Inverse Aspect Ratio Research Articles

Fast reconnection in relativistic plasmas: the magnetohydrodynamics tearing instability revisited

Fast reconnection operating in magnetically dominated plasmas is often invoked in models for magnetar giant flares, for magnetic dissipation in pulsar winds, or to explain the gamma-ray flares observed in the Crab nebula, hence its investigation is of paramount importance in high-energy astrophysics. Here we study, by means of two dimensional numerical simulations, the linear phase and the subsequent nonlinear evolution of the tearing instability within the framework of relativistic resistive magnetohydrodynamics, as appropriate in situations where the Alfven velocity approaches the speed of light. It is found that the linear phase of the instability closely matches the analysis in classical MHD, where the growth rate scales with the Lundquist number S as S^-1/2, with the only exception of an enhanced inertial term due to the thermal and magnetic energy contributions. In addition, when thin current sheets of inverse aspect ratio scaling as S^-1/3 are considered, the so-called "ideal" tearing regime is retrieved, with modes growing independently on S and extremely fast, on only a few light crossing times of the sheet length. The overall growth of fluctuations is seen to solely depend on the value of the background Alfven velocity. In the fully nonlinear stage we observe an inverse cascade towards the fundamental mode, with Petschek-type supersonic jets propagating at the external Alfven speed from the X-point, and a fast reconnection rate at the predicted value R~(ln S)^-1.

Numerical Study of Motion and Stability of Falling Columnar Crystals

Abstract Understanding of the flow field and falling patterns of ice crystals is fundamental to cloud physics and radiative transfer, and yet the complex shape hampers a comprehensive understanding. In order to create better understanding of falling patterns of columnar crystals, this study utilizes a computational fluid dynamics package and explicitly simulates the motion as well as the flow fields. Three modes of patterns (i.e., strong damping, fluttering, and unstable modes) were identified in the space of inverse aspect ratio (q) and Reynolds number (Re). The boundary of stability depicts the “L” shape as found in a previous experimental study. This study newly found that the range of Re for stable motion increases with a decrease in q. Decomposition of hydrodynamic torques indicates that, for stable mode, the pressure and viscous torques acting on the lower prism faces counteract the rotation when the inclination angle becomes 0°. The unstable motion was attributed to the pressure torque acting on the upper prism faces, which is associated with eddies that lag behind the oscillating boundary. Observed Re–q relationships of columns suggest that the strong damping mode is most likely to occur in the atmosphere, but the fluttering mode is also possible. Furthermore, the time scales of oscillation and damping were parameterized as a function of q and Re. The impact of the fluttering on the riming process is limited at the beginning, which supports the current formulation in numerical weather and climate models.

Application of MFS–MPS to the current-hole simulation in a Tokamak

A meshless method based on fundamental and particular solutions (MFS–MPS) has been implemented for the current-hole simulation in cylindrical tokamaks. We first benchmark the method by solving the Grad–Shafranov (GS) equation for zero as well as nonzero inverse aspect ratios and noncircular cross-sections. Thereafter, the method is implemented to solve the time-dependent reduced resistive MHD equations for the current-hole simulation. The initial current density profile with a negative current density near the center is chosen and the corresponding equilibrium magnetic flux profile is first computed using the GS equation. These profiles are then used to solve the coupled nonlinear system of MHD equations using MFS–MPS and a semi-implicit time differencing scheme. After an initial linear phase extending up to a few thousand Alfvén times, the nonlinear oscillations are observed which continue for several Alfvén times. This oscillating behavior is in agreement with the previous simulations using other numerical methods. It is also found that these oscillations are damped out at higher resistivity.

Comparison of experiment and models of geodesic acoustic mode frequency and amplitude geometric scaling in ASDEX Upgrade

In a set of dedicated ASDEX Upgrade shape-scan experiments, the influence of plasma geometry on the frequency and amplitude behaviour of the geodesic acoustic mode (GAM), measured by Doppler reflectometry, is studied. In both limiter and divertor configurations, the plasma elongation was varied between circular and highly elongated states (). Also, the edge safety factor was scanned between 3 < q < 5. The GAM frequency and amplitude are used to test several models (heuristic, fluid and gyrokinetic based), which incorporate various plasma geometry effects. The experimentally observed effect of decreasing with increasing κ is predicted by most models. Other geometric factors, such as inverse aspect ratio ε and Shafranov shift gradient are also seen to be influential in determining a reliable lower boundary. The GAM amplitude is found to vary with boundary elongation and safety factor q. The collisional damping is compared to multiple models for the collisionless damping. Collisional damping appears to play a stronger role in the divertor configuration, while collisional and collisionless damping both may contribute to the GAM amplitude in the limiter configuration.

Visco-resistive plasmoid instability

The plasmoid instability in visco-resistive current sheets is analyzed in both the linear and nonlinear regimes. The linear growth rate and the wavenumber are found to scale as S1/4(1+Pm)−5/8 and S3/8(1+Pm)−3/16 with respect to the Lundquist number S and the magnetic Prandtl number Pm. Furthermore, the linear layer width is shown to scale as S−1/8(1+Pm)1/16. The growth of the plasmoids slows down from an exponential growth to an algebraic growth when they enter into the nonlinear regime. In particular, the time-scale of the nonlinear growth of the plasmoids is found to be τNL∼S−3/16(1+Pm)19/32τA,L. The nonlinear growth of the plasmoids is radically different from the linear one, and it is shown to be essential to understand the global current sheet disruption. It is also discussed how the plasmoid instability enables fast magnetic reconnection in visco-resistive plasmas. In particular, it is shown that the recursive plasmoid formation can trigger a collisionless reconnection regime if S≳Lcs(ϵclk)−1(1+Pm)1/2, where Lcs is the half-length of the global current sheet and lk is the relevant kinetic length scale. On the other hand, if the current sheet remains in the collisional regime, the global (time-averaged) reconnection rate is shown to be 〈dψ/dt|X〉≈ϵcvA,uBu(1+Pm)−1/2, where ϵc is the critical inverse aspect ratio of the current sheet, while vA,u and Bu are the Alfvén speed and the magnetic field upstream of the global reconnection layer.

Facile endothelial cell micropatterning induced by reactive oxygen species on polydimethylsiloxane substrates

Sophisticated cell pattern provides unique cellular assay platform for studying cell to cell interaction, cellular differentiation and signaling, high-throughput cell response to chemicals. In this study, we demonstrated reactive oxygen species (ROS) mediated endothelial cell micropatterning on a polydimethylsiloxane (PDMS) substrate. The exposure of UV/O radiation led to the formation of ROS on the surface of PDMS, which could selectively prevent adhesion of endothelial cells. The degree of ROS amount was monitored according to the UV/O irradiation time, and at least 36 μM of ROS resulted in the precise cellular micropattern on the PDMS. The presence of ROS affected not only cellular detachment from the substrate, but also endothelial cell morphology such as cell spreading area, confluence, nuclear area and nuclear inverse aspect ratio. In addition, we could observe that the actin cytoskeleton of cells was also constricted due to ROS, thereby minimizing the focal adhesion area of vinculin. Compared with previously reported methods which use chemical treatment or nano/microstructure on the substrate, the proposed methodology is quite simple, accurate, and harmless to the patterned endothelial cells.

Connectivity percolation in suspensions of attractive square-well spherocylinders.

We have studied the connectivity percolation transition in suspensions of attractive square-well spherocylinders by means of Monte Carlo simulation and connectedness percolation theory. In the 1980s the percolation threshold of slender fibers has been predicted to scale as the fibers' inverse aspect ratio [Phys. Rev. B 30, 3933 (1984)PRBMDO1098-012110.1103/PhysRevB.30.3933]. The main finding of our study is that the attractive spherocylinder system reaches this inverse scaling regime at much lower aspect ratios than found in suspensions of hard spherocylinders. We explain this difference by showing that third virial corrections of the pair connectedness functions, which are responsible for the deviation from the scaling regime, are less important for attractive potentials than for hard particles.

Tokamak elongation – how much is too much? Part 2. Numerical results

The analytic theory presented in Paper I is converted into a form convenient for numerical analysis. A fast and accurate code has been written using this numerical formulation. The results are presented by first defining a reference set of physical parameters based on experimental data from high performance discharges. Scaling relations of maximum achievable elongation (${\it\kappa}_{max}$) versus inverse aspect ratio (${\it\varepsilon}$) are obtained numerically for various values of poloidal beta (${\it\beta}_{p}$), wall radius $(b/a)$ and feedback capability parameter (${\it\gamma}{\it\tau}_{w}$) in ranges near the reference values. It is also shown that each value of ${\it\kappa}_{max}$ occurs at a corresponding value of optimized triangularity (${\it\delta}$), whose scaling is also determined as a function of ${\it\varepsilon}$. The results show that the theoretical predictions of ${\it\kappa}_{max}$ are slightly higher than experimental observations for high performance discharges, as measured by high average pressure. The theoretical ${\it\delta}$ values are noticeably lower. We suggest that the explanation is associated with the observation that high performance involves not only $n=0$ MHD stability, but also $n\geqslant 1$ MHD modes described by ${\it\beta}_{N}$ in the Troyon limit and transport as characterized by ${\it\tau}_{E}$. Operation away from the $n=0$ MHD optimum may still lead to higher performance if there are more than compensatory gains in ${\it\beta}_{N}$ and ${\it\tau}_{E}$. Unfortunately, while the empirical scaling of ${\it\beta}_{N}$ and ${\it\tau}_{E}$ with the elongation (${\it\kappa}$) has been determined, the dependence on ${\it\delta}$ has still not been quantified. This information is needed in order to perform more accurate overall optimizations in future experimental designs.

Semi-analytic approach for determination of poloidal beta limits using plasma internal inductance in Damavand tokamak

The Grad–Shafranov equation plays a very important role in analysis of the plasma equilibrium in magnetic confinement configurations such as the tokamak. In tokamaks which are operating in Ohmic heating regime, the Grad–Shafranov equation can be expanded through the inverse aspect ratio parameter. Consequently, the first order of poloidal flux function and the poloidal/radial components of the magnetic field are obtained. In this study, by considering the effect of tokamak non-circularity, a semi-analytic model which is based on magnetic measurements was developed and highest and lowest values of plasma internal inductance and poloidal beta were estimated by means of the poloidal and radial magnetic field experimental data acquired from Damavand tokamak magnetic probes.

Percolation in suspensions of hard nanoparticles: From spheres to needles

We investigate geometric percolation and scaling relations in suspensions of nanorods, covering the entire range of aspect ratios from spheres to extremely slender needles. A new version of connectedness percolation theory is introduced and tested against specialised Monte Carlo simulations. The theory accurately predicts percolation thresholds for aspect ratios of rod length to width as low as 10. The percolation threshold for rod-like particles of aspect ratios below 1000 deviates significantly from the inverse aspect ratio scaling prediction, thought to be valid in the limit of infinitely slender rods and often used as a rule of thumb for nanofibres in composite materials. Hence, most fibres that are currently used as fillers in composite materials cannot be regarded as practically infinitely slender for the purposes of percolation theory. Comparing percolation thresholds of hard rods and new benchmark results for ideal rods, we find that i) for large aspect ratios, they differ by a factor that is inversely proportional to the connectivity distance between the hard cores, and ii) they approach the slender rod limit differently.

Understanding of the fundamental differences in JET and JT-60U AT discharges

Plasma current density simulations of JET and JT-60U shots in reverse-q advanced scenarios based on the previous data analysis of the identity plasma experiments have been performed. The effects of the main differences between the shots (neutral beam current density (jnbi), electron density and geometry) have been studied. The reversed q-profile (which was the target in this identity experiment and is observed at the beginning of each shot) was sustained in JT-60U while it became flat in JET towards the end of the shot. In JET, jnbi is peaked on-axis whereas in JT-60U it is peaked off-axis (at ρ = 0.5) while the NBI fraction of the selected shots is the same (22–24%). A strong density ITB appeared (at ρ = 0.5) in JT-60U but not in JET. The plasma geometry was mainly set to match but it was not identical. In addition, the extrapolation to JET steady-state operation has been done by testing the sensitivity of q to different externally driven currents, electron density and geometry in predictive current diffusion simulations. Moreover, critical bootstrap current density has been analysed.The reasons for the different time evolution of q-profile have been studied with predictive current simulations with the 1.5D transport code JETTO. The current diffusion model was validated against reverse-q shots, and simulations were performed with experimental data profiles, jNBI given by ASCOT and neoclassical resistivity and bootstrap current calculated by NCLASS.Bootstrap current density was the most efficient way to sustain the beneficial reverse shape of q-profile. Replacing the JET ne profile with one from JT-60U leads to an increase of 0.2–0.3 MA in the bootstrap current (f bs increases from 15% to 30%). However, sustaining the stationary reverse q is not achieved in JET with bootstrap current induced by the density gradient of JT-60U. Even 10 times larger gradient than in JT-60U helps to sustain the shape of the q-profile longer than the experimentally observed density profile in JET but the minimum value of q moves closer to central plasma and the shape of q is not stationary in a 10 s simulation. The effect of different shape of NBI current density profile is negligible due to quite small fraction. Sustaining the reverse q requires 45% or larger added off-axis fraction. However, increasing the inverse aspect ratio increases bootstrap current and decreases the critical bootstrap current more effectively than increasing the density gradient: two times larger inverse aspect ratio produces almost three times larger bootstrap fraction but ten times larger density gradient only two times larger bootstrap fraction. The conclusions based on these simulations indicate that the need for bootstrap current is larger in JET and the same conditions cause smaller bootstrap fraction, which suggests that achieving steady-state operation in JET under these conditions is unlikely.

RESISTIVE MAGNETOHYDRODYNAMICS SIMULATIONS OF THE IDEAL TEARING MODE

We study the linear and nonlinear evolution of the tearing instability on thin current sheets by means of two-dimensional numerical simulations, within the framework of compressible, resistive magnetohydrodynamics. In particular we analyze the behavior of current sheets whose inverse aspect ratio scales with the Lundquist number S as S 1=3 . This scaling has been recently recognized to yield the threshold separating fast, ideal reconnection, with an evolution and growth which are independent of S provided this is high enough, as it should be natural having the ideal case as a limit for S! 1. Our simulations conrm that the tearing instability growth rate can be as fast as 0:6 A 1 , where A is the ideal Alfv enic time set by the macroscopic scales, for our least diusive case with S = 10 7 . The expected instability dispersion relation and eigenmodes are also retrieved in the linear regime, for the values of S explored here. Moreover, in the nonlinear stage of the simulations we observe secondary events obeying the same critical scaling with S, here calculated on the local, much smaller lengths, leading to increasingly faster reconnection. These ndings strongly support the idea that in a fully dynamic regime, as soon as current sheets develop, thin and reach this critical threshold in their aspect ratio, the tearing mode is able to trigger plasmoid formation and reconnection on the local (ideal) Alfv enic timescales, as required to explain the explosive aring activity often observed in solar and astrophysical plasmas. Subject headings: plasmas { MHD { methods: numerical.

Mode coupling and aspect ratio effects on low and high-n plasma instabilities

In magnetically confined toroidal plasmas such as tokamaks, magnetohydrodynamic (MHD) instabilities experience strong toroidal and nonlinear mode coupling effects. Resistive MHD simulations with the M3D code show the importance of mode coupling and compressible MHD effects, which contribute to stronger mode coupling. For the m/n = 1/1 internal kink mode and sawtooth crash and for the edge localized mode (ELM) at higher n, MHD reproduces many features of the experimental observations, including the fast sawtooth crash and the moderate n ∼ 10 toroidal harmonics of the ELM. A general property of the perpendicular momentum equation in toroidal fusion plasmas is that the unbalanced radial forces remain relatively small, so that the terms that are lowest order in small inverse aspect ratio mostly cancel. The higher order terms then have significant effects, even at small r/Ro and small amplitude. Effects are strongest for the lowest toroidal harmonics n ≃ 1 and the most strongly driven ones with highest amplitude. Unlike the n = 1 internal kink mode, the small amplitude ELM ballooning/peeling-type mode, and thus ELM MHD marginal stability, may be reasonably described by the lowest order in aspect ratio, for moderate and large n ≳ 10. The ELM crash, however, depends on higher order.

Drifts of electron orbits induced by toroidal electric field in tokamaks

The drifts of electron orbits induced by the toroidal electric field in tokamaks are analyzed. Based on the relativistic Hamiltonian equations for guiding centre motion, the formula for the drift velocity vdr is derived. It describes the outward drift of passing particles as well as the inward drift (the Ware pinch) of trapped particles. Unlike the approximate formula for vdr given in Guan et al. [Phys. Plasmas 17, 092502 (2010)] for circular electron orbits, it describes qualitatively new features of the outward drift of electron orbits. Particularly, the new formula describes the evolution of the orbit's shape, the formation of X-point and the associated separatrix. It is shown that the outward drift velocity is proportional to the inverse aspect ratio of tokamaks.

An ultra-high gain low power two stage CMOS op-amp based on inverse aspect ratio self cascode structures

A very high gain (137 dB) two stage CMOS operational amplifier having structural simplicity of classical Widlar architecture has been presented. The differential input stage of proposed operational...

Perturbation analysis of electromagnetic geodesic acoustic modes

Lagrangian displacement and magnetic field perturbation response to the geodesic acoustic mode is analyzed by using the ideal magnetohydrodynamic equations in a large-aspect-ratio tokamak. δBθ, the poloidal component of magnetic field perturbation, has poloidal wave number m = 2 created by the poloidal displacement ξθ. The parallel perturbation of magnetic field, δB∥, has a poloidally asymmetric structure with m = 1 and is on the same order of magnitude with δBθ to the leading order. The radial displacement ξr is of order O(βϵξθ) but plays a significant role in determining δB∥, where β is the plasma/magnetic pressure ratio and ϵ is the inverse aspect ratio.

Parametric excitation of axisymmetric toroidal electrostatic mode by drift wave turbulences

The axisymmetric toroidal electrostatic mode discussed in this paper refers collectively to the nearly ideal electrostatic fluid mode with zero toroidal mode number in magnetically confined toroidal plasmas like tokamak, including geodesic acoustic mode, sound waves and the so-called nearly zero-frequency zonal flow. Use is made of cold ion fluid model in the toroidal coordinate system with a circular cross section to develop the theory of parametric excitation for the three above mentioned modes systematically to the first order of inverse large aspect ratio, which ends up with the four following observations: (1) The density zonal flow is only associated with the excitation of the first harmonic cosine sound wave and is independent of the potential zonal flow. (2) The geodesic acoustic mode is the high frequency branch of the dispersion in the form of coupling between the first harmonic sine sound wave and the nearly zero-frequency zonal flow due to geodesic curvature, while the low frequency branch of the same dispersion is identified to be the ‘toroidally modified nearly zero-frequency zonal flow’. (3) Only a weak coupling exists between the second harmonic sine sound wave and the nearly zero-frequency zonal flow. (4) All cosine sound waves and sine sound waves beyond the second harmonic are decoupled to the nearly zero-frequency zonal flow. A Gaussian type of drift wave energy spectrum with only a few parameters is introduced for calculation. Emphasis is laid on the effects resulting from the finite radial spectrum width such as double Landau-singularity, which reveal a significant modification to the δ -spectrum, thus resulting in serious restriction to the parametric excitation of geodesic acoustic mode and nearly zero-frequency zonal flow. Also discussed is the possibility of excitation of density zonal flow in the high q region. Numerical results are presented graphically and discussed in the reasonable physical regime. It is indicated that the geodesic acoustic mode and the nearly zero-frequency zonal flow cannot be parametrically excited at the same radii, and that if the geodesic acoustic mode is parametrically excited, the density zonal flow is expectedly to be observed.

Ion-Banana-Orbit-Width Effect on Bootstrap Current for Small Magnetic Islands

A simple and direct theoretical method has been proposed to investigate the so-called ion-banana-orbit-width (IBW) effect on the bootstrap current in the region of magnetic islands generated by the neoclassical tearing mode (NTM). The result shows that, when the IBW approaches the island width, the (ion) bootstrap current can be partly restored inside the island while the pressure profile is flattened. This can lead to the reduction of the bootstrap current drive on the NTM. The strength of the IBW effect on the NTM is related to the safety factor and the inverse aspect ratio on the rational surface.

Improved criterion for sawtooth trigger and modelling

We discuss the role of neoclassical resistivity and local magnetic shear in the triggering of the sawtooth in tokamaks. When collisional detrapping of electrons is considered the value of the safety factor on axis, q(0, t), evolves on a new time scale, , where τη = 4πa2/[c2η(0)] is the resistive diffusion time, ν* = νe/(ϵ3/2ωte) is the electron collision frequency normalized to the transit frequency and ϵ = a/R0 is the tokamak inverse aspect ratio. Such an evolution is characterized by the formation of a structure of size around the magnetic axis, which can drive rapid evolution of the magnetic shear and decrease in q(0, t). We investigate two possible trigger mechanisms for a sawtooth collapse corresponding to crossing the linear threshold for the m = 1, n = 1 instability and non-linear triggering of this mode by a core resonant mode near the magnetic axis. The sawtooth period in each case is determined by the time for the resistive evolution of the q-profile to reach the relevant stability threshold; in the latter case it can be strongly affected by ν*.

Dependence of radial thermal diffusivity on parameters of toroidal plasma affected by resonant magnetic perturbations

We investigate how the neoclassical thermal diffusivity of an axisymmetric toroidal plasma is modified by the effect of resonant magnetic perturbations (RMPs), using a drift-kinetic simulation code for calculating the radial thermal diffusivity of ion in the perturbed region under an assumption of zero electric field. Here, the perturbed region is assumed to be generated on and near the resonance surfaces, and is wedged in between the regular closed magnetic surfaces. We find that the dependence of the radial thermal diffusivity on parameters of the toroidal plasma is represented as , where is the neoclassical thermal diffusivity and c0 is a positive coefficient. Here, ωb is the bounce frequency, νeff is the effective collision frequency, Δb is the banana width, 〈‖δBr‖2〉1/2 is the strength of the RMPs in the radial directions, and |Bt0| is the strength of the magnetic field on the magnetic axis. The value of is significantly reduced to in the simulations because of the drift motion affected by the Coulomb collision, as contrasted with predicted by the so-called field-line diffusion theory, where q is the safety factor, Rax is the major radius of the magnetic axis, and ϵt is the inverse aspect ratio.