Radial Profile Of Plasma Density Research Articles

Effect of electron and ion mobility on edge biasing in tokamak plasmas

Abstract We present an improved model for the study of edge biasing in a tokamak plasma that incorporates electron and ion mobility contributions. The non-ambipolar nature of the drifts due to the electron/ion mobility terms influences the space charge separation due to edge biasing and affects plasma dynamics in the edge and SOL regions in a significant manner. In contrast to earlier studies, the present model enables simulation studies at higher biasing voltages. The inclusion of mobility enhances/decreases the effect of negative/positive biasing. The radial profiles of plasma density, electron temperature, radial electric field, and its shear for positive as well as negative biasing are investigated as a function of mobility.

Effects of low-frequency voltage on nonlinear standing wave excitation, plasma uniformity, and ion dynamics in dual-frequency asymmetric capacitive discharges

It is known that in very-high-frequency (VHF) capacitively coupled plasmas, the higher harmonics generated by nonlinear sheath motion can enhance the standing wave effect (SWE), which can lead to center-peaked plasma density profiles. In this work, an improved nonlinear electromagnetic model incorporating a transmission line model, an electron momentum balance model, a bulk plasma model, a collisionless nonlinear numerical sheath model, and an ion Monte-Carlo collision (MCC) model is developed to study the effects of low-frequency (LF) voltage VL on the nonlinear standing wave excitation, plasma uniformity, and ion energy and angular distribution functions (IEDFs and IADFs) in dual-frequency (DF) asymmetric capacitive argon discharges at relatively low pressure of 3 Pa. The plasma diffusion in the radial direction and ion dynamics within the LF oscillating sheath are self-consistently considered. The LF voltage VL at 2 MHz varies from 0 to 700 V while the HF voltage VH at 60 MHz is fixed at 100 V. Simulation results indicate that without the addition of an LF source (i.e. VL= 0 V), there are a considerable number of high-order harmonics with short wavelengths, leading to significant SWE and central peak in the radial plasma density profile. Nevertheless, the high-order harmonic excitations tend to be weakened and merely occur around the phase of the full LF sheath collapse due to a shorter characteristic damping time of the surface waves as VL increases. This, combined with increased surface wavelengths of both the driving frequency and the higher harmonics at a higher VL , leads to suppressed standing waves and improved plasma uniformity. Meanwhile, the simulations show that both the low and the high energy peaks of IEDF move towards higher energies, and the energy peak separation width ΔE becomes wider with the increase of VL . The IEDF at the radial center of the powered electrode exhibits a broader ΔE than that at the edge. For the IADF, an increased VL results in more ions incident on the electrode with a smaller deflection angle. Because of a thinner sheath and a higher sheath voltage at the electrode center, the peak value of IADF at the electrode center is greater than that at the edge.

Dispersed Relativistic Electron Precipitation Patterns Between the Ion and Electron Isotropy Boundaries

AbstractRelativistic electron precipitation to the Earth's atmosphere is an important loss mechanism of inner magnetosphere electrons, contributing significantly to the dynamics of the radiation belts. Such precipitation may be driven by electron resonant scattering by middle‐latitude whistler‐mode waves at dawn to noon; by electromagnetic ion cyclotron (EMIC) waves at dusk; or by curvature scattering at the isotropy boundary (at the inner edge of the electron plasma sheet anywhere on the nightside, from dusk to dawn). Using low‐altitude ELFIN and near‐equatorial THEMIS measurements, we report on a new type of relativistic electron precipitation that shares some properties with the traditional curvature scattering mechanism (occurring on the nightside and often having a clear energy/L‐shell dispersion). However, it is less common than the typical electron isotropy boundary and it is observed most often during substorms. It is seen equatorward of (and well separated from) the electron isotropy boundary and around or poleward of the ion isotropy boundary (the inner edge of the ion plasma sheet). It may be due to one or more of the following mechanisms: EMIC waves in the presence of a specific radial profile of the cold plasma density; a regional suppression of the magnetic field enhancing curvature scattering locally; and/or electron resonant scattering by kinetic Alfvén waves.

Effects of a radial variation of surface coefficients on plasma uniformity in capacitive RF discharges

With the increasing demands toward large area plasma etching and deposition, the radial uniformity of capacitively coupled plasmas (CCPs) becomes one of the key factors that determine process performance in industrial applications. However, there is a variety of parasitic effects, e.g. electromagnetic and electrostatic edge effects, that typically lead to the formation of nonuniform radial plasma density profiles at various discharge conditions with a density peak appearing either at the center or near the edges of the electrodes. Moreover, in commercial CCPs different surface materials are in contact with the plasma at various positions as parts of boundary surfaces such as focus rings, masks, showerhead electrodes, wall and/or target materials. Via complex material specific plasma-surface interactions, the presence of such different surface materials affects plasma uniformity in a way that is typically not understood and, thus, not controlled. In this work, aided by 2d3v graphics processing unit accelerated particle-in-cell/Monte Carlo collision simulations, we study the effects of radial variations of electrode materials on the plasma via their different ion and electron induced secondary electron emission as well as electron reflection coefficients on the discharge characteristics. Based on such fundamental understanding we tailor the radial variation of boundary surface materials to improve plasma uniformity in low pressure CCPs. Such investigations are performed at different neutral gas pressures, where both center and edge high radial plasma density profiles form in the presence of radially uniform surface coefficients that resemble the presence of a single electrode material. It is demonstrated that by radially varying the surface coefficients at the grounded electrode, the radial plasma density profile can be finely adjusted and the plasma uniformity above the wafer placed at the powered electrode can be improved in both cases.

Simulation of nonlinear standing wave excitation in very-high-frequency asymmetric capacitive discharges: roles of radial plasma density profile and rf power

It is recognized that in large-area, very-high-frequency capacitively coupled plasma (VHF CCP) reactors, the higher harmonics generated by nonlinear sheath motion can lead to enhanced standing wave excitation. In this work, a self-consistent electromagnetic model, which couples a one-dimensional, radial nonlinear transmission line model with a bulk plasma fluid model, is employed to investigate the nonlinear standing wave excitation in a VHF driven, geometrically asymmetric capacitive argon discharge operated at low pressure. By considering a radially non-uniform plasma density profile (case I) calculated self-consistently by the nonlinear electromagnetic model and the corresponding radially-averaged, uniform plasma density profile (case II), we first examine the effect of the plasma density non-uniformity on the propagation of electromagnetic surface waves in a 3 Pa argon discharge driven at 100 MHz and 90 W. Compared to case II, the higher plasma density at the radial center in case I determines a higher plasma series resonance frequency, yielding stronger high-order harmonic excitations and more significant central peak in the harmonic current density J z,n and the harmonic electron power absorption p n profiles. Therefore, under the assumption of the radially uniform plasma density in a CCP discharge, the self-excitation of higher harmonics at the radial center should be underestimated. Second, using the self-consistent electromagnetic model, the effect of the rf power on the excitation of nonlinear standing waves is investigated in a 3 Pa argon discharge driven at 100 MHz. At a low power of 30 W, the discharge is dominated by the first two harmonics. The higher harmonic excitations and the nonlinear standing waves are observed to be enhanced with increasing the rf power, resulting in a more pronounced central peak in the radial profiles of the total electron power absorption density p e, the electron temperature T e, and the electron density n e. For all rf powers, the calculated radial profiles of n e show good agreement with the experimental data obtained by a floating double probe.

The role of neutral gas in validated global edge turbulence simulations

To make predictions for and design fusion reactors, a multitude of physical processes must be considered. In the edge and scrape-off layer (SOL), turbulent fluctuations intertwine with the plasma background, which is largely determined by neutral gas, and magnetic geometry plays an important role. A diffusive neutrals model has now been implemented in the global Braginskii edge turbulence code GRILLIX. The code is based on the flux-coordinate independent (FCI) approach, which allows efficient turbulence simulations in diverted equilibria. We validate simulations across the ASDEX Upgrade edge and SOL against measurements in discharge #36190, and find much better agreement thanks to the neutrals. Disentangling the effects of the neutral gas, we find that it affects the plasma in several ways. Firstly, the ionization of neutrals modifies the radial profiles of plasma density and temperature, leading to a transition of the turbulence drive from the general ballooning type to the ion temperature gradient type. Secondly, strong poloidal asymmetries can be induced due to divertor recycling, depending on the ionization pattern. As ballooned perpendicular plasma transport is stronger at the low-field side, neutrals penetrate deeper into the plasma at the high-field side, leading to significant ionization and radiation there. With increasing divertor neutrals density, the targets cool down while plasma density increases, more strongly at the high-field side. Much of the dynamics take place directly around the X-point and along the separatrix, which can be resolved by the FCI approach. Potential remains in extending the model and the code, but our results build confidence that predictive capability is within reach for major design questions for fusion reactors, such as the near SOL fall-off length.

GAS DISCHARGE IN PLASMA-METAL WAVEGUIDE WITH VARYING RADIUS OF METAL ENCLOSURE PARTIALLY FILLED BY RADIALLY NON-UNIFORM MAGNETIZED PLASMA

The article presents the results of theoretical study of phase and attenuation characteristics of the symmetric electromagnetic wave in long waveguide structure that partially filled by radially non-uniform plasma immersed in external steady magnetic field. The results of theoretical study of stationary gas discharge sustained by this wave in the considered waveguide structure with slightly varying radius of metal enclosure in the framework of electrodynamic model are presented as well. It was studied the influence of the effective plasma collision frequency on the phase and attenuation wave properties and on the plasma density axial distribution in gas discharge considered for different radial plasma density profiles.

Steady state densities in a plasma confined by a dipole magnet: Diffusion induced transport explored through direct measurements and modeling

Steady state densities in a plasma confined by a permanent dipole magnet are determined through detailed experiments and modeling. Two diffusion models are developed, and the resulting equations are solved numerically to yield the radial and angular plasma density profiles, which are compared with those obtained experimentally. The models consider the fluid and continuity equations along with Fick’s law and take into account the experimentally determined electron temperature (Te) and the static dipole magnetic fields (B) in space, as a common input. In model I, the equation of motion for both charges (ions and electrons) is used to self-consistently generate the ambipolar electric field (E), while model II considers the electron equation of motion and takes into account the experimentally determined plasma potential (Vs) as another input, whose gradient provides the ambipolar electric field. Results indicate that the plasma density peaks around r ∼ (2–12) cm depending on the polar angle and the discharge pressure and decreases for large r, while its angular variation shows a maximum in the equatorial plane (θ = 90°) and decreases toward the polar regions. Te and Vs are higher in the polar cusp regions and decrease toward the equatorial plane, with the profiles becoming more spherically symmetric away from the magnet. The numerically obtained density profiles from the models agree well with those obtained experimentally. The phenomenon of inward diffusion resulting in peaked density profiles as reported by earlier authors is found to be a natural outcome of the solution of the diffusion equation.

Estimation of plasma density perturbation from dusty plasma injection by laser irradiation on tungsten target in DiPS

To investigate the interaction of dusty plasma with magnetized plasmas at divertor plasma simulator, radial profiles of plasma density (ne) and electron temperature were measured in terms of plasma discharge currents and magnetic flux intensity by using a fast scanning probes system with triple tips. Dusty plasma with dusts (a generation rate of 3 μg s−1 and a size of 1–10 μm) was produced via interactions between a high-power laser beam and a full tungsten target. As ne increases, the scale of the effects of dusty plasma injection on magnetized plasmas was decreased. Also, the duration of transient fluctuation was reduced. For numerical estimation of plasma density perturbation due to dusty plasma injection, the result was ∼10% at a core region of the magnetized plasma with ne of (2–5) × 1011 cm−3 at steady state condition.

Electron cyclotron resonance plasma excitation in a toroidal plasma

In this article, Electron Cyclotron Resonance (ECR) absorption, Upper-Hybrid Resonance (UHR) absorption and Electron Bernstein Wave (EBW) conversion are systematically confirmed in magnetically confined KT-5D plasma which is sole-excited by a magnetron source. A 2.45 GHz ECR system has been developed on the toroidal helimak KT-5D to produce and sustain a steady-state plasma. 0.98 kW electron cyclotron wave produced by the magnetron is injected into the vacuum chamber through rectangular waveguides with a power absorption efficiency of 40∼50%. A steady-state plasma is excited with a density of several 1016/m3 and electron temperature of up to 30 eV. The radial profile of plasma density shows that ECR absorption dominates the power deposition with a higher hydrogen pressure of at the order of 10-1 Pa, while UHR absorption dominates with a lower hydrogen pressure of at the order of 10-2 Pa. Plasma density in the discharge with a superimposed magnetic shear has demonstrated the wave conversion from ECR to EBW.

Influence of neutral beam attenuation on beam emission spectroscopy and charge exchange recombination spectroscopy.

Neutral beam attenuation is simulated by means of consulting the ADAS (Atomic Data and Analysis Structure) database based on experimentally diagnosed radial plasma density and electron temperature profiles on the Experimental Advanced Superconducting Tokamak (EAST). Two-dimensional distributions of beam emission and charge exchange recombination photon flux are simulated, taking neutral beam attenuation into account, together with comparison with experimental results of Beam Emission Spectroscopy (BES) and Charge eXchange Recombination Spectroscopy (CXRS). A photon number which is over 1014 promises a sufficient photon flux for typical detectors of BES, CXRS, and UltraFast-CXRS (UF-CXRS) diagnostics. Evidence shows that the ADAS database overvalues neutral beam injection effective stopping coefficient on the EAST tokamak. The joint diagnostic of BES and UF-CXRS which is under development to measure plasma pressure with a high temporal resolution of 1 μs will have strong signals in a radial range of 0.6 < ρ < 0.8. The steep gradients of plasma density and C6+ density at ρ ∼ 1 bring great difficulty to edge plasma investigation by this joint diagnostic.

Experimental investigation of standing wave effect in dual-frequency capacitively coupled argon discharges: role of a low-frequency source

It is well known that the plasma non-uniformity caused by the standing wave effect has brought about great challenges for plasma material processing. To improve the plasma uniformity, a low-frequency (LF) power source is introduced into a 100 MHz very-high-frequency (VHF) capacitively coupled argon plasma reactor. The effect of the LF parameters (LF voltage amplitude ϕL and LF source fL) on the radial profile of plasma density has been investigated by utilizing a hairpin probe. The result at a low pressure (1 Pa) is compared to the one obtained by a 2D fluid-analytical capacitively coupled plasma model, showing good agreement in the plasma density radial profile. The experimental results show that the plasma density profile exhibits different dependences on ϕL and fL at different gas pressures/electrode driven types (i.e., the two rf sources are applied on one electrode (case I) and separate electrodes (case II)). At low pressures (e.g., 8 Pa), the pronounced standing wave effect revealed in a VHF discharge can be suppressed at a relatively high ϕL or a low fL in case I, because the HF sheath heating is largely weakened due to strong modulation by the LF source. By contrast, ϕL and fL play insignificant roles in suppressing the standing wave effect in case II. At high pressures (e.g., 20 Pa), the opposite is true. The plasma density radial profile is more sensitive to ϕL and fL in case II than in case I. In case II, the standing wave effect is surprisingly enhanced with increasing ϕL at higher pressures; however, the center-high density profile caused by the standing wave effect can be compensated by increasing fL due to the enhanced electrostatic edge effect dominated by the LF source. In contrast, the density radial profile shows a much weaker dependence on ϕL and fL in case I at higher pressures. To understand the different roles of ϕL and fL, the electron excitation dynamics in each case are analyzed based on the measured spatio-temporal distributions of the electron-impact excitation rate by phase resolved optical emission spectroscopy.

Development of a helicon ion source: Simulations and preliminary experiments.

In the present context, the extraction system of a helicon ion source has been simulated and constructed. Results of the ion source commissioning at up to 20 kV are presented as well as simulations of an ion beam extraction system. Argon current of more than 200 μA at up to 20 kV is extracted and is characterized with a Faraday cup and beam profile monitoring grid. By changing different ion source parameters such as RF power, extraction voltage, and working pressure, an ion beam with current distribution exhibiting a central core has been detected. Jump transition of ion beam current emerges at the RF power near to 700 W, which reveals that the helicon mode excitation has reached this power. Furthermore, measuring the emission line intensity of Ar ii at 434.8 nm is the other way we have used for demonstrating the mode transition from inductively coupled plasma to helicon. Due to asymmetrical longitudinal power absorption of a half-helix helicon antenna, it is used for the ion source development. The modeling of the plasma part of the ion source has been carried out using a code, HELIC. Simulations are carried out by taking into account a Gaussian radial plasma density profile and for plasma densities in range of 1018-1019 m-3. Power absorption spectrum and the excited helicon mode number are obtained. Longitudinal RF power absorption for two different antenna positions is compared. Our results indicate that positioning the antenna near to the plasma electrode is desirable for the ion beam extraction. The simulation of the extraction system was performed with the ion optical code IBSimu, making it the first helicon ion source extraction designed with the code. Ion beam emittance and Twiss parameters of the ellipse emittance are calculated at different iterations and mesh sizes, and the best values of the mesh size and iteration number have been obtained for the calculations. The simulated ion beam extraction system has been evaluated using optimized parameters such as the gap distance between electrodes, electrodes aperture, and extraction voltage. The gap distance, ground electrode aperture, and extraction voltage have been changed between 3 and 9 mm, 2-6.5 mm, and 10-35 kV in the simulations, respectively.

Nightside Pi2 Wave Properties During an Extended Period With Stable Plasmapause Location and Variable Geomagnetic Activity

AbstractThe frequencies and amplitudes of inner magnetosphere Pi2 waves are affected by the radial plasma density profile. Variable geomagnetic activity and external driving conditions can affect both wave properties and density profiles simultaneously. When interpreting observations, this can lead to ambiguity about whether changing wave properties are due to changing external conditions, density profiles, or a combination of factors. We present a case study using multipoint ground‐based and in situ measurements to examine Pi2 wave properties during a period of variable geomagnetic activity. Multiple satellite passes demonstrate the density profile and plasmapause location are stable for at least 2 h over a wide range of magnetic local time. This stability allows us to examine how factors besides the radial density profile affect Pi2 wave properties. We find evidence for Pi2 waves with a broadband frequency spectrum as well as a discrete frequency plasmaspheric virtual resonance (PVR) that is observed at low, middle, and high latitudes and both inside and outside the plasmapause. The PVR is excited in repeated bursts before, during, and after (1) the development of a substorm, (2) several auroral intensifications, (3) the development of Subauroral Polarization Stream flows/electric fields/conductivities, and (4) variable interplanetary magnetic field conditions. Through all these changes the PVR frequency remains remarkably stable (8.2 ± 0.53 mHz, based on low‐latitude ground magnetometer observations), suggesting that these variations have little effect on the frequency. This is consistent with PVR model predictions for a stationary plasmapause.

Eigen electromagnetic waves of a coaxial waveguiding structure filled by a non‐uniform dissipative plasma with azimuthal magnetic field

This paper studies the propagation and spatial attenuation of high‐frequency eigen‐symmetric and dipolar electromagnetic waves along a coaxial plasma–metal waveguiding structure that contains a slightly axial and strong radial non‐uniform cylindrical plasma slab in an external azimuthal non‐uniform magnetic field. The influence of such parameters as the effective electron collision frequency, the direct current value producing the external azimuthal magnetic field, parameters that characterize plasma density radial profile, and waveguide geometric parameters on the dispersion, spatial attenuation, and radial field structure of the waves is considered. The regions of waveguiding structure parameters where the electromagnetic wave properties can be effectively controlled are studied and analyzed.

Modeling of Resonant Surface Wave Excitation in a Large CCP Reactor

Low-pressure plasmas produced in capacitively coupled plasma (CCP) reactors are used extensively in the plasma processing industry. Although the physics of small scale CCP reactors operated under low pressure is fairly well understood, larger scale CCP reactors constructed to meet the industrial needs often exhibit surprising behavior in experiments, which affects discharge parameters of importance to the industrial applications. This can be explained by the resonant excitation of surface modes that a CCP reactor can support. Limitations of the drift-diffusion approximation in description of the surface mode phenomena in low-pressure plasmas are discussed. It is shown that a particular class of the surface modes can be adequately modeled using the electrostatic approximation if the finite electron inertia is taken into account. Continuing a previous work [1] , the present study demonstrates how such modes are triggered and how they affect the radial plasma density profile uniformity. This is done by using a self-consistent 2d3v electrostatic implicit PIC/MCC code. It is shown that in highly collisional plasmas, the nonuniformities caused by the modes disappear due to the large mode damping.

Experimental investigations of the plasma radial uniformity in single and dual frequency capacitively coupled argon discharges

In the current work, the radial plasma density has been measured by utilizing a floating double probe in single and dual frequency capacitively coupled argon discharges operated in a cylindrical reactor, aiming at a better understanding of electromagnetic effects and exploring a method of improving the radial uniformity. The experimental results indicate that for single-frequency plasma sustained at low pressure, the plasma density radial profile exhibits a parabolic distribution at 90 MHz, whereas at 180 MHz, the profile evolves into a bimodal distribution, and both cases indicate poor uniformities. With increasing the pressure, the plasma radial uniformity becomes better for both driving frequency cases. By contrast, when discharges are excited by two frequencies (i.e., 90 + 180 MHz), the plasma radial profile is simultaneously influenced by both sources. It is found that by adjusting the low-frequency to high-frequency voltage amplitude ratio β, the radial profile of plasma density could be controlled and optimized for a wide pressure range. To gain a better plasma uniformity, it is necessary to consider the balance between the standing wave effect, which leads to a maximum plasma density at the reactor center, and the edge field effect, which is responsible for a maximum density near the radial electrode edge. This balance can be controlled either by selecting a proper gas pressure or by adjusting the ratio β.

Role of neutral gas in scrape-off layer of tokamak plasma in the presence of finite electron temperature and its gradient

The role of neutral gas molecules in the Scrape-off Layer (SOL) region of tokamak plasma is important as it is expected to modify the plasma turbulence. Two-dimensional model has been used that consists of electron continuity, molecular ion continuity, quasi-neutrality, electron energy, and neutral molecular gas continuity equations in the presence of electron impact molecular ionizations and other non-ionizing collisions. The growth rate obtained from these equations has been presented using linear theory. It is observed that the growth rate increases with the neutral gas ionization coefficients. The nonlinear equations are solved numerically in the presence and absence of the neutral gas molecules. Radial profiles of plasma density, electron temperature, and electric field have been obtained. It is found that the neutral gas reduces electric fields. More significant reduction of the poloidal electric field has been found by the neutral gas. Time series obtained from the numerical data has been analyzed. A strong decrease in fluctuation of the plasma density, electron temperature, and potential has been found at the outer region the SOL plasma in the presence of the gas molecules.

Analytical Model of an Asymmetric Sunspot with a Steady Plasma Flow in its Penumbra

A new exact analytical solution to the stationary problem of ideal magnetohydrodynamics is derived for an unipolar asymmetric sunspot immersed in a realistic solar atmosphere. The radial and vertical profiles of pressure, plasma density, and temperature in the visible layers of the sunspot are calculated. The reduction in plasma density in the magnetic funnel of the sunspot, corresponding to the Wilson depression, is also obtained. The magnetic structure of the sunspot is given analytically in a realistic way: a part of the magnetic flux of the sunspot approaches the surrounding photosphere at the outer edge of the penumbra. The magnetic field of the sunspot is not assumed to be axially symmetric. For the first time, the angular dependence of the physical variables in this model allows us to simulate not only a deviation from the circular shape of the sunspot, but also a fine filamentary structure of the sunspot penumbra. The Alfven Mach number (the ratio of the plasma speed to the Alfven speed) is zero at the center of the sunspot and rises slowly toward the periphery of the sunspot; this corresponds to the structure of the Evershed flow in the penumbra. The Evershed flow in our model is mainly concentrated in dark penumbral filaments, as is observed.

Radial magnetic compression in the expelled jet of a plasma deflagration accelerator

A spectroscopic study of a pulsed plasma deflagration accelerator is carried out that confirms the existence of a strong compression in the emerging jet at the exit plane of the device. An imaging spectrometer is used to collect broadened Hα emission from a transaxial slice of the emerging jet at high spatial resolution, and the radial plasma density profile is computed from Voigt fits of the Abel inverted emissivity profiles. The plasma temperature, determined via Doppler broadening of impurity line emission, is compared against the temperature predictions of a radial magnetohydrodynamic equilibrium model applied to the measured density profiles. Empirical scaling laws developed for the plasma density, combined with the measured and predicted temperatures, indicate that a radially equilibrated Z-pinch is formed within the expelled plasma jet at the exit plane during the deflagration process.