Effects of diamagnetic drift on nonlinear interaction between multi-helicity neoclassical tearing modes

A numerical study of the diamagnetic drift effect on the nonlinear interaction between multi-helicity neoclassical tearing modes(NTMs) is carried out using a set of four-field equations including two-fluid effects.The results show that,in contrast to the single-fluid case,5/3 NTM cannot be completely suppressed by 3/2 NTM with diamagnetic drift flow.Both modes exhibit oscillation and coexist in the saturated phase.To better understand the effect of the diamagnetic drift flow on multiple-helicity NTMs,the influence of typical relevant parameters is investigated.It is found that the average saturated magnetic island width increases with increasing bootstrap current fraction f_(b) but decreases with the ion skin depth δ.In addition,as the ratio of parallel to perpendicular transport coefficients χ_(‖)/χ_(⊥) increases,the average saturated magnetic island widths of the 3/2 and 5/3 NTMs increase.The underlying mechanisms behind these observations are discussed in detail.

Effects of counter-current driven by electron cyclotron waves on neoclassical tearing mode suppression

Through theoretical analysis,we construct a physical model that includes the influence of counter-external driven current opposite to the plasma current direction in the neoclassical tearing mode(NTM).The equation is used with this model to obtain the modified Rutherford equation with co-current and counter-current contributions.Consistent with the reported experimental results,numerical simulations have shown that the localized counter external current can only partially suppress NTM when it is far from the resonant magnetic surface.Under some circumstances,the Ohkawa mechanism dominated current drive(OKCD)by electron cyclotron waves can concurrently create both co-current and counter-current.In this instance,the minimal electron cyclotron wave power that suppresses a particular NTM was calculated by the Rutherford equation.The result is marginally less than when taking co-current alone into consideration.As a result,to suppress NTM using OKCD,one only needs to align the co-current with a greater OKCD peak well with the resonant magnetic surface.The effect of its lower counter-current does not need to be considered because the location of the counter-current deviates greatly from the resonant magnetic surface.

Effect of Finite-Ion-Banana-Width on the Polarization Contribution to the Neoclassical Tearing Modes Evolution

In the previous analytical description of the neoclassical polarization current effect on the neoclassical tearing modes （NTMs）, it is usually assumed that the magnetic island is much larger than the finite-ion-banana-width （FBW）. This assumption is questionable when the experimentally observed seed island width of the NTMs is comparable to the FBW. We introduce a simple and direct theoretical method to investigate the FBW effect on the neoclassical polarization contribution to the NTM evolution in collisional plasmas. The results show that, the FBW effect can strongly modify the neoclassical polarization current profile near the island separatrix, and thus weaken its probably stabilizing effect on the NTMs.

New Version of IS-LM:Neoclassical Monetarism

This study argues three policies for economies.The aim of those policies is to increase total demand by money supply.Global economy currently faces lack of money in markets and recession effect.First,neomerchantalism is to use national currency in bilateral trade.Second,limited money supply is to supply money to sub-regions of economy.Third,neoclassical monetary uses channels in monetary supply.Channels in NCM policy are financial banks and firms.Financial banks and firms distribute money into business markets.Global economies may apply propositions of NCM currently to refresh economies with money.

Effects of resonant magnetic perturbation on locked mode of neoclassical tearing modes

The effects of externally applied resonant magnetic perturbation (RMP) on the locked mode of the neoclassical tearing mode (NTM) are numerically investigated by means of a set of reduced magnetohydrodynamic equations.It is found that,for a small bootstrap current fraction,three regimes,namely the slight suppression regime,the small locked island (SLI) regime and the big locked island (BLI) regime,are discovered with the increase of RMP strength.For a much higher bootstrap current fraction,however,a new oscillation regime appears instead of the SLI regime,although the other regimes still remain.The physical process in each regime is analyzed in detail based on the phase difference between the NTM and the RMP.Moreover,the critical values of the RMP in both SLI and BLI regimes are obtained,and their dependence on key plasma parameters is discussed as well.

Neoclassical tearing mode stabilization by electron cyclotron current drive for HL-2M tokamak

Investigation of neoclassical tearing mode and its suppression by electron cyclotron current drive(ECCD)has been carried out in HL-2 M tokamak.The current driving capability of the electron cyclotron wave is evaluated.It is found that the deposition location can be effectively controlled by changing the poloidal angle.The validation of electron cyclotron wave heating and current driving has been demonstrated for the upper launcher port.We show that 3.0 MW and2.5 MW modulated ECCD can completely stabilize(2,1)and(3,2)NTMs,respectively.The non-modulated ECCD,radial misalignment as well as current profile broadening have deleterious effect on the NTM stabilization.The time required for suppression of(3,2)mode is shorter than that required for the suppression of(2,1)mode.Moreover,the time needed for complete stabilization at different initial island width has been quantitatively presented and analyzed.

A brief review:effects of resonant magnetic perturbation on classical and neoclassical tearing modes in tokamaks

This paper reviews the effects of resonant magnetic perturbation(RMP)on classical tearing modes(TMs)and neoclassical tearing modes(NTMs)from the theory,experimental discovery and numerical results with a focus on four major aspects:(i)mode mitigation,where the TM/NTM is totally suppressed or partly mitigated by the use of RMP;(ii)mode penetration,which means a linearly stable TM/NTM triggered by the externally applied RMP;(iii)mode locking,namely an existing rotating magnetic island braked and finally stopped by the RMP;(iv)mode unlocking,as the name suggests,it is the reverse of the mode locking process.The key mechanism and physical picture of above phenomena are revealed and summarized.

Suppression of Neoclassical Tearing Modes Towards Stationary High-Beta Plasmas in JT-60U

Results from stabilization of neoclassical tearing modes （NTMs） in JT-60U are described. NTM stabilization and confinement improvement have been demonstrated by employing a real-time NTM stabilization system, where the identification of the location of an NTM and the optimization of the injection angle of the electron cyclotron wave are performed in real time. Also, a high-beta plasma with the normalized beta of 3 has been sustained by suppressing NTM by applying the electron cyclotron current drive （ECCD） before the onset （＇preemptive ECCD＇）. In addition, a simulation code for analysis of the NTM evolution has been developed by combining the modified Rutherford equation with the transport code TOPICS. It is found that the simulation well reproduces the NTM behavior in JT-60U. The simulation also shows that the ECCD width is also important for NTM stabilization, and that the EC wave power for complete stabilization can be reduced by narrowing the ECCD profile.

Stabilization of Neoclassical Tearing Modes by rf Current

Neoclassical tearing mode (NTM) can degrade plasma confinement or even cause disruptions in existing tokamaks. Stabilization of the NTMs by radio frequency (rf) current is investigated by the modified Rutherford equation (MRE) in this paper. In a range of parameters, the required rf current for mode stabilization is obtained, which is linearly proportional to the bootstrap current density for both modulated current drive (MCD) and non-modulated current drive (NMCD), linearly (quadratically) to the radial width of the rf current for MCD (NMCD), and quadratically to the radial deviation of the rf current from the rational surface for both MCD and NMCD.

Neoclassical Kinetic Theory for the Shaped Tokamaks

Neoclassical transport for the shaped tokamak with X point is investigated using Hamiltonian formalism. For a set of Soloveev's configurations, the neoclassical diffusion coefficient is rigorously derived for the plateau regime which is inversely proportional to the connection length. When an X point appears on plasma boundary, the diffusion coefficient is greatly reduced by a much longer connection length compared with a circular cross-section plasma. Since the formalism is not limited for aspect ratio, for A = 1.3, it may be valid in a very narrow range of collisionality, 0.8 < V*i < 1.0, at / o = 0.95. In the range of collisionality, the detrapping rate is very high.

Novel results on attractivity of a neoclassical growth system incorporating multiple pairs of time-varying delays

In this paper,we analyze the global dynamics of a neoclassical growth system incorporating patch structure and multiple pairs of time-varying delays.First,we derive the global existence,positiveness and boundedness of solutions for the addressed system.Then,by employing some novel differential inequality analyses and the fluctuation lemma,both delay-independent and delay-dependent criteria are established to ensure that all solutions are convergent to a unique positive equilibrium point vector,which does not possess the same components.Our results supplement and improve some existing results.Ultimately,some numerical examples are afforded to prove the effectiveness and feasibility of the theoretical findings.

Saudi-Qatar Diplomatic Rapprochement:A Perspective of Neoclassical Realism

On 5 June 2017,Saudi Arabia announced the severance of diplomatic relations with Qatar.Saudi Crown Prince Mohammed had hoped that the blockade against Qatar would make Qatar no longer hold an independent and autonomous foreign policy and away from the influence of Iran and Turkey.However,the Saudi blockade against Qatar has not only failed to bring the latter to its knees but has allowed it to stand on its own feet and gradually reduced its dependence on imports.At the same time,Qatar has strengthened its ties with Iran and Turkey,bringing the two powers directly into the Gulf region and challenging Saudi Arabia’s hegemony in the Gulf.However,on 5 January 2021,Saudi Arabia announced the restoration of diplomatic relations with Qatar.Based on neoclassical realism,this paper presents a comprehensive analysis of the reasons for the resumption of diplomatic relations between Saudi Arabia and Qatar through both the international system and domestic factors,ultimately concluding that the reasons for the resumption of diplomatic relations between the two countries are related to Turkish and Iranian forces,the attitude of the United States,as well as GCC unity,the change in the Crown Prince’s diplomatic philosophy,the preservation of Sunnis and the promotion of economic cooperation.

Effects of plasma radiation on the nonlinear evolution of neo-classical tearing modes in tokamak plasmas with reversed magnetic shear

Effects of plasma radiation on the nonlinear evolution of neo-classical double tearing modes(NDTMs)in tokamak plasmas with reversed magnetic shear are numerically investigated based on a set of reduced magnetohydrodynamics(MHD)equations.Cases with different separations △_(rs)=|r_(s2)-r_(s1)|between the two same rational surfaces are considered.In the small △_(rs)cases,the plasma radiation destabilizes the NDTMs and makes the kinetic energy still grow gradually in the late nonlinear phase.Moreover,the NDTM harmonics with high mode numbers reach a high level in the presence of plasma radiation,forming a broad spectrum of MHD perturbations that induces a radially broadened region of MHD turbulence.As a result,the profiles of safety factors also enter a nonlinear oscillation phase.In the intermediate △_(rs)case,the plasma radiation can advance the explosive burst of kinetic energy that results from the fast driven reconnection between the two rational surfaces,because it can further promote the destabilizing effects of bootstrap current perturbation on the magnetic island near the outer rational surfaces.In the large △_(rs)case,through destabilizing the outer islands significantly,the plasma radiation can even induce the explosive burst in the reversed magnetic shear configuration where the burst cannot be induced in the absence of plasma radiation.

Numerical analysis of the optimized performance of the electron cyclotron wave system in a HL-2M tokamak

The capabilities of current drive, neoclassical tearing mode （NTM） stabilization, and sawtooth control are analyzed for the electron-cyclotron wave （ECW） system in a HL-2M tokamak. Better performance of the upper launcher is demonstrated in comparison with that of a dropped upper launcher, in terms of JEc/Jbs for NTM stabilization and 1ECCD/（Aptor）2 for sawtooth control. 1-MW ECW power is enough for the 3/2 NTM stabilization, and 1.8-MW ECW power is required to suppress 2/1 NTM in a single null divertor equilibrium with 1.2-MA toroidal current with the upper launcher. Optimization simulation of electron-cyclotron current drive （ECCD） is carried out for three mirrors in an equatorial port, indicating that the middle mirror has a good performance compared with the top and bottom mirrors. The results for balanced co- and counter-ECCD in an equatorial port are also presented.

Effects of resonant magnetic perturbations on radial electric fields in DIII-D tokamak

Gyrokinetic simulations of DIII-D tokamak equilibrium find that resonant magnetic perturbation(RMP)drives a neoclassical non-ambipolar electron particle flux,which causes a rapid change of equilibrium radial electric fields consistent with experimental observations during the suppression of the edge localized mode(ELM).The simulation results provide a support for the conjecture that RMP-induced changes of radial electric fields lead to the enhanced turbulent transport at the pedestal top during the ELM suppression(Taimourzadeh et al 2019 Nucl.Fusion59046005).Furthermore,gyrokinetic simulations of collisionless damping of zonal flows show that resonant responses to the RMP decrease the residual level of the zonal flows and damp the geodesic acoustic mode.

Modeling of the influences of multiple modulated electron cyclotron current drive on NTMs in rotating plasma

In this work, physical models of neoclassical tearing modes （NTMs） including bootstrap current and multiple modulated electron cyclotron current drive model are applied. Based on the specific physical problems during the suppression of NTMs by driven current, this work compares the efficiency of continuous and modulated driven currents, and simulates the physical processes of multiple modulated driven currents on suppressing rotating magnetic island. It is found that when island rotates along the poloidal direction, the suppression ability of continuous driven current can be massively reduced due to current deposition outside the island separatrix and reverse deposition direction at the X point, which can be avoided by current drive modulation. Multiple current drive has a better suppressing effect than single current drive. This work gives realistic numerical simulations by optimizing the model and parameters based on the experiments, which could provide references for successful suppression of NTMs in future advanced tokamak such as international thermonuclear experimental reactor.

To Theory One Class Linear Model Noclassical Volterra Type Integral Equation with Left Boundary Singular Point

In this work, we investigate one class of Volterra type integral equation, in model case, when kernels have first order fixed singularity and logarithmic singularity. In detail study the case, when n = 3. In depend of the signs parameters solution to this integral equation can contain three arbitrary constants, two arbitrary constants, one constant and may have unique solution. In the case when general solution of integral equation contains arbitrary constants, we stand and investigate different boundary value problems, when conditions are given in singular point. Besides for considered integral equation, the solution found cane represented in generalized power series. Some results obtained in the general model case.

The Parameters of the Stellarator as a Neutron Source for a Subcritical Reactor

The possibility of developing a stellarator-based neutron source designed for the nuclear reaction initiation in the blanket of hybrid reactor is studied. An analog of the Large Helical Device （LHD） stellarator design, with linear dimensions increased by a factor of 1.5 is taken for the magnetic system. Plasma parameters and the deuterium-tritium （DT） mixture fusion power are calculated using the space-time numerical code under the assumption of the neoclassical transport in the ambipolarity regime. Using the 10 MW plasma heating sources, it is possible to obtain the DT fusion power of one-to-two tens MW.

Information Models for Forecasting Nonlinear Economic Dynamics in the Digital Era

The aim of this study was to develop an adequate mathematical model for long-term forecasting of technological progress and economic growth in the digital age (2020-2050). In addition, the task was to develop a model for forecast calculations of labor productivity in the symbiosis of “man + intelligent machine”, where an intelligent machine (IM) is understood as a computer or robot equipped with elements of artificial intelligence (AI), as well as in the digital economy as a whole. In the course of the study, it was shown that in order to implement its goals the Schumpeter-Kondratiev innovation and cycle theory on forming long waves (LW) of economic development influenced by a powerful cluster of economic technologies engendered by industrial revolutions is most appropriate for a long-term forecasting of technological progress and economic growth. The Solow neoclassical model of economic growth, synchronized with LW, gives the opportunity to forecast economic dynamics of technologically advanced countries with a greater precision up to 30 years, the time which correlates with the continuation of LW. In the information and digital age, the key role among the main factors of growth (capital, labour and technological progress) is played by the latter. The authors have developed an information model which allows for forecasting technological progress basing on growth rates of endogenous technological information in economics. The main regimes of producing technological information, corresponding to the eras of information and digital economies, are given in the article, as well as the Lagrangians that engender them. The model is verified on the example of the 5th information LW for the US economy (1982-2018) and it has had highly accurate approximation for both technological progress and economic growth. A number of new results were obtained using the developed information models for forecasting technological progress. The forecasting trajectory of economic growth of developed countries (on the example of the USA) on the upward stage of the 6th LW (2018-2042), engendered by the digital technologies of the 4th Industrial Revolution is given. It is also demonstrated that the symbiosis of human and intelligent machine (IM) is the driving force in the digital economy, where man plays the leading role organizing effective and efficient mutual work. Authors suggest a mathematical model for calculating labour productivity in the digital economy, where the symbiosis of “human + IM” is widely used. The calculations carried out with the help of the model show: 1) the symbiosis of “human + IM” from the very beginning lets to realize the possibilities of increasing work performance in the economy with the help of digital technologies;2) the largest labour productivity is achieved in the symbiosis of “human + IM”, where man labour prevails, and the lowest labour productivity is seen where the largest part of the work is performed by IM;3) developed countries may achieve labour productivity of 3% per year by the mid-2020s, which has all the chances to stay up to the 2040s.

Development of Optimal City Size Theory: A Critical View

Nowadays more and more people reside in metropolitan areas,and the impact of this phenomenon is clearly creating challenges for the environment,the economy and the society at large.It is therefore useful and instructive to consider the issue of optimal city size and review the literature over the past decades on optimal city size theory.Based on the progress in recent years of comparative analysis and inductive research,from both theoretical and empirical perspectives,this paper outlines the original definitions proposed for optimal city size and discusses some of the advantages and disadvantages of the various theories.The two prevailing models in the classical analysis of optimal city size,the Henry George Theorem(HGT)and the neoclassical approach,are examined later.This paper then introduces the supply oriented dynamic model(SOUDY model)and offers a plausible model for optimal city size based on the general equilibrium analysis,which is related to sustainable development.The results show that:(1)Simple optimal city size theories come from the cost-benefit analysis developed by main stream economics,and therefore cannot overcome the defect that the optimal size of cities is the same since the same production function;(2)The Henry George Theorem,which is one of the classical analysis paradigms of optimal city size,has been used more frequently in recent years to research the issues of optimal tax and public goods and has gradually lost its connection to the topic of optimal city size;(3)The neoclassical approach to optimal city size consists of externalities influencing optimal city size,the equilibrium and optimal models for city size,the optimal town,product variety and city size distribution.This kind of research is still in the mainstream of the study of optimal city size.Compared to single optimal city size,more attention is paid to the optimal distribution of city size;and(4)The supply-oriented dynamic model allows for the integration of a spatial dimension into the economic research of optimal city size,and the constraint between city level and city size is relaxed and this has more power to explain real-world problems.At the same time,the general equilibrium analysis,as a significant economic research method,provides a new perspective for the study of optimal city size.The supply-oriented dynamic model and general equilibrium analysis are two new research paradigms that deserve more attention in the analysis of optimal city size.