopy, with high temporal resolution, shows that wave-particle interactions play a fundamental role in sustaining capacitively coupled rf plasmas. The measurements are in excellent agreement with a simple particle-in-cell simulation. Excitation and ionization mechanisms are dominated by beam-like electrons, energized through the advancing and retreating electric fields of the rf sheath. The associated large-amplitude electron waves, driven by a form of two-stream instability, result in power dissipation through electron trapping and phase mixing.

Electrical characterization of a capacitive rf plasma sheath

The authors report on an experimental system designed to investigate and characterize capacitive radio frequency (rf) sheaths. An electrode mounted in an inductive plasma reactor and driven with separate rf and direct current (dc) power sources is used. The advantage of this design is that the electrode sheath is decoupled from the plasma parameters. This allows detailed investigation of the sheath with different bias conditions without perturbing the bulk plasma parameters. Power coupled to ions and electrons through the sheath, at low pressure, is investigated and a method to determine the electron conduction current to the electrode, using the external dc bias, is presented.

A self-consistent hybrid model of a dual frequency sheath: Ion energy and angular distributions

This paper presents a self-consistent hybrid model including the fluid model which can describe the characteristics of collisional sheaths driven by dual radio-frequency (DF) sources and Monte Carlo (MC) method which can determine the ion energy and angular distributions incident onto the dual rf powered electrode. The charge-exchange collisions between ions and neutrals are included in the MC model in which a self-consistent instantaneous electric field obtained from the fluid model is adopted. In the simulation, the driven method we used is either the current-driven method or the voltage-driven method. In the current-driven method, the rf current sources are assumed to apply to an electrode, which is the so-called the equivalent circuit model and is used to self-consistently determine the relationship between the instantaneous sheath potential and the sheath thickness. In the voltage-driven method, however, the rf voltage sources are assumed to apply to an electrode. The dual rf sheath potential, sheath thickness, ion flux, ion energy distributions (IEDs), and ion angular distributions (IADs) are calculated for different parameters. The numerical solutions show that some external parameters such as the bias frequency and power of the lower-frequency source as well as gas pressure are crucial for determining the structure of collisional dual rf sheaths and the IEDs. The shapes of the IADs, however, are determined mainly by the gas pressure. Furthermore, it is found that the results from the different driven methods behave in the same way although there are some differences in some quantities.

A radio-frequency sheath boundary condition and its effect on slow wave propagation

Predictive modeling of radio-frequency wave propagation in high-power fusion experiments requires accounting for nonlinear losses of wave energy in the plasma edge and at the wall. An important mechanism of “anomalous” power losses is the acceleration of ions into the walls by rf sheath potentials. Previous work computed the “sheath power dissipation” non-self-consistently by postprocessing fields obtained as the solution of models which did not retain sheaths. Here, a method is proposed for a self-consistent quantitative calculation of sheath losses by incorporating a sheath boundary condition (SBC) in antenna coupling and wave propagation codes. It obtains the self-consistent sheath potentials and spatial distribution of the time-averaged power loss in the solution for the linear rf fields. It can be applied for ion cyclotron and (in some cases) lower hybrid waves. The use of the SBC is illustrated by applying it to the problem of an electron plasma wave propagating in a waveguide. This model problem is relevant to understanding the low heating efficiency in direct ion-Bernstein wave launch. Implications for calculating sheath voltages driven by fast-wave antennas are also discussed.

Effects of Ion Temperature on Collisionless and Collisional RF Sheath

A numerical two-fluid simulation of the non-ionized radio frequency (rf) sheath model, has been carried out. This model is ``global'' and thus applicable to the sheath, pre-sheath and plasma regions, In the model all variables in the ion force balance equation, including the electrical force, ion pressure and neutral particle friction, are considered. The model is solved through a finite difference scheme and sheath characteristics are obtained. The effects of the ion temperature on both the collisionless and collisional sheath characteristics are discussed. Then it is concluded that 1) the model is in a good agreement with Bohm Theorem; 2) the ion temperature has significant effects on the rf sheath characteristics. The effects are far more significant on a collisional rf sheath than on a collisionless sheath.