Influence Of Collisions Research Articles

Influence of collisions on trapped-electron modes in tokamaks and low-shear stellarators

The influence of collisions on the growth rate of trapped-electron modes (TEMs) in core plasmas is assessed through both analytical linear gyrokinetics and linear gyrokinetic simulations. Both methods are applied to the magnetic geometry of the DIII-D tokamak, as well as the Helically Symmetric eXperiment (HSX) and Wendelstein 7-X (W7-X) stellarators, in the absence of temperature gradients. Here we analytically investigate the influence of collisions on the TEM eigenmode frequency by a perturbative approach in the response of trapped particles to the mode, using an energy-dependent Krook operator to model collisions. Although the resulting growth rates exceed perturbative thresholds, they reveal important qualitative dependencies: a geometry-dependent stabilization rate occurs for all wavenumbers at high collisionality, while at low collisionality, a geometry-sensitive mixture of collisionless, resonantly driven, and collisionally destabilized modes is found. Additionally, linear gyrokinetic simulations have been performed with a rigorous pitch-angle scattering operator for the same geometries. In the case of DIII-D and large wavenumber modes in HSX, the trends predicted by analytical theory are reproduced. Dissimilarities are, however, obtained in W7-X geometry and for low wavenumber modes in HSX, which are shown to be due to a collision-induced transition to the Universal Instability as the dominant instability at marginal collisionality.

Influence of collision between Friction Pendulum System and shear key on displacement response

Complex collision phenomena can occur between the Friction Pendulum System (FPS) and shear keys under earthquake, potentially resulting in shear keys sheared off. Based on a single-degree of freedom Spring-Friction Isolation System with shear keys, this article considers the independent shearing of each shear key due to collision effects, enabling precise simulation of each collision between FPS and shear keys under earthquakes. Additionally, the study investigates how this collision phenomenon affects the displacement response of FPS under various conditions. The findings reveal that collisions do not merely lead to displacement amplification effects on FPS. Instead, these effects depend closely on the spring stiffness and friction coefficient of FPS. Increased spring stiffness mitigates the displacement amplification caused by collisions. The timing of collisions occurrence also influences their impact on displacement. In cases where a structure exhibits resonance with substantial spring stiffness, frequent collisions can disrupt the resonance, significantly reducing the structural displacement response of FPS. Furthermore, friction plays a role in attenuating the collision's effect on FPS displacement amplification. However, when friction effect dominates in FPS, collisions can cause fluctuations in the FPS displacement time-history curve. The magnitude of this change is determined by the velocity increment resulting from the collision and the duration of this increment.

Influence of collisions on the validation of global gyrokinetic simulations in the edge and scrape-off layer of TCV

Understanding and predicting turbulent transport in the edge and scrape-off-layer (SOL) of magnetic confinement fusion devices is crucial for developing feasible fusion power plants. In this work, we present the latest improvements to the gyrokinetic turbulence code GENE-X and validate the extended model against experimental results in the TCV tokamak (“TCV-X21”). GENE-X features a full-f electromagnetic gyrokinetic model and is specifically targeted for edge and SOL simulations in diverted geometries. GENE-X can model the effect of collisions using either a basic Bhatnagar–Gross–Krook (BGK) or more sophisticated Lenard–Bernstein/Dougherty (LBD) collision operator. We present the results of a series of GENE-X simulations using the BGK or LBD collision models, contrasting them to collisionless simulations. We validate the resulting plasma profiles, power balance, and SOL heat flux against experimental measurements. The match to the experiment significantly improves with the fidelity of the collision model chosen. We analyze the characteristics of the turbulence and find that in almost all cases in the confined region the turbulence is driven by trapped electron modes (TEM). Both the simulations without collisions and those with the BGK collision operator do not accurately describe turbulence driven by TEMs. The more sophisticated LBD collision operator presents a minimum requirement for accurate gyrokinetic edge turbulence simulations.

Influence of collisions on the effect of electromagnetic-induced transparency in cells of finite sizes with anti-relaxation coating of walls

Based on the semiclassical theory of the interaction of two-frequency laser radiation with a resonant atomic medium, an analytical expression is obtained that describes the form of resonances of electromagnetically induced transparency detected in a cell with a finite direction in the longitudinal laser beam direction with an anti-relaxation coating of walls, taking into account the motion of atoms and collisions with walls. The following types of reflection from walls are considered: diffuse, specular, and specular-incoherent. It is found that in a number of cases the diffuse type of reflection exhibits the properties of a mirror-incoherent one. It is also shown that the nondegeneracy of the excited state in a number of cases significantly changes the shape of the transparency resonance. Keywords: Electromagnetically induced transparency, Gas cell, anti-relaxation coating, diffuse reflection, specular reflection, specular-incoherent reflection.

Gas kinetics of galactic disks explains rotation curves of S-type galaxies without a need for dark matter

In this paper, I show that the generally accepted methods of classical mechanics are not applicable for calculating the outer parts of the rotation curves (RCs) of galaxies, where the influence of collisions on gas dynamics becomes dominant. In addition, the hydrodynamic approach cannot be used for this purpose due to an extreme rarefaction of the gas. I develop a new approach for describing the gas dynamics in outer regions of galactic disks, where the gas dynamics is determined mainly by collisions. Equations (free from restrictions imposed on hydrodynamics) are obtained that describe the dynamics of rarefied gas. The resulting equation [Formula: see text] (14) relates two quantities: the tangential velocity of the gas as a function of the distance from the center of a galaxy (RC) and the radial distribution of the gas density. It is shown that if the physical properties of the rarefied gas are properly taken into account, then dark matter (DM) is not required, and the “nonphysical” (non-Keplerian) RCs of the outer parts of the galactic disks are tailwinds that can be described within the framework of conventional gas kinetics. To illustrate the correctness of the obtained model, two galaxies with flat RCs (NGC7331 and NGC3198) are considered. From the observed RCs, using Eq. ( 14 ), the radial densities of the gas are calculated. An excellent agreement was obtained between the calculated gas densities and their observed values, which is a serious argument in favor of the developed model. Thus, the nonphysical RCs of spiral galaxies represent the tailwinds of gas, the dynamics of which is naturally described by the kinetic equation without involving the concept of DM. Total masses of two galaxies NGC7331 and NGC3198 have been calculated. Implications for cosmology are discussed.

Aerosol deposition in the pulmonary acinar region: Influence of wall motion and interparticle collisions

It is critical to accurately estimate the deposition of inhaled particles in the pulmonary acinus to reduce the damage of ambient aerosols or maximize drug particles' efficacy. However, interparticle interactions were always neglected in the simulation of aerosol deposition in human acinus. A four-generation human acinar model with varying sizes of each generation was developed. Two boundary conditions, rigid wall and moving wall were investigated to simulate the effect of wall motion on the flow field and aerosol deposition for the size range of 0.1–5 μm. Results show that wall motion has a net effect on particles' location and deposition, especially for submicron particles. Moreover, interparticle collisions were employed to gain richer aerosol particle dynamics. Results demonstrate that the minimum concentration of particles for coalescence is 8.5 × 104 particles/cm3 in the acinar region. The coalescence of particles is influenced by particle concentration and diameter, and wall motion and has a non-negligible effect on particle deposition. Furthermore, it should be noted that the influence of collision would be more significant during more respiratory cycles. Our findings demonstrate that wall motion and interparticle collisions play a non-negligible role in the aerosol deposition.

Vacuum pressure measurement based on <sup>6</sup>Li cold atoms in a magneto-optical trap

Ultra-high vacuum measurement and extremely high vacuum (UHV/XHV) measurement play an important role in high-tech fields such as deep space exploration, particle accelerators, and nanoscience; with the continuous extension of the lower limit of measurement, especially when it reaches the order of 10<sup>–10</sup> Pa, higher requirements are placed on the accuracy of the measurement. At present, in the field of UHV/XHV measurement, ionization gauges based on the principle of neutral gas ionization are commonly applied to the vacuum measurement. However, traditional ionization vacuum gauges during use can create electronic excitation desorption effects, soft X-rays, and the effect of hot cathode outgassing, thereby affecting the accuracy of measurement and limiting the lower limit of measurement. Compared with the traditional measurement technology, this method uses the relationship between the loss rate and pressure caused by the collision of cold atoms trapped in the trap depth with the background gas to calculate the gas density and inversely calculate the vacuum pressure. Based on the intrinsic quantum mechanical properties of cold atom collisions, this method is expected to be developed into a new vacuum traceability standard. In this paper, based on the small-angle approximation and impulse approximation under the quantum scattering theory, the loss rate coefficient of the collision of <sup>6</sup>Li cold atoms with background gas molecules is calculated. According to the ideal gas equation, the pressure inversion formula is obtained. The collision loss rate is extracted by accurately fitting the loss curve of the cold atom. In order to improve the accuracy of vacuum inversion and reduce the influence of quantum diffractive collision on loss rate measurement, the trap depth under the conditions of a certain cooling laser intensity, detuning, and magnetic field gradient is determined by the photoassociation method. Finally, in a range of 1 × 10<sup>–8</sup>–5 × 10<sup>–6</sup> Pa, the inverted pressure value is compared with the measured value of the ionization meter, proving that this method has good accuracy and reliability in the inversion of vacuum pressure. At present, the main factor restricting the improvement of accuracy is the influence of the collision between the excited atoms in the magneto-optical trap and the background gas on the loss rate measurement. In the future, with the proportion of excited atoms and the excited state <i>C</i><sub>6</sub> coefficient to be precisely determined, the uncertainty of vacuum pressure measurement can be further reduced.

The Development and Application of a Kinetic Theory for Modeling Dispersed Particle Flows

Abstract This Freeman Scholar article reviews the formulation and application of a kinetic theory for modeling the transport and dispersion of small particles in turbulent gas-flows. The theory has been developed and refined by numerous authors and now forms a rational basis for modeling complex particle laden flows. The formalism and methodology of this approach are discussed and the choice of closure of the kinetic equations involved ensures realizability and well posedness with exact closure for Gaussian carrier flow fields. The historical development is presented and how single-particle kinetic equations resolve the problem of closure of the transport equations for particle mass, momentum, and kinetic energy/stress (the so-called continuum equations) and the treatment of the dispersed phase as a fluid. The mass fluxes associated with the turbulent aerodynamic driving forces and interfacial stresses are shown to be both dispersive and convective in inhomogeneous turbulence with implications for the build-up of particles concentration in near wall turbulent boundary layers and particle pair concentration at small separation. It is shown how this approach deals with the natural wall boundary conditions for a flowing particle suspension and examples are given of partially absorbing surfaces with particle scattering and gravitational settling; how this approach has revealed the existence of contra gradient diffusion in a developing shear flow and the influence of the turbulence on gravitational settling (the Maxey effect). Particular consideration is given to the general problem of particle transport and deposition in turbulent boundary layers including particle resuspension. Finally, the application of a particle pair formulation for both monodisperse and bidisperse particle flows is reviewed where the differences between the two are compared through the influence of collisions on the particle continuum equations and the particle collision kernel for the clustering of particles and the degree of random uncorrelated motion (RUM) at the small scales of the turbulence. The inclusion of bidisperse particle suspensions implies the application to polydisperse flows and the evolution of particle size distribution.

Influence of Collisions with Hydrogen Atoms on Non-LTE Effects for K I and Ca II in Stellar Atmospheres

We have constructed a new K I model atom using currently available atomic data. We have performed calculations for K I by abandoning the assumption of local thermodynamic equilibrium (non-LTE) for the Sun and three moderately metal-poor dwarf stars. To take into account the inelastic processes in collisions with hydrogen atoms, for the first time we have used the rate constants calculated by including the fine structure of K I levels and analyzed the influence of their application on the non-LTE results compared to the use of the rate constants calculated for combined levels. In agreement with the non-LTE studies available in the literature, K I is subject to overrecombination, which leads to a strengthening of spectral lines and negative abundance corrections. The non-LTE effects are shown to weaken when using new collisional data. We reached the same conclusion when comparing the non-LTE corrections calculated for the Ca II 8662 A line in model atmospheres with $$\textrm{[Fe/H]}={-}4.5$$ using the Ca II $$+$$ H I collision rates derived with and without allowance for the fine structure of Ca II levels. However, the effect is very small for the other two triplet lines, Ca II 8498 and 8542 A. The solar non-LTE abundance $$\log\varepsilon_{\textrm{K}}=5.09\pm 0.08$$ derived from five lines is consistent with the meteoritic one within 0.01 dex. Despite the fact that in the atmospheres of the program stars the departures from LTE are larger than those in the Sun, the differential abundance [K/H] is almost independent of which collisional data set is used: the one calculated with or without allowance for the fine structure of K I levels.

The influence of collisions and thermal escape in Callisto's atmosphere

A molecular kinetic method is applied to simulate intermolecular collisions and thermal escape in single and multi-component Callisto-like atmospheres. The 1D atmospheres at noon and midnight are composed of radiolytically produced volatiles (CO2, O2, H2) which are assumed to permeate the regolith and thermally desorb. The escaping H2 is shown to have a critical effect on the atmosphere as it is the dominant collision partner, it cools the background gases producing non-isothermal profiles, and its diffusion through the O2 and CO2 affects the vertical structure. Therefore, at the densities inferred from observations, molecular collisions must be included when describing the structure of and escape from Callisto's atmosphere.

Influence of Collisions with Hydrogen on Titanium Abundance Determinations in Cool Stars

We performed the non-local thermodynamic equilibrium (non-LTE) calculations for Ti I-II with the updated model atom that includes quantum-mechanical rate coefficients for inelastic collisions with hydrogen atoms. We have calculated for the first time the rate coefficients for bound-bound transitions in inelastic collisions of titanium atoms and ions with hydrogen atoms and for the charge-exchange processes: Ti I + H <-> Ti II + H- and Ti II + H <-> Ti III + H-. The influence of these data on non-LTE abundance determinations has been tested for the Sun and four metal-poor stars. For Ti I and Ti II, the application of the derived rate coefficients has led to an increase in the departures from LTE and an increase in the titanium abundance compared to that, obtained with approximate formulas for the rate coefficients. In metal-poor stars, we have failed to achieve consistent non-LTE abundances from lines of two ionization stages. The known in the literature discrepancy in the non-LTE abundances from Ti I and Ti II lines in metal-poor stars cannot be solved by improvement of the rates of inelastic processes in collisions with hydrogen atoms in non-LTE calculations with classical model atmospheres.

Sandstone-Shale Geochemistry of Miocene Surma Group in Bandarban Anticline, SE Bangladesh: Implications for Provenance, Weathering, and Tectonic Setting

The present study analyzes the geochemical composition of sandstone and shale of the Miocene Surma Group to decipher the provenance, tectonic settings and paleoweathering condition of source area in the Bandarban Anticline which is at the western margin of Indo-Burmese Hill Ranges. Statistical empirical index of chemical weathering of the sediments that have been extracted by the Principal Component Analysis (PCA) is used to understand the weathering profile of the sediments of the study area. The PCA of the geochemical composition yields three principal components (PC–1, PC–2, and PC–3), which capture total variance 52.83%, 17.58% and 6.94%, respectively. The PC–1 shows the loss of SiO₂ during weathering of preexisting source rocks; PC–2 reveals the enrichment of Na₂O, CaO, and P₂O₅ due to leeching and carried by groundwater during weathering; highest loadings with MnO and Cr shows in PC–3 due to redox environment during early diagenetic of marine sediments. The MFW and A–CN–K diagrams show an intense weathering trend, and backward trend of the MFW diagram and the major elements provenance discriminant diagram refers to the mature polycyclic quartzes provenance and originated dominantly from felsic to intermediate igneous rocks. The trend of the SiO₂/Al₂O₃–Na₂O/K₂O shows the hydraulic sorting effect and sediments were originated primarily from a recycled sedimentary provenance. The CIA (67.68–80.89), ICV (0.60–1.29, avg. 0.83) and K₂O/Na₂O ratios show a moderate to high maturity of the sediments and is derived from both weak and intensively weathered source rocks. Discriminate diagrams related to tectonic provenance refer to the deposit of the sediment dominantly under the influence of collision (active continental collision, compression) and mature sediment derived to the depositional basin after upliftment of the source areas after that collision.

The effect of drill\u2013pipe rotation on improving hole cleaning using polypropylene beads in water-based mud at different hole angles

Hole cleaning is always a problem, particularly during drilling operations, and drilling fluid plays an important role in transporting drill cuttings through an annular section of wellbore to the surface. To transport the cuttings, a water-based mud with added polypropylene beads was selected since it is environmentally friendly and cost efficient. The polypropylene beads help to transport cuttings by providing an additional buoyancy force that lifts the cuttings to the surface via the influence of collision and drag forces. This experiment was performed using a 20 ft test section, 10 ppg drilling mud and 0.86 m/s annular velocity in a laboratory scale rig simulator, and the concentration of polypropylene beads was varied from 0 to 8 ppb. As the concentration of polypropylene increases, the cutting transport ratio also increases. It was observed that the fewest cuttings are lifted at a critical angle of 60°, followed by 45°, 30°, 90° and 0°. Additionally, cutting sizes had moderate effects on the cutting lifting efficiency, where smaller cutting sizes (0.5–1.0 mm) are easier to lift than larger cutting sizes (2.0–2.8 mm). Furthermore, a study of buoyancy force and impulsive force was conducted to investigate the cutting lifting efficiencies of various concentrations of polypropylene beads. This lifting capacity was also assisted by the presence of polyanionic cellulose (PAC), which increases the mud carrying capacity and is effective for smaller cuttings. The results show that in the presence of pipe rotation, the cutting lifting efficiency is slightly enhanced due to the orbital motion provided by the drill pipe for better hole cleaning. In conclusion, polypropylene beads combined with pipe rotation increase the cutting transport ratio in the wellbore.

Influence of collisions in a fluid model for the warm-ion sheath around a cylindrical Langmuir probe

A long cylindrical Langmuir probe immersed in a collisional plasma is modelled by using fluid equations in which the collision term is introduced assuming a constant ion mean free path. The physical magnitudes of the system are expanded in a perturbation series in the collision parameter, that is, the ratio between the Debye length and the ion mean free path, and the system is thus separated into zeroth-order and first-order perturbation systems. The ion temperature is arbitrary and a continuous solution from the plasma to the probe is obtained for the perturbation systems. Using this methodology, a continuous solution for the ion sheath around a cylindrical Langmuir probe is obtained for long ion mean free path, for any ion temperature with no need of two-scale study or asymptotic matching. It is found that the collisions and the ion temperature have opposite effects, and these effects are quantified. The solution for cold ions cannot be obtained directly using this method, but it can be recovered from the warm-ion solution. The methodology is usable for long cylindrical probes in which the scale of the probe is much higher than the scale of the sheath, so that the geometry is essentially cylindrical. The model is numerically solved to obtain the potential profile, the ion temperature profile, the ion density profile and the ion velocity profile, and the dependence of the sheath on the ion mean free path and the ion temperature is studied. The ion-current to probe-potential profiles for different probe radius are obtained. Finally, the Sonin plot is calculated, in order to use the solution in plasma diagnosis.

Crustal structure from onshore-offshore wide-angle seismic data: Application to Northern Sulu Orogen and its adjacent area

The Northern Sulu Orogen is the northeastern part of the Dabie-Sulu Orogen, which formed during the Triassic collision between the North China Block (NCB) and the South China Block (SCB). The lack of detail in the onshore-offshore seismic model in the crustal levels means that the deep boundaries and subduction polarity of the Northern Sulu Orogen remain ambiguous. To obtain insight into the contact relationship between the NCB and SCB and their tectonic implication, we processed the onshore-offshore wide-angle seismic data from 32 sections that were acquired in 2013 in order to achieve a continuous 2-D velocity and interface model. The results show that three parts exhibit significant differences in the P-wave velocities, interface depths and intra-crustal structures, which all correlate well with the regional geology and tectonics. In the northern and southern parts of the survey area, the upper crust displays low-velocity layers that represent the NCB and the SCB, respectively. The Northern Sulu Orogen is characterized by the relatively faster p-waves, which result from the influence of collision and exhumation. The undulating interfaces together reveal that the southern and northern boundaries of the Northern Sulu Orogen are deep faults that deeply cut through the Moho and have northwest dips in the middle and lower crust. The different crustal nature of three regions suggests that the NCB and SCB crusts have different responses to the continental collision. Our observations, combined with data from previous studies, support that the Northern Sulu Orogen developed during the Indosinian Orogeny, with a northward subduction polarity of the SCB beneath the NCB.

Influence of collisions on ion dynamics in the inner comae of four comets.

Collisions between cometary neutrals in the inner coma of a comet and cometary ions that have been picked up into the solar wind flow and return to the coma lead to the formation of a broad inner boundary known as a collisionopause. This boundary is produced by a combination of charge transfer and chemical reactions, both of which are important at the location of the collisionopause boundary. Four spacecraft measured ion densities and velocities in the inner region of comets, exploring the part of the coma where an ion-neutral collisionopause boundary is expected to form. The aims are to determine the dominant physics behind the formation of the ion-neutral collisionopause and to evaluate where this boundary has been observed by spacecraft. We evaluated observations from three spacecraft at four different comets to determine if a collisionopause boundary was observed based on the reported ion velocities. We compared the measured location of the ion-neutral collisionopause with measurements of the collision cross sections to evaluate whether chemistry or charge exchange are more important at the location where the collisionopause is observed. Based on measurements of the cross sections for charge transfer and for chemical reactions, the boundary observed by Rosetta appears to be the location where chemistry becomes the more probable result of a collision between H2O and H2O+ than charge exchange. Comparisons with ion observations made by Deep Space 1 at 19P/Borrelly and Giotto at 1P/Halley and 26P/Grigg-Skjellerup show that similar boundaries were observed at 19P/Borrelly and 1P/Halley. The ion composition measurements made by Giotto at Halley confirm that chemistry becomes more important inside of this boundary and that electron-ion dissociative recombination is a driver for the reported ion pileup boundary.

Indirect Influence of Humidity on Atmospheric Spectra Near 4 μm

AbstractWe give the first demonstration that humidity has indirect effects on atmospheric spectra near 4 μm, through the influence of collisions with H2O on both the collision‐induced band of N2 and the wings of the CO2 lines. This is shown by comparing computed and measured values of atmospheric transmissions and outgoing radiances. The usual assumption that collisions with H2O and dry air have equal effect on the N2 and CO2 absorptions leads to significantly underestimated absorptions for humid atmospheres. This bias is considerably reduced when the influences of H2O on the N2 and CO2 contributions to the spectra are taken into account using proper spectroscopic models. This opens perspectives of increased accuracy near 4 μm where the atmosphere is relatively transparent, for astronomical observations of outer objects from ground as well as for retrievals of the Earth land/sea surface temperatures from radiances recorded from space.

Strong decay modes of warm space-charge waves in thermal plasma waveguides

The strong collisional decay modes of warm space-charge waves are derived in a thermal plasma waveguide composed of warm collisional electrons and cold ions. The kinetic theory is applied to obtain the dispersion relation of the space-charge wave. In addition, the analytic expressions of the real part and the damping rate of the wave frequency are obtained for a plasma waveguide including the influence of collision and geometric configuration. It is found that the space-charge wave has the strong decay mode in small wave numbers. In these decay modes, the damping rate increases with an increase of the collision frequency and decreases with an increase of the order of the root of the Bessel function. It is found that the damping rate of the space-charge wave increases with an increase of the radius of the plasma waveguide. It is also found that the space-charge wave is always highly damped in the propagation domain. In addition, the influence of geometric configuration on the damping rate is found to be much significant in high-harmonic cases.

Theory of Electromagnetic Surface Waves in Plasma with Smooth Boundaries

A theory of nonpotential surface waves in plasma with smooth boundaries is developed. The complex frequencies of surface waves for plasma systems of different geometries and different profiles of the plasma density are calculated. Expressions for the rates of collisionless damping of surface waves due to their resonance interaction with local plasma waves of continuous spectrum are obtained. The influence of collisions in plasma is also considered.

Ion temperature gradient turbulence close to the finite heat flux threshold

The dependence of the heat flux on the temperature gradient length in collisionless ion temperature gradient turbulence has recently been revisited. It has been found that the heat flux is discontinuous at a finite heat flux threshold larger than the (Dimits) interpolated threshold. In this paper, the influence of collisions on the heat flux close to the threshold is investigated. It is found that up to relatively high collision frequencies, relevant to the modern day experiments, a discontinuous behaviour of the heat flux as a function of the gradient length persists. Collisions, however, do lead to a reduction in the gradient length at which the discontinuity is observed. Below the finite heat flux threshold, a state of low turbulence with a vanishing small heat flux persists, which can drive the zonal flow against the collisional dissipation. This state is characterised by the fully developed staircases in the radial ExB shearing profile. Increasing the collision frequency at a fixed gradient length leads to the loss of the fully developed staircase structure with the ExB shearing profile having the form of a sawtooth that allows for avalanche formation and a finite heat flux. At very high collision frequencies or gradient lengths well above the threshold the staircase structure is lost. The simulations indicate that the long wave length zonal flow saturates through a mechanism that directly involves the turbulence intensity.