Simulation of the Radial Electric Field Shear in the Edge Plasma of Small Size Divertor Tokamak

The simulation of the radial electric field shear, which is responsible for L-H transition by means B2SOLPS0.5.2D transport code, gives the dependence of this shear on plasma parameters. Also, as result of uni-directional neutral beam heating, internal transport barrier is formed and ion radial heat flux q _ir starts to decrease. Furthermore, the dependence of radial electric field shear on ion temperature gradient ITG has also investigated.     

Simulation of the Radial Electric Field in the Small Size Divertor Tokamak for Discharge with Neutral Beam Injection (NBI)

The radial electric field in the edge plasma of small size divertor tokamak can be simulated by B2SOLPS0.5.2D fluid transport code. The simulation provides the follow results: (1) Switching on and off the part of the parallel plasma viscosity driven by parallel ion diamagnetic heat flux (Bekheit in J. Fusion Energ 27(4), 338–345, 2008; Schneider et al. in Nucl. Fusion 41:387, 2001) and Counter-NBI plasma heating change profile of radial electric field significantly. (2) Switching on and off the parallel plasma viscosity driven by parallel ion diamagnetic heat flux leads to the radial electric field is toroidal magnetic field dependence (3) For the case of counter-NBI plasma heating, the switching on and off the current driven by part parallel plasma viscosity depends on the ion diamagnetic heat flux leads to the ion poloidal velocity is toroidal magnetic field B_T dependence. (4) The profile of the radial electric field in edge plasma of small size divertor tokamak is consistent with poloidal rotation velocity.     

Modelling of Small Size Divertor Tokamak Plasma Edge in the Higher Confinement Regime

A version of the B2SOLPS0.5.2D fluid transport code is the new version of B2SOLPS fluid transport code, which is suited technique to simulate the edge plasma of small size divertor tokamak in the H- regime. The results of simulation provide the following: (1) the radial electric field inside the transport barrier is consistent with the neoclassical nature of the radial electric field. (2) The absolute value of the radial electric field shear at inner side of internal transport barrier is small and consistent with the value of shear before the L–H transition, while the value of shear at barrier is significantly large. (3) As a result of strong radial electric field shear and strong barrier formation the diffusion coefficient reduced by factor ~3 with respect to L-mode while ion heat conductivity reduced by factor ~22 with respect to L-mode inside the barrier. (4) The toroidal (Parallel) flux is directed along co-current direction as L-mode but at inner side of barrier is significantly large in absolute value. (5) The radial profile of toroidal rotation in vicinity of transition layer is determined by the parameter δ (width of the transition layer) depending on the collisionality and anomalous diffusion coefficient.     

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.     

Formation of Electron Internal Transport Barrier in Edge Plasma of Small Size Divertor Tokamak

The formation of electron internal transport barrier (EITB) during using counter-neutral beam injection (NBI) heating in the edge plasma of small size divertor tokamak can be simulated by using fluid transport code B2SOLPS0.5.2D. The results of simulations give us the following: (1) Plasma heating with counter-neutral beam injection leads to, strong, parabola type electron internal transport barrier (EITB) was formed in the edge plasma of small size divertor tokamak. (2) In case of plasma heating by counter-neutral beam injection, the radial electric field shear (E _r –gradient) was increased, while electron transport coefficients were reduced in conjunction with the formation of electron internal transport barrier (EITB). (3) The plasma heating by counter-neutral beam injection play significantly role in redistribution of parallel (toroidal) velocity in edge plasma of small size divertor tokamak.     

The Behavior of Radial Electric Field and Toroidal Rotation in the Edge Plasma of Divertor Tokamak

A new method for describing the nature of radial electric field and its relation with toroidal rotation in edge plasma of small size divertor tokamak is proposed in this work. The expression of radial electric field in the edge plasma of small size divertor tokamak can be divided into two parts. The first part E _r ⁽⁰⁾ is related to electrostatic potential of plasma in edge plasma of this tokamak. The second part E _r ⁽¹⁾ is related to contribution of toroidal rotation of radial current in edge plasma of this tokamak. The results of this work provide the following: (1) A new one-dimensional ordinary differential equation for toroidal velocity is obtained. The one-dimensional ordinary differential equation suggest new tool to explaining tokamak experiments involving measurements of plasma rotation and radial electric field. (2) Also the results of this work shows that, the main contribution to the radial electric field inside separatrix (plasma core) gives the term E _r ⁽¹⁾.     

Simulation of Low–High Transition by Neutral Beam Injection in Edge Plasma of Small Size Divertor Tokamak

This paper reports simulation of L–H transition by fluid transport code B2SOLPS0.5.2D at low ion plasma density on neutral beam injection (NBI) in the edge plasma of small size divertor tokamak. The simulation provides the following results: (1) the transition is possible at plasma density 2 × 10¹⁹ m^?3 with NBI at temperature heating T^heating 3.62 keV. (2) The simulation predicts the generation of large negative radial electric field E _r, which is thought to help L–H transition during NBI, is suggested in the edge plasma of small size divertor tokamak. (3) The toroidal current density in the edge plasma of small size divertor tokamak is plasma density and direction of NBI dependence. (4) Parallel flux transport by anomalous viscosity (turbulent) through separatrix leads to the variation of toroidal current density.     

Plasma Confinement Modification in IR-T1 Tokamak by Velocity Shear Stabilization

E × B velocity shear effects on the plasma confinement were investigated in the IR-T1 tokamak. The investigations have been done at the presence of external applied electric and Resonant Helical magnetic Fields (RHF). In this work, experimental data have been measured by using two arrays of the Langmuir probes in both the radial and poloidal directions. A velocity shear stabilization mechanism has also been proposed to be responsible for an improvement in plasma confinement. The results show that E_r × B drift velocity (V_E×B) reduces about 90 % due to applied biasing and RHF at edge plasma. We have also observed that positive biasing and RHF lead to a significant decrease (>80 %) for radial turbulent transport (Γ_E×B) at edge plasma. In this paper, the electrostatic Reynolds stress (Rs) and the shearing rate γ_E×B have been calculated. We have also compared the Rs and γ_E×B at presence of the biasing and RHF and without biasing and RHF. A good correlation between confinement modifications and E_r × B velocity shear has been found suggesting that confinement enhancement originates at the edge plasma as a consequence of the formation of a particle transport barrier just inside the limiter.     

Simulation of Small Size Divertor Tokamak Plasma Edge in the L-regime with ion Transport Barrier

Simulations of L-regimes of small size divertor tokamak plasma edge have been performed with the B2SOLPS5.0 2D fluid transport code for wide range parameters. A conclusion has been made that, radial electric field in the vicinity and inside separatrix is near to neoclassical electric field value. The poloidal E × B drifts and compensating parallel fluxes in the scrape off layer are large in the L-regime with ITB due to steeper gradients while the qualitative pattern of the flows is similar to that of the L-mode.     

Energy Confinement Scaling Predictions for the Stabilized Tandem Mirror

The absence of toroidal curvature and the relatively weak internal parallel currents in a tandem mirror gives the system favorable stability and transport properties. GAMMA-10 experiments demonstrate that sheared plasma rotation suppresses turbulent radial losses through control of the radial potential profiles. Recent achievements of the GAMMA-10 include 3 keV ion confinement potentials and T _e ≥ 800 eV. Total energy confinement times for the GAMMA-10 experiment exceed by an order of magnitude the corresponding empirical confinement times in toroidal devices. At the temperatures achieved in the GAMMA-10, the end loss rate τ_p ≃ 100 ms so that radial losses determine τ_E, as intended in tandem mirror reactor designs. Drift-wave results on radial confinement times developed using Bohm, gyro-Bohm, and electron temperature gradient (ETG) scalings imply that the tandem mirror has a qualitatively different form of drift-wave radial transport from that in toroidal devices. Drift-wave eigenmodes for the GAMMA-10 are analyzed for the fluctuating electrostatic potential and magnetic perturbations.     

Turbulent Transport in the Tokamak Edge Plasma and SOL Region

In this work, the turbulent transport in the edge plasma and Scrape-Off Layer (SOL) region of IR-T1 tokamak at the presence of biased limiter has been investigated and analyzed. The time and radial evolution of floating potential, electric field and turbulent transport have been measured by using two arrays of the Langmuir probes in both the radial and poloidal directions. The analyses have been done by the Fast Fourier Transport method and spectral features of them are obtained with the help of the standard Auto-Correlation technique and modified covariance power spectral density estimate. The probability distribution function and actual transfer function magnitude of the radial and poloidal turbulent transport (Γ_r and Γ_p) have been investigated and compared in the edge plasma and SOL region. Also the histogram of turbulent transport has been analyzed and compared in the edge and SOL at presence of positive limiter biasing. The results show that in the edge plasma poloidal turbulent transport (Γ_p) is about of 60 % more than SOL region whereas radial turbulent transport (Γ_r) is about of 40 % less. During the application of positive biasing, it was found that Γ_r in the IR-T1 reduces by about 80 % in the edge plasma and 45–50 % in the SOL. Increase of Γ_p is about of 50 % after applied positive biasing in the edge while it increases 70 % nearly, in the SOL. Consequently, the improvement in confinement can be obtained for positive limiter biasing.     

Axial SPN and Radial MOC Coupled Whole Core Transport Calculation

The Simplified P_N (SP_N) method is applied to the axial solution of the two-dimensional (2-D) method of characteristics (MOC) solution based whole core transport calculation. A sub-plane scheme and the nodal expansion method (NEM) are employed for the solution of the one-dimensional (1-D) SP_N equations involving a radial transverse leakage. The SP_N solver replaces the axial diffusion solver of the DeCART direct whole core transport code to provide more accurate, transport theory based axial solutions. In the sub-plane scheme, the radial equivalent homogenization parameters generated by the local MOC for a thick plane are assigned to the multiple finer planes in the subsequent global three-dimensional (3-D) coarse mesh finite difference (CMFD) calculation in which the NEM is employed for the axial solution. The sub-plane scheme induces a much less nodal error while having little impact on the axial leakage representation of the radial MOC calculation. The performance of the sub-plane scheme and SP_N nodal transport solver is examined by solving a set of demonstrative problems and the C5G7MOX 3-D extension benchmark problems. It is shown in the demonstrative problems that the nodal error reaching upto 1,400 pcm in a rodded case is reduced to 10pcm by introducing 10 sub-planes per MOC plane and the transport error is reduced from about 150pcm to 10pcm by using SP₃. Also it is observed, in the C5G7MOX rodded configuration B problem, that the eigenvalues and pin power errors of 180 pcm and 2.2% of the 10 sub-planes diffusion case are reduced to 40 pcm and 1.4%, respectively, for SP₃ with only about a 15% increase in the computing time. It is shown that the SP₅ case gives very similar results to the SP₃ case.     

Effects of Sheared Flow on Microinstabilities and Transport in Plasmas

Theoretical and experimental studies associated with electric field effects on the stability and transport are briefly surveyed. The effects of radial electric field on the suppression and/or enhancement of various microinstabilities such as drift waves, flute mode and temperature gradient modes are discussed. The suppression of flow shear on the electron temperature gradient mode in plasmas with slightly hollow density profiles is investigated by solving the gyrokinetic integral eigenvalue equation. Comparison between theoretical predictions and experimental observations based on the HIBP measurements with high temporal and spatial resolutions is made in bumpy tori and heliotron (CHS) devices.     

Experiment Results about the Relationship of Edge Turbulence and Atomic Processes in the HT-7 Tokamak

Using a reciprocating Langmuir probe system, the boundary plasma behaviors were investigated before and after lithium/silicon coating. Accompanying the effective reduction of impurity radiation, strong shears of radial electric field and poloidal velocity came into being and the turbulence suppression and de-correlation were observed in the edge region of coated wall plasma. All these led to the reduction of the edge transport and improvement of plasma confinement. In the central line averaged density scanning experiments, an enhanced shear of the radial electric field was observed in the edge plasma with the increase of the density, which may account for the enhancement of the transport barrier and the improvement of particle confinement.The results suggest a close link between wall conditions and boundary plasma. In addition to the relationship, (～Te)/Te ～(～n)n/ne and θ_(～T)e(～n)e ～π, had been observed in the plasma edge region, which indicates the important role of the ionization and radiation in turbulence driving.     

Global Energy Confinement Scaling Predictions for Tandem Mirrors

For an MHD stable system, we investigate the interplay between drift wave (ETG and gyro-Bohm) radial transport and axial losses in the GAMMA-10 experimental facility and the proposed kinetically stabilized tandem mirror (KSTM) fusion reactor. Numerical coefficients in the models are taken to be consistent with tokamak and stellarator databases. The trade off between radial losses and the Pastukhov end losses is examined. We propose the use of a genetic algorithm to optimize the fusion power amplification Q = P _fusion/P _injected as a function of the key system parameters.     

Influence of temperature, strain rate and specimen geometry on the microscopic cleavage fracture stress

The aim of this work is to determine the influence of temperature, strain rate and specimen geometry on the microscopic cleavage fracture stress σ_f*. Besides, the dependence of the initiation temperature for shear fracture T_i and the temperature for general yield T_gy on strain rate is investigated. Finally, the local values of stress triaxiality and equivalent plastic strain at the occurrence of cleavage fracture for several steels and specimen types are compared with the failure curve for ductile fracture to check the validity of the theory of stress controlled cleavage fracture and the strain/triaxiality controlled shear fracture in the transition region. Based on experimental tests, the results are obtained by finite element analyses. The investigation shows, that σ_f* is dependent on temperature and strain rate and increases with decreasing test temperature and increasing strain rate. The transition temperatures T_i and T_gy increase with increasing strain rate. The theories of stress controlled cleavage fracture and of shear fracture controlled by equivalent plastic strain and stress triaxiality seem to be valid. That fracture mechanism occurs for which the critical condition is reached first.     

Tokamak edge plasma rotation in the presence of the biased electrode

Electrode biasing system was designed, constructed, and installed on the IR-T1 tokamak, and then biasing experiments were carried out. Also, using a Mach probes the effects of radial electric field (produced by biased electrode) on the poloidal and toroidal components of the edge plasma velocity were investigated. The results showed an increase in both toroidal and poloidal components of the edge plasma velocity during biasing regime. Results compared and discussed. During positive biasing, increased E_r tends to slow the poloidal rotation in the electron diamagnetic drift direction, i.e., to speed up rotation in the ion diamagnetic drift direction. An increased toroidal rotation velocity has the opposite effect on the poloidal rotation.     

负径向电场对带电粒子俘获率影响的数值模拟

本文采用数值方法求解Grad-Shafranov方程反演EAST典型长脉冲放电实验(炮号33068)的平衡位形和磁场分布,进而结合粒子在托卡马克电磁场中的运动方程,模拟氘离子在负径向电场存在时的运动轨迹,并统计不同负径向电场下的氘离子俘获率。结果表明：随负径向电场的增大,氘离子轨迹由扩张通行轨迹向外翻香蕉轨迹再向内翻香蕉轨迹,最后向压缩通行轨迹演变;氘离子俘获率随负径向电场的增大而减小,氘离子初始速度越小,其变化越大。     

Electron transport coefficients in N2O in RF electric and magnetic fields

A Monte Carlo simulation technique is used to investigate electron transport in N₂O in crossed RF electric and magnetic fields. Our work has resulted in a database of transport parameters which can be used for correct implementation in modeling RF discharges. A behavior of transport coefficients under the influence of the magnitude and the frequency of the fields was studied separately revealing some complex features in the time dependence, most notably anomalous anisotropic diffusion and time-resolved negative differential conductivity.     

Utilizing RF Electric Field for Injection-Trapping High Energy Molecular Ions in Mirror Field, (I)

A method of using rf electric field in a device for high-energy injection is described, and the behavior of the molecular ions injected into a system combining rf and DC magnetic fields is investigated by calculation and observation.

In this method, some of the injected molecular ions are decelerated by the rf field, and trapped in a small region between the mirror fields, where they are dissociated by collision with the background gas or with the plasma particles, and are thus trapped in the form of atomic ion. The relation between the rf frequency ω and the Larmor frequencies ΩN⁺ ₂, ΩN⁺ ₁ is given by ω=N/2· ΩN⁺ ₂=N/4· ΩN⁺ ₁, where N is the number of rf electrodes. The number N is chosen so that N/2 is an integer and N/4 a non-integer.

Calculation shows that the ions injected in a certain favorable phase are stably decelerated despite their initially possessing a precessional motion. This is proven by observation of actual electron behavior.