Gradient Scale Length Research Articles

Simulation of Toroidal Rotation Effect on Heat Flux Transport in the Edge Plasma of Small Size Divertor Tokamak

The effect of toroidal rotation on heat flux transport in the edge plasma of small size divertor was simulated by B2SOLP0.5.2D transport code. The main results of simulation shows that, the following: (1) the radial heat flux is strongly influenced by toroidal rotation. (2) The amplification of conduction part of radial heat flux imposes nonresilient profile of ion temperature, under which the effect of toroidal rotation on ion temperature profile is strong. (3) The ion distribution and its gradients are lower for counter-injection neutral beam than for co-injection neutral beam. (4) Reversal of toroidal rotation during using neutral beam injection result in reverses of radial electric field and E × B drift velocity. (5) The toroidal rotation strong influence on the ion temperature scale length of the ion temperature gradient (ITG). (6) Switch on and off all drifts leads to higher change in the ion density distribution in edge plasma of small size divertor tokamak when the unbalance neutral beam injection are considered (7) the comparison between radial heat flux at different momentum input shows that, the radial ion heat flux with larger ion temperature scale length in the case of co-injection neutral beam is larger than the ion heat flux with smaller ion temperature scale length in the case of counter-injection neutral beam.

Experimental production and identification of electron temperature gradient modes

The electron temperature gradient (ETG) mode, which is believed to be one of the strongest candidates for the anomalous electron energy transport in plasmas, is difficult to detect in experiments because of its high frequency (∼MHz) and short wavelength (k⊥ρe≤1). Using a dc bias heating scheme of the core plasma, we are able to produce a sufficiently strong ETG for exciting ETG modes in the Columbia linear machine [R. Scarmozzino, A. K. Sen, and G. A. Navratil, Phys. Fluids 31, 1773 (1988)]. A high frequency mode at ∼2 MHz, with azimuthal wave numbers m∼14–16 and parallel wave number k∥∼0.01 cm−1, has been observed. The frequency range is consistent with the result of a kinetic dispersion relation of slab ETG modes with appropriate E⃑×B⃑ Doppler shift. The scaling of its fluctuation level with the temperature gradient scale length and the radial structure are found to be roughly consistent with theoretical expectations. Therefore, this is one of the first direct definitive identifications of ETG modes.

Statistical characterization of blob turbulence across the separatrix in HL-2A tokamak

Blob statistical characteristics across the separatrix of HL-2A tokamak plasma have been studied using a reciprocating Langmuir five-probe array. The radial profile of inverse pressure gradient scale length has a maximum just inside the last closed flux surface (LCFS), where the skewness is close to zero. Conditional average reveals that the density holes and blobs are produced just inside the LCFS and they propagate in opposite directions. The poloidal velocity of blobs changes its sign when it is across the separatrix, which is consistent with E × B drift flow. The dramatic change in phase shift between density and potential fluctuations across the separatrix suggests the distinct properties of turbulence when the magnetic field line changes from a closed to an open one. The dependence of a weak three-wave interaction in terms of wavelet bicoherence on strong time-asymmetry blobs is observed for the first time. Moreover, the effective blob generation rate is estimated as 8.0 × 103 s−1 and the convective particle flux induced by the ejective blobs can lead to about 58% loss of radial particle flux.

Numerical Diagnostics of the Electrostatic Potential Perturbed by Magnetic Islands

Nonlinear dynamics of a magnetic island is simulated using a set of reduced two-fluid equations, and the excitation of the electric field in the vicinity of the magnetic island is observed. An impact of the error field (external symmetry-breaking magnetic perturbation) on the electric field is examined, and its global structure changes with a small error field. A numerical measurement simulating the heavy ion beam probe is carried out on the field given by the nonlinear simulation. An effect of the finite width of the injected beam is taken into account, and the spatial resolution is evaluated. It is found that the measuring error due to the finite beam width is significant when the radial gradient scale length of the electrostatic potential is comparable to the beam width.

The seasonal and solar cycle variations of electron density gradient scale length, vertical drift and layer height during magnetically quiet days: Implications for Spread F over Trivandrum, India

Abstract A study has been carried out on the behaviour of electron density gradient scale length, L, vertical drift and layer height, around post sunset hours, during the magnetically quiet days of summer, winter and equinox seasons of solar maximum (2002) and minimum years (1995), using ionosonde data of Trivandrum (8.5°N, 76.5°E, dip = 0.5°N) in the Indian longitude sector. The results indicate a clear seasonal and solar cycle variation in all the three parameters. Further, the seasonal variation of equatorial Spread F (ESF) during the above period is examined in terms of the relative roles of L, the vertical drift and layer height (of the F layer) in the triggering of the collisional Rayleigh-Taylor instability. The results, show for the first time, that L also plays an important role, in controlling the quiet time seasonal and solar cycle variability of ESF; whereas in earlier studies this parameter had been taken to be constant. The detailed results are presented and discussed.

Electric field and ionization-gradient effects on inertial-confinement-fusion implosions

The generation of strong, self-generated electric fields (108–109 V m−1) in direct-drive, inertial-confinement-fusion capsules has been reported (Li et al 2008 Phys. Rev. Lett. 100 225001). Various models are considered herein to explain the observed electric field evolution, including the potential roles of electron pressure gradients near the fuel–pusher interface and plasma polarization effects that are predicted to occur across shock fronts (Zel'dovich and Raizer 2002 Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena (Mineola, NY: Dover) p 522). In the latter case, strong fields in excess of 1010 V m−1 and localized to 10–100 nm may be consistent with the data obtained from proton radiography. Such field strengths are similar in magnitude to the criterion for runaway electron generation that could lead to plasma kinetic effects and potential shock-front broadening. The observed electric field generation may also be partly due to plasma ionization gradients localized near the fuel–pusher interface. A model is proposed that allows for differing electron- and ion-density gradient scale lengths in the presence of ionization gradients while preserving overall charge neutrality. Such a redistribution of electrons compared with standard, charge-neutral, single-fluid radiation-hydrodynamics modelling may affect the interpretation of imploded-core x-ray diagnostics as well as alter alpha particle deposition in the thermonuclear fuel.

Overview of results from the National Spherical Torus Experiment (NSTX)

The mission of the National Spherical Torus Experiment (NSTX) is the demonstration of the physics basis required to extrapolate to the next steps for the spherical torus (ST), such as a plasma facing component test facility (NHTX) or an ST based component test facility (ST-CTF), and to support ITER. Key issues for the ST are transport, and steady state high β operation. To better understand electron transport, a new high-k scattering diagnostic was used extensively to investigate electron gyro-scale fluctuations with varying electron temperature gradient scale length. Results from n = 3 braking studies are consistent with the flow shear dependence of ion transport. New results from electron Bernstein wave emission measurements from plasmas with lithium wall coating applied indicate transmission efficiencies near 70% in H-mode as a result of reduced collisionality. Improved coupling of high harmonic fast-waves has been achieved by reducing the edge density relative to the critical density for surface wave coupling. In order to achieve high bootstrap current fraction, future ST designs envision running at very high elongation. Plasmas have been maintained on NSTX at very low internal inductance li ∼ 0.4 with strong shaping (κ ∼ 2.7, δ ∼ 0.8) with βN approaching the with-wall β-limit for several energy confinement times. By operating at lower collisionality in this regime, NSTX has achieved record non-inductive current drive fraction fNI ∼ 71%. Instabilities driven by super-Alfvénic ions will be an important issue for all burning plasmas, including ITER. Fast ions from NBI on NSTX are super-Alfvénic. Linear toroidal Alfvén eigenmode thresholds and appreciable fast ion loss during multi-mode bursts are measured and these results are compared with theory. The impact of n > 1 error fields on stability is an important result for ITER. Resistive wall mode/resonant field amplification feedback combined with n = 3 error field control was used on NSTX to maintain plasma rotation with β above the no-wall limit. Other highlights are results of lithium coating experiments, momentum confinement studies, scrape-off layer width scaling, demonstration of divertor heat load mitigation in strongly shaped plasmas and coupling of coaxial helicity injection plasmas to ohmic heating ramp-up. These results advance the ST towards next step fusion energy devices such as NHTX and ST-CTF.

Mechanics of strain gradient plasticity with particular reference to decomposition of the state variables into energetic and dissipative components

The results of recent studies on strengthening and hardening mechanisms for micro/nano structured materials indicate that the use of only one type of energetic or dissipative description may be insufficient to accurately describe the size effects exhibited in metallic components. Therefore, it is important to incorporate more than one description of the thermodynamic processes into the modeling in order to have a better understanding of the hardening and strengthening mechanisms for micro/nano structured materials. The research presented here is based on this deficiency and the goal is to develop a strain gradient theory based on the decomposition of the state variables into energetic and dissipative components. This, in turn, endowed the constitutive equations to have both energetic and dissipative gradient length scales ℓ en and ℓ dis , respectively. The effect of the material microstructural interface between two materials is also incorporated into the proposed formulation. Hence four material length scales are introduced: two for the bulk and the other two for the interface. The resulting formulation exhibits the following important physical phenomena: (i) standard energetic hardening associated with plastic strain and nonlocal energetic hardening associated with plastic strain gradients; (ii) size dependent increase in yield strength which is characterized by the dissipative strengthening associated with plastic strain gradient rate; (iii) the effect of interfacial yield strength and hardening; (iv) description of the boundary layer; and (v) the effect of the different boundary conditions. The problem is solved analytically by using for example, a thin film on elastic substrate under uniaxial uniform tension or a single phase bicrystal under uniform tension where the interface represents the grain boundary. The interface model here describes the internal boundary of the plastic region and characterizes the physical understanding of the dislocation mechanics at the interface between two phases. The results of the analytical results indicate that the proposed theory qualitatively captures the overall physical behavior. However there is strong debate in the literature on the choice of accurate physical boundary conditions at the elastic plastic boundaries. Therefore, more elaborate studies are needed for better assessment of the boundary conditions of the higher-order strain gradient plasticity theories.

The seasonal and solar cycle variations of electron density gradient scale length during magnetically disturbed days: implications for Spread F

Abstract The behaviour of electron density gradient scale length, L, around post-sunset hours during the magnetically disturbed days of the summer, winter and equinox seasons of solar maximum (2002) and minimum years (1995) has been studied, using ionosonde data of Trivandrum (8.5°N, 76.5°E, dip = 0.5°N) in the Indian longitude sector. The results indicate a clear seasonal and solar cycle variation in L. Seasonal variations of the maximum vertical drift of the F layer were also examined on these days. In particular, the seasonal variation of the Equatorial Spread F (ESF) during this period is examined in terms of the relative roles of L and the vertical drift of the F layer in the triggering of the collisional Rayleigh-Taylor instability. Our results on the clear-cut seasonal and solar cycle variation in L for disturbed days and its control of ESF occurrence are presented and discussed.

Plasma elongation effects on temperature gradient driven instabilities and geodesic acoustic modes

Plasma shaping effects on temperature gradient driven instabilities and geodesic acoustic oscillations are investigated with gyrokinetic theory and a local magnetohydrodynamic equilibrium model. In particular, we focus on the effect of the elongation κ, including its radial derivative sκ = (r/κ)(∂κ/∂r), in the large aspect ratio limit. An analytical formula of the dependence of the geodesic acoustic mode (GAM) frequency on the elongation is given. It is found that the GAM frequency sharply decreases with increasing elongation by the dependence of [(2 − αsκ)/(κ2 + 1)]1/2 with α = 0.5–1, which comes from the modification of ion classical polarization balanced by that of curvature drift polarization. The dependence of the critical threshold of the ETG/ITG instability on the elongation is numerically studied and a semi-analytical formula is given as (R0/LTc)/(R0/LTc)sκ=0,κ=1 = (1 + 0.36sκ)[1 + 0.11(κ − 1)], where R0 is the major radius and LTc is the critical scale length of the temperature gradient.

An equation of motion for particles of finite Reynolds number and size

In order to simulate the motion of bubbles, drops, and particles, it is often important to consider finite Reynolds number effects on drag, lift, torque, and history force. Herein, an equation of motion is developed for spherical particles with a no-slip surface based on theoretical analysis, experimental data, and surface-resolved simulations. The equation of motion is then extended to account for finite particle size. This extension is critical for particles which will have a size significantly larger than the grid cell size, particularly important for bubbles, and low-density particles. The extension to finite particle size is accomplished through spatial-averaging (both volume-based and surface-based) of the continuous flow properties. This averaging is consistent with the Faxen limit for solid spheres at small Reynolds numbers and added mass and fluid stress forces at inviscid limits. The finite Re p corrections are shown to have good agreements with experiments and resolved-surface simulations. The finite size corrections are generally fourth-order accurate and an order of magnitude more accurate than point-force expressions (which neglect quadratic and higher spatial gradients) for particles with size on the order of the gradient length-scales. However, further work is needed for more quantitative assessment of the truncation terms and the overall model robustness and accuracy in complex flows.

Role of stable eigenmodes in gyrokinetic models of ion temperature gradient turbulence

Investigation of ion temperature gradient turbulence in gyrokinetic models shows that some of the key features of reduced models associated with saturation by nonlinearly excited damped eigenmodes carry over to gyrokinetics. For nonzonal wavenumbers the frequency spectrum in gyrokinetics is broader by a factor of 10 than simple nonlinear broadening of the most unstable eigenmode. The width, including its variations with wavenumber and temperature gradient scale length, closely tracks accessible stable eigenmodes as approximated by a gyro-Landau fluid model for the same parameters. Cross-phase probability distribution functions (pdfs) and fluxes show nonlinear behavior consistent with stable eigenmodes in nonzonal wavenumbers contributing to 30% of the fluctuation energy. Phase pdfs and cross-phase time histories show that multiple eigenmodes [in addition to high frequency geodesic acoustic modes (GAMs)] are a significant part of the ky=0 spectrum. Two possible roles of zonal modes in saturation are proposed. First, known nonlinearly accessible stable zonal eigenmodes (in addition to zonal flows and GAMs) are discussed and it is suggested that if these eigenmodes are excited they may be the primary arbiter of saturation. Second, zonal modes may facilitate energy transfer from unstable eigenmodes to stable eigenmodes at finite ky.

Campaign Investigation of Ionospheric Plasma Irregularities in Sporadic E Region Using FORMOSAT-3/COSMIC Satellite and Chung-Li 30 MHz Coherent Radar

In this article, we present an electron density profile retrieved from total electron density estimated from the difference in phase path excess between GPS frequencies L1 and L2 measured by the FORMOSAT-3/COSMIC satellite, in which the radio occultation inversion technique is employed for retrieval. Except for a regular F layer peak located at a height of about 290 km and a minor peak centered at a height of 140 km, a pronounced sporadic E layer was observed at a height of about 105 km. This intense electron density layer with thickness of about 10 km has very sharp boundaries on the top and bottom sides with scale lengths of -22 and 13 km, respectively. At the time when COSMIC GPS radio occultation took place in the vicinity of Taiwan, the Chung-Li 30 MHz coherent radar detected strong backscatter from 5-meter plasma irregularities. The peak radar backscatter is situated at a height of about 110 km in the topside of the Es layer with a very steep electron density gradient. Interferometry measurement made by the four separate and independent receiving channels of the Chung-Li 30 MHz radar indicates that the configuration of the large scale plasma structure constituted by 5-meter scale field-aligned irregularities is patch-like, and a 2-minute oscillation in zonal displacement of the plasma structure was found. From the temporal displacement of the echo patterns from the plasma irregularities in the bottom side of the layer, the plasma structure in the bottom side of the Es layer was found to move westward at a trace velocity of about 6.2 m s^(-1). The exceedingly small drift velocity combined with the relatively large scale length of the electron density gradient seem to suggest that the 5-meter plasma irregularities are very unlikely generated through the non-linear cascade process of the large plasma structure at kilometer scale induced by gradient drift instability. Moreover, in light of the fact that both the observed drift velocity (less than 15 m s^(-1)) of the kilometer-meter scale plasma wave and the measured Doppler velocity (about 50 m s^(-1)) of the 5-m plasma irregularities are much smaller than the 280 m s^(-1) that is required to directly excite plasma waves through gradient drift instability, it suggests that the 5-m plasma irregularities observed by the Chung-Li 30 MHz radar are very unlikely the result of direct excitation through gradient drift instability.

Gyrokinetic microinstabilities in ASDEX Upgrade edge plasmas

Results of linear gyrokinetic simulations of ASDEX Upgrade [O. Gruber et al., Nucl. Fusion 39, 1321 (1999)] edge plasmas, with experimentally determined geometry and input parameters, are presented. It is found that in the near-edge region, microtearing modes can exist under conditions found in conventional tokamaks. As one enters the steep-gradient region, the growth rate spectrum is dominated—down to very low wavenumbers—by electron temperature gradient modes. The latter tend to peak near the X-point(s) and possess properties which may explain the ratios of the density and temperature gradient scale lengths that have been observed in various experiments over the last decade.

Dependence of heat transport on toroidal rotation in conventional H-modes in JT-60U

The relation between heat transport in the plasma core and the toroidal rotation profile was examined in conventional ELMy H-mode plasmas in JT-60U. Heat transport in the plasma core is not strongly influenced locally by toroidal rotation. The large increase in heat conduction imposes a resilient profile of ion temperature, under which the local effect of the toroidal rotation profile on scale length of the ion temperature gradient is very weak. Energy confinement improvement is observed with toroidal rotation which increases in the co-direction with respect to the plasma current. In this case, the increase in the ion temperature in both the plasma core and the pedestal region is observed. However, heat transport in the plasma core varies while maintaining self-similar temperature profiles as the toroidal rotation profile is varied. Pressure at the H-mode pedestal becomes slightly larger with the toroidal rotation in the co-direction. Thus, energy confinement enhanced with co-toroidal rotation is determined by increased pedestal height and reduced transport brought on by profile resilience. When pedestal temperature was fixed between the cases of co- and counter-NBI by adjusting the plasma density, identical temperature profiles were obtained in spite of totally different toroidal rotation profiles.

Crack Initiation in Functionally Graded Materials Under Mixed Mode Loading: Experiments and Simulations

In this work, quasistatic crack initiation under mixed mode loading in planar (two-dimensional plane stress) functionally graded materials (FGMs) is studied. The goal of this work is to directly compare experiments and simulations so as to evaluate the applicability of the maximum tangential stress (MTS) criterion in predicting crack kinking in FGMs. Initially, crack initiation in the homogeneous material, which forms the basis of our FGM—polyethylene—is studied. The (generalized) maximum tangential stress is applied through the use of finite elements to determine crack initiation angles in the same graded configurations studied experimentally. Computational results of fracture parameters (stress intensity factors and T-stress), and crack initiation angles are compared to experimental results and good agreement is obtained. It is seen that the MTS criterion is applicable to FGM crack initiation prediction if the inherent material gradient length scale is larger than the fracture process zone.

Fluid model for relativistic, magnetized plasmas

Many astrophysical plasmas and some laboratory plasmas are relativistic: Either the thermal speed or the local bulk flow in some frame approaches the speed of light. Often, such plasmas are magnetized in the sense that the Larmor radius is smaller than any gradient scale length of interest. Conventionally, relativistic magnetohydrodynamics (MHD) is employed to treat relativistic, magnetized plasmas. However, MHD requires the collision time to be shorter than any other time scale in the system. Thus, MHD employs the thermodynamic equilibrium form of the stress tensor, neglecting pressure anisotropy and heat flow parallel to the magnetic field. Recent work has attempted to remedy these shortcomings. This paper re-examines the closure question and finds a more complete theory, which yields a more physical and self-consistent closure. Beginning with exact moments of the kinetic equation, we derive a closed set of Lorentz-covariant fluid equations for a magnetized plasma allowing for pressure and heat flow anisotropy. Basic predictions of the model, especially of the dispersion relation’s dependence upon relativistic temperature, are examined.

Modes and characteristics of low‐frequency MHD waves in the near‐Earth magnetotail prior to dipolarization: Fitting method

Spacecraft observations indicate that low‐frequency (0.006–0.025 Hz) fluctuations of the magnetic field appear a few min prior to a substorm‐associated dipolarization. These fluctuations are examined on the basis of the linear magnetohydrodynamic (MHD) fluid theory. We propose a “low‐frequency fitting method” for identifying the characteristics of the MHD waves, such as the mode, the wavevector, and the frequency. Using the magnetic field and the ion velocity data, the frequency in the plasma rest frame is obtained by removing the Doppler shift. The fitting method takes the inhomogeneity of the ambient magnetic field into account, so that the parameter which is equivalent to the sum of the field line curvature and the gradient scale length of the ambient magnetic field is obtained as an output. We applied the method to a selected dipolarization event in which Geotail remained in the vicinity of the magnetic equator and also in the same magnetic local time as the onset region of an auroral breakup. The low‐frequency fluctuations were detected from ∼4 min before the local dipolarization onset. What has been found are as follows: (1) the parallel magnetic field fluctuations had a strong correlation with the perpendicular ion velocity fluctuations, which indicates that the observed waves were explained as magnetosonic modes. The slow magnetosonic wave was identified ∼3 min before the dipolarization onset, whereas the fast magnetosonic wave was identified ∼1.5 min before the dipolarization onset. This fast wave was estimated to be propagating tailward with a phase velocity of 400 km/s and a period of 70 s in the plasma frame. (2) The perpendicular fluctuations of the magnetic field and the ion velocity were only weakly correlated, which indicates the presence of a mode that cannot be captured by the present method. Using the variance analysis, we show that this mode is likely to be a drift mode, which had almost zero frequency in the plasma frame and was propagating duskward together with the plasma bulk flow. A possible interpretation of the observed waves is briefly discussed with a relevance to previously proposed substorm initiation models. Particularly, the drift wave can be interpreted as a linear stage of the ballooning instability.

Laser-acceleration of high-energy protons in small-scale gradients

The parameters of proton beams accelerated by a high-intensity short pulse laser from a thin foil are studied for various small plasma gradients created on the rear-surface of the foil. Compared to the case of an initially cold foil, the proton beam maximum energy as well as the beam spectral slope reduce steadily when increasing the gradient scale length. The measurements are in good agreement with simulations. For future ion-driven Fast Ignition of fusion targets, multi-kJ Peta Watt laser pulses will induce target preheat due to the leading part of the laser pulse. Estimates of such preheat in these conditions suggest that it should modify by less than 10 % the ion beam parameters compared to the case of a unheated target.

VELOCITY SHEAR ION-CYCLOTRON INSTABILITY WITH PERPENDICULAR AC ELECTRIC FIELD

Current driven electrostatic ion cyclotron instability has been studied for parallel flowvelocity shear w ith perpendicular a.c. electric field to the ambient magnetic field for bi-Maxwellian density drift distribution function. The method adopted for expression for dispersion relation and growth rate is kinetic approach and method of characteristic solution for ionospheric plasma. The effect of a.c. frequency, density gradient, and velocity shear scale length has been discussed.