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This paper presents a graybox methodology to model the resistive wall mode instability by combining first principle approach and system identification technique. In particular we propose a separate ...

Collisional particle transport is examined in several toroidal plasma devices in the presence of perturbations typical of modes leading up to a disruption, of saturated tearing modes, or of unstable Alfven modes. The existence of subdiffusive transport for electrons is found to occur in some cases at very low mode amplitudes and to also exist even for ions of high energy. Orbit resonances can produce long time correlations and traps for particle trajectories at perturbation amplitudes much too small for the orbits to be represented as uniformly chaotic. The existence and nature of subdiffusive transport is found to depend on the nature of the mode spectrum and frequency as well as the mode amplitudes.

This paper reviews measurements of edge plasma turbulence in toroidal magnetic fusion devices with an emphasis on recent results in tokamaks. The dominant feature of edge turbulence is a high level of broadband density fluctuations with a relative amplitude delta n/n - 5-100%, accompanied by large potential and electron temperature. fluctuations. The frequency range of this turbulence is -10 kHz-1 MHz, and the size scale is typically -0.1-10 cm perpendicular to the magnetic field but many metres along the magnetic field, i.e. the structure is nearly that of 2D 'filaments'. Large intermittent bursts or 'blobs' are usually observed in the scrape-off layer. Diagnostic and data analysis techniques are reviewed and the main experimental results are summarized. Recent comparisons of experimental results with edge turbulence theory are discussed, and some directions for future experiments are suggested.

Plasma density fluctuations in the edge plasma of the RFX-mod device are measured through the Gas Puffing Imaging Diagnostics. Statistical features of the signal are quantified in terms of the Probability Distribution Function (PDF), and computed for several kinds of discharges. The PDFs from discharges without particular control methods are found to be adequately described by a Gamma function, consistently with the recent results by Graves et al [J.P. Graves, et al, Plasma Phys. Control. Fusion 47, L1 (2005)]. On the other hand, pulses with external methods for plasma control feature modified PDFs. A first empirical analysis suggests that they may be interpolated through a linear combination of simple functions. An inspection of the literature shows that this kind of PDFs is common to other devices as well, and has been suggested to be due to the simultaneous presence of different mechanisms driving respectively coherent bursts and gaussian background turbulence. An attempt is made to relate differences in the PDFs to plasma conditions such as the local shift of the plasma column. A simple phenomenological model to interpret the nature of the PDF and assign a meaning to its parameters is also developed., Comment: 27 pages. Published in PPCF

A Thomson scattering diagnostic is used in the RFX reversed field pinch experiment to measure single pulse, multipoint electron temperature (T-e) profiles. Recent significant improvements have provided reliable and routine operation of the diagnostic. Custom developed CAMAC charge analog-to-digital converters have been introduced, which sample the plasma light 170 ns after the laser light and have greater sensitivity. The spectrometer configuration and the calibration procedure have been optimized. These upgrades have finally led to better fitted scattering spectra and more regular estimates of T-e profiles, allowing the measurement of temperatures as low as 20 eV. The introduction of a second spectrometer has recently added a further ten positions to the original ten point profile, resolving the often steep T-e edge gradient. On axis values are in good agreement with other T-e measurements from SXR diagnostics (either SiLi and double filter method). T-e profiles are typically rather flat, but some dependence on the plasma parameters, like density and pinch parameter, has been drawn. Significant T-e profile modifications have been observed during transient events like pulsed poloidal current drive and pellet injection. The diagnostic will be completed soon, allowing production of 27 point profiles, with the introduction of the third spectrometer. Double pulse operation of the laser is in progress. (C) 1999 American Institute of Physics. [S0034-6748(99)69401-1].

In the framework of adding new information to the reversed field pinch (RFP) confinement database, the radiation emitted by RFX plasmas has been investigated using an eight chord bolometric camera, whose detectors have been calibrated absolutely. From the experimental data the emissivity profiles have been reconstructed by means of a generalized tomography reconstruction algorithm. This analysis confirms that the radiation emitted in RFX is systematically concentrated at the edge. The dependence of the emitted power on the plasma density shows that the radiation increases approaching the high density regime, but it rarely goes beyond 30% of the input power for stationary discharges. This behaviour is strongly dependent on the concentration of impurities but, in any case, in RFX there is no evidence of disruptions. A simple local energy balance allows a preliminary evaluation of the radial heat flux profile to be obtained. These measurements indicate that an active impurity screening mechanism is acting in the edge and that transport is the major energy loss mechanism in RFX.

The work presented in this thesis is inserted in the field of the research on plasma physics conducted with magnetically confined devices, whose ultimate goal is the demonstration of the feasibility of the energy production through fusion reactions between nuclei of hydrogen isotopes. One of the major issues in the operation of a magnetically confined plasma, both in a present device and in a future reactor, is the presence in the plasma of other elements besides the main gas: the so called impurities. These originate mainly by the interaction of the hot plasma with the plasma facing materials, which can both be eroded and release atmospheric gases previously adsorbed. Once these impurities enters the plasma they get ionised and start emitting radiation through bremsstrahlung and atomic processes (line and recombination radiation). If impurities accumulate in the core plasma, where the temperature is highest, this can lead to a dramatic increase in radiation losses, drive radiative instabilities and dilute the plasma with negative consequences on plasma reactivity. In this regard it is extremely important to keep as low as possible the total impurity content and to control the impurity peaking, i.e. where impurities accumulate. The first point can be addressed by a correct choice of the plasma facing components and by conditioning the first wall. The second point needs a study of the impurity transport in different scenarios, understanding what prevents the accumulation of ions in the core. The radial impurity flux is usually expressed by means of two transport coefficients: the diffusion coefficient and the convective velocity. The determination of these coefficients in different scenarios allows to understand and control the impurity peaking. The Ph.D. activity developed during these three years is focused on this topic: the understanding of the impurity transport behaviour in different scenarios by means of the determination of the transport coefficients. This analysis has been conducted on a particular magnetic configuration: the reversed-field pinch. It has been carried out on the two main devices operating in this configuration: RFX-mod located in Padua (Italy) and MST located in Madison (WI, USA). The analysis method consists in the reproduction by means of a 1D impurity transport code of the plasma signals which are mainly affected by the presence of impurities. In order to discriminate the two coefficients, transients in the plasma signals are needed, which are then reproduced by the code. These transients are usually induced by means of artificially introduced impurities; the code reproduces the variations in the emission patterns or in the impurity density (depending on the available measurements) which are caused by the introduced atoms. By matching the simulation with the measurements an estimation of the transport coefficients is obtained. Once the coefficients have been estimated, they are compared with theoretical models in order to understand the nature of the transport in a particular plasma scenario. For both machines, through the application of this method, the transport of different species of impurities (intrinsic and not) in different magnetic regimes has been studied. In RFX-mod, experiments with injected pellets of carbon and lithium have been carried out and subsequently reproduced with the code, allowing to determine the transport coefficients for the two elements. Moreover, first experiments with introduced tungsten have been conducted; its emission spectrum has been acquired and its penetrating capability investigated. In MST time-dependent impurity density measurements were available for different intrinsic species in two magnetic regimes; their reproduction with the transport code allowed to estimate the transport coefficients. This manuscript is organised in two main parts: first three chapters form the introductory part, chapters four and five form the original work of this thesis. Chapter 1 introduces the role of impurities in fusion plasmas. The production processes are described as well as the impurity effects on the plasma properties. Emitted radiation from impurities is divided into its components (continuum and produced by atomic processes) and briefly characterised. Then the different models used to describe the ion populations are presented: coronal, local thermodynamic and collisional-radiative. Finally the impurity radial transport is depicted in its analytical form, according to the classical and neo-classical formulation. Chapter 2 describes the reversed-field pinch magnetic configuration. Particle transport in this configuration is analytically presented. Chapter 3 gives the details of the simulation tool used in this thesis for reproducing experimental measurements. The code consists of a transport model coupled to a collisional-radiative model for various species. Both models are detailed as well as the inputs and outputs to the code. Chapter 4 reports the analysis performed at RFX-mod on impurity transport. The transient experiments conducted through pellets injection of carbon and lithium are described and the results presented. Transport coefficients are estimated for the different species in different magnetic scenarios. Then experiments with tungsten injection through the laser-blow off technique are presented and the results discussed and compared with reports from other devices. Chapter 5 deals with the analysis realised at MST on impurity transport. Impurity density measurements carried out for different intrinsic species in different plasma regimes are reproduced with the code. The estimated transport coefficients are presented and compared with theoretical models. Chapter 6 concludes the thesis with a discussion of the most important results achieved and an overview of possible future developments.

RFX-mod reliably operates at 1.5 MA, the highest current ever achieved on a reversed field pinch device thanks to the the feedback control on multiple magnetohydrodynamic modes. In these high current discharges magnetic topology spontaneously self-organizes in an Ohmic helical symmetry, the quasi single helicity (QSH) state, in which the magnetic dynamics is dominated by the innermost resonant mode, with the new magnetic axis helically twisting around the geometrical axis of the torus. Inside the helical structure energy confinement is enhanced and electron temperatures exceeding 1 keV are measured, with steep gradients, which identify an internal transport barrier. Separatrix expulsion and symmetric electron temperature profiles with high gradients are obtained for ratios between the dominant mode and total B above about 4%. The measured electron temperature peak involves a large fraction of the plasma cross section, corresponding to an improvement in the global electron energy confinement up to a factor 2. The steep temperature profiles obtained in QSH conditions correspond to an electron thermal diffusivity reduced by more than one order of magnitude. Perturbative experiments (pellets and impurity laser blow off injections) have been performed to study particle confinement inside and outside the thermal island. Inside the helical structure experimental evidence of main gas confinement increase has been obtained, while for impurities there is no evidence of confinement increase.

A two-dimensional array of saddle coils at Mc poloidal and Nc toroidal positions is used on the EXTRAP T2R reversed-field pinch (Brunsell P R et al 2001 Plasma Phys. Control. Fusion 43 1457) to study active control of resistive wall modes (RWMs). Spontaneous growth of several RWMs with poloidal mode number m = 1 and different toroidal mode number n is observed experimentally, in agreement with linear MHD modelling. The measured plasma response to a controlled coil field and the plasma response computed using the linear circular cylinder MHD model are in quantitive agreement. Feedback control introduces a linear coupling of modes with toroidal mode numbers n, n' that fulfil the condition |n − n'| = Nc. Pairs of coupled unstable RWMs are present in feedback experiments with an array of Mc × Nc = 4 × 16 coils. Using intelligent shell feedback, the coupled modes are generally not controlled even though the field is suppressed at the active coils. A better suppression of coupled modes may be achieved in the case of rotating modes by using the mode control feedback scheme with individually set complex gains. In feedback with a larger array of Mc × Nc = 4 × 32 coils, the coupling effect largely disappears, and with this array, the main internal RWMs n = −11, −10, +5, +6 are all simultaneously suppressed throughout the discharge (7–8 wall times). With feedback there is a two-fold extension of the pulse length, compared to discharges without feedback.

The momentum balance has been applied to the ExB flow in the edge region of a reversed field pinch (RFP) configuration. All terms, including those involving fluctuations, have been measured in stationary condition in the edge region of the Extrap-T2R RFP experiment. It is found that the component of the Reynolds stress driven by electrostatic fluctuations is the term playing the major role in driving the shear of the ExB flow to a value marginal for turbulent suppression, so that the results are in favor of a turbulence self-regulating mechanism underlying the momentum balance at the edge. Balancing the sheared flow driving and damping terms, the plasma viscosity is found anomalous and consistent with the diffusivity due to electrostatic turbulence.

The reversed-field pinch exhibits a strong tendency to self-organize into a helical equilibrium as the plasma current is increased. The helical reversed-field pinch is characterized by reduced magnetic stochasticity and by the formation of electron internal transport barriers. The paper gives an update on recent experimental and modelling work on helical states in RFX-mod (Sonato et al 2003 Fusion Eng. Des. 66 161), also discussing similarities with 3D equilibria in tokamaks. The helical equilibrium is modelled with 3D codes developed for stellarators, such as VMEC/V3FIT. The reconstructed safety factor profile has low or reversed magnetic shear in the core, which may be related to transport barrier formation. A significant extension of the RFX-mod database to high current and density confirms the dependence observed before of various helical state properties on macroscopic quantities. Even under conditions where it does not form spontaneously, such as at low current or high density, the 3D magnetic equilibrium can be stimulated and robustly controlled with external fields applied by an extensive set of non axi-symmetric coils. An advanced magnetic feedback algorithm that compensates for error fields induced by eddy currents in the 3D wall structures has been developed. This work stimulated similar experiments in RFX-mod run as a tokamak, where external 3D fields are applied to control a m = 1/n = 1 helical equilibrium.

The transport of intrinsic impurities is investigated during standard and improved confinement regimes of the Madison Symmetric Torus (MST) reversed-field pinch. The impurity diffusion coefficient (D) and pinch velocity (v) are obtained through comparing the time evolution of experimental impurity density profiles with the results of a one-dimensional impurity transport code. Experimental hollow fully stripped (C, O, B) ion populations in improved confinement discharges are reproduced with the transport code indicating outward convection of impurity ions. Estimated D and v are low and close to classical values. Standard MST discharges are characterized by a high level of stochasticity and nearly flat radial profiles of the fully stripped carbon. To reproduce this flat impurity profile a high outward convective velocity and high central D are assumed in the simulation.

High current (Ip = 1-1.7 MA) operations in the ohmic reversed field pinch RFX-mod spontaneously access the quasi-single helicity (QSH) regime, in which the magnetic dynamics is dominated by the innermost resonant mode (m = 1, n = -7), the magnetic chaos level is reduced and the internal magnetic field configuration is close to a pure helix. During the QSH state strong electron temperature (Te) gradients can show up, identifying an electron transport barrier (Puiatti 2011 Nucl. Fusion 51 073038). Results and advancements obtained in recent RFX-mod high current campaigns are reported in this paper. The best plasma performances at high Ip (i.e. high power) in QSH regimes have been reached with marginally reversed values of the safety factor q at the edge (-0.01 < qa < 0) when the lowest amplitudes of secondary m = 0, 1 modes are obtained. The QSH magnetic states are not stationary and show back transitions to the multiple helicity regime; however, the total persistency of the QSH is found to increase with the plasma current and at Ip > 1.5 MA it exceeds 90% of the plasma current flat-top. The high electron temperature gradients (>2 keV m-1) do not persist throughout the magnetic QSH cycle, as documented by a new high time resolution SXR double-filter multichord system, however, they last 5 to 10 ms, more than the energy confinement time. In the barrier region the profile of the electron heat diffusivity χe falls around 2-20 m2 s-1, well below ∼40-100 m-2 s-1 typical of the outer regions. The experimental evaluation of χe across the thermal barrier is consistent with a microtearing mode driven heat transport.

The two-dimensional (2D) density distribution of a particle beam can be reconstructed using a diagnostic based on tomographic techniques, which measures the D? light. This paper presents investigations and tests concerning the reliability of such a diagnostic, applied to the beam produced in MITICA (Megavolt ITER Injector & Concept Advancement) the full-size prototype of the neutral beam injector, which will be used for additional heating on ITER. It aims at developing the technologies to guarantee the correct operation of the injectors to be installed in ITER. The main target of the tomographic diagnostic is the measurement of the beam uniformity with sufficient contrast and spatial resolution, and of its evolution throughout the pulse duration. In particular the ITER beam uniformity is required to be within 10%, thus the error of the tomographic reconstruction has to be lower than this value. The conceptual design of the diagnostic is presented, with a description of the layout and main components. The portholes around the vessel and the geometry of the lines of sight are arranged so as to cover the whole area of the beam. A tomographic algorithm based on the simultaneous algebraic reconstruction technique (SART) is developed to reconstruct the beam intensity profile. Phantoms reproducing different experimental beam configurations are simulated and reconstructed with this technique. The role of noise in the line-integrated signals is studied and its effect on the reconstructed emission is investigated. The unsatisfactory results suggested the introduction of a regularization algorithm, to reduce the effect of the noise in the beam reconstruction. In this way, the simulated phantoms are correctly reconstructed and their 2D spatial non-uniformity is correctly estimated, up to a noise level of 10%.

Plasma–wall interaction is one of the most important issues that present magnetic confinement devices have to face. In the RFX-mod reversed field pinch experiment plasma–wall interaction has become a hard point increasing plasma current up to the RFX-mod maximum design value of 2 MA, since in this case local power deposition can be as high as 10 MW m−2. Since the first wall of RFX-mod is entirely covered by graphite tiles different techniques have been tested to control hydrogen wall influx: He glow discharges cleaning, He discharges at high plasma currents, wall boronization and baking. With the best results obtained by boronization, at high plasma currents all such techniques improve the situation but do not allow a complete and stationary hydrogen influx reduction. Furthermore, in the presence of localized high power load the wall still responds providing very high influxes. In order to improve this situation wall conditioning by lithium has been tested. As a first lithization method to deposit a controllable amount of lithium on the wall, a room temperature pellet injector has been used (maximum pellet diameter of 1.8 mm and maximum length of 5 mm). Lithium coatings with a theoretical thickness of about 10 nm have been applied both to clean graphite tiles and over boronized ones. Lithization demonstrated to be effective in lowering hydrogen wall recycling to a value smaller than that of boronized graphite, with the effect lasting 20–30% more than in the boronized case. Compared with boronization, lithization slightly improves (by about 30%) particle confinement time and also clearly affects edge particle transport providing a lower edge density and more peaked density profiles. Lithization also reduces carbon content by about 10% over boronization but still no clear improvement has been observed in terms of energy confinement. Similar results have been obtained performing lithization over boronized graphite.

Nonlinear three-dimensional magnetohydrodynamic(MHD) simulations were applied to a reversed-field pinch(RFP) plasma to reveal the physical mechanism of the formation of helical structures such as the so-called quasi-single helicity and single helical axis states. The simulations were executed using the MHD Infrastructure for Plasma Simulation (MIPS) code in a realistic experimental geometry of the REversed field pinch of Low-Aspect ratio eXperiment (RELAX) device with reconstructed initial equilibria calculated by the RELAXFit code. Long-term evolutions showed remarkable formation of n = 4 structures as a result of the dominant growth of resistive modes. The resultant relaxed helical state consists of a bean-shaped, hollow pressure profile in the poloidal cross section for both the cases of resonant and non-resonant triggering instabilities.

In the reversed field pinch experiment RFX-mod, plasma currents larger than 1 MA show a spontaneous transition from an axisymmetric to a helical configuration, where electron internal transport barriers (eITB) are observed in the proximity of the maximum of the q safety factor. 3D MHD simulations predict a helical flow pattern associated with the helical deformation of the magnetic flux surfaces. This paper reports the recent experimental findings on plasma flow in these helical regimes. Passive spectroscopy measurements of carbon and boron line Doppler shift allow the reconstruction of the m = 1 component of the velocity pattern associated with the helical equilibrium in a poloidal cross-section. The helical plasma flow is observed to form a m = 1 convective cell creating a localized sheared flow outside the region of strong electron temperature gradients characterizing the eITB. The experimental pattern is compared with the results of 3D MHD simulations (by means of the SpeCyl code). While the code predicts a flow shear peaking in the proximity of the null of the magnetic shear, where the safety factor is maximum, experimentally the maximum flow shear is found to be more external, leaving as a still open question the role played by the flow shear for the thermal barrier formation in RFX-mod helical plasmas.

Quasi-single-helicity (QSH) states, characterized by a magnetic spectrum dominated by the innermost resonant tearing mode, are common to all the reversed field pinch (RFP) experiments. The internal magnetic field structure produced by the dominant mode is investigated for the QSH observed in the Madison Symmetric Torus (MST) RFP in discharges with zero toroidal magneticfield at the plasma boundary. The reconstruction is based on an MHD modelcoupledtoedgemeasurementsofthemagneticfield. Themodeldiscards pressure, which has little effect on the equilibrium magnetic profile of present RFP plasmas, but adopts a realistic toroidal geometry. The technique is the adaptation to the MST configuration of a procedure already applied in RFXmod, but a more general radial profile for the current density is needed for an adequate reconstruction of the MST case. The emerging features are similar to those found in RFX-mod. The helical flux surfaces of the dominant mode provide, with a good degree of reliability, a basis for mapping kinetic quantities such as electron density and soft-x-ray emissivity. (Some figures in this article are in colour only in the electronic version)

Helical equilibria have been experimentally found in the RFX-mod reversed field pinch both as spontaneous and induced states. These states are associated with a dominant helicity in the spectrum of magnetic field fluctuations producing a helical deformation of magnetic surfaces in a large fraction of the plasma core. In particular, they are also characterized by an improvement in global plasma performances in terms of electron temperature and energy confinement time with respect to the standard axisymmetric configuration with multiple helicities in the magnetic spectrum. These observations suggest that one should also expect an improvement in terms of particle confinement although this has never been experimentally observed due to the lack of a particle source in the core of RFX-mod plasmas. To address this point perturbative experiments were done in RFX-mod by injecting pellets (a known particle source) both inside and outside the helical magnetic structure present during such states. These experiments show that plasma density asymmetries and variations in the ablation rate of pellets are correlated with the internal magnetic field structure obtained by means of a line tracing code based on an equilibrium reconstructed in toroidal geometry using external measurements. In particular, they prove that particle transport is significantly reduced in the helical states with respect to axisymmetric configurations. An increase by a factor 2–3 was determined for the global electron particle confinement time calculated with a zero-dimensional model taking into account the helical geometry.

In the edge region of fusion devices coherent structures (blobs) are commonly observed. In order to investigate their evolution and the possible driving mechanisms, we studied the relationship between the size of the coherent structures and the local characteristic length L(p) of the edge electron pressure profile P(e)(r), together with the effect of magnetic fluctuations on del P(e). The results show an increase in the blob size with both Lp and magnetic fluctuations, suggesting an interplay between electron pressure gradient, magnetic fluctuations and edge turbulence generation. Measurements of the spatial scales of the edge turbulence structures and the corresponding toroidal phase velocity are obtained in the reversed field pinch RFX-mod by means of a gas puffing imaging diagnostic, while the local edge profiles of electron density n(e)(r) and temperature T(e)(r) and therefore P(e)(r) have been measured via the line intensity ratio technique of helium emission lines.

The high-frequency range of power spectra of turbulent fluctuating quantities measured at the edge of magnetized plasmas displays a variety of trends: from power laws with different spectral indices to exponential. We propose a model able to account for the whole phenomenology simply by tuning the distribution in the duration of the signal spikes. Comparisons with data from RFX-mod and Alcator C-Mod experiments are performed. An attempt to relate the statistics of the bursts with their generating mechanism is made.

In the reversed field pinch RFX-mod device, the achievement of high plasma currents (I p ⩾ 1.3 MA) has allowed the appearance of a new kind of large thermal structures emerging in the plasma core during the so-called quasi-single helicity (QSH) regimes. These structures correspond to a helical equilibrium established in the plasma, which has been dubbed as the single helical axis (SHAx) state. The topological features of this new type of thermal structures covering most of the plasma core have been experimentally investigated here. Analyses have been performed by means of three diagnostics, simultaneously and routinely running on RFX-mod: the soft x-ray (SXR) camera, the Thomson scattering diagnostic for the electron temperature (T e) profile estimation and the SXR tomography. In particular, a 2D map reconstruction of T e has been performed: the core electron temperature asymmetries mostly account for the ones in the reconstructed SXR emissivity. The magnetic topology of these QSH thermal structures has also been analysed and numerically investigated by the Hamiltonian guiding centre code ORBIT: magnetic and thermal structures have been identified, in position and topological features. Also the T e profile temporal evolution, provided by the tomographic diagnostic and the SXR camera, has been investigated, showing that the transition to SHAx does not develop in a unique way.

Electron density is scanned using fast gas puffing in the reversed-field pinch (RFP) device, TPE-RX. The gas puffing technique extends the operating range of I P/N from 12 to 2 ×10-14 Am (I P and N denote the plasma current and line density, respectively). It is estimated that the poloidal beta, βP, increases as I P/N decreases. This βP scaling with I P/N in TPE-RX confirms a similar tendency previously obtained in other RFP plasmas. The radiation fraction increases from ∼20% in the low-density regime to ∼35% in the highest-density regime. This result indicates that the lowest I P/N limit in RFP is similar to the density limit in tokamak plasmas.

The transport of injected impurities is investigated in the multiple helicity (MH) and improved confinement quasi single helicity (QSH) magnetic regimes of RFX-mod reversed-field pinch. Impurities are introduced through injections of room temperature pellets of carbon (in MH and QSH) and lithium (in MH). Simulation of experimental spectroscopic measurements, including line and soft x-rays emission, electron density and radiated power is carried out with a 1D collisional-radiative impurity transport code, allowing to determine the transport parameters: diffusion coefficient and convective velocity. The transport coefficients were found close to those deduced in previous experiments through the introduction of Ni and Ne, confirming the existence of an external velocity barrier also for light impurities.