On the dynamic fracture toughness and crack tip strain behavior of nuclear pressure vessel steel: Application of electromagnetic force

This paper is concerned with the application of the electromagnetic force to the determination of the dynamic fracture toughness of materials. Taken is an edge-cracked specimen which carries a transient electric current I and is simply supported in a steady magnetic field B. As a result of their interaction, the dynamic electromagnetic force occurs in the whole body of the specimen, which is then deformed to fracture in the opening mode of cracking.Using the electric potential and the J - R curve methods to determine the dynamic crack initiation point in the experiment, together with the finite element method to calculate the extended J-integral with the effects of the electromagnetic force and inertia, the dynamic fracture toughness values of nuclear pressure vessel steel A508 class 3 are evaluated over a wide temperature range from lower to upper shelves.The strain distribution near the crack tip in the dynamic process of fracture is also obtained by applying a computer picture processing.     

Natural Convection Heat Transfer of Liquid Lithium under Transverse and Parallel Magnetic Fields

Stagnant liquid lithium contained in a vertically 1.3 m long and 46 mm I.D. 316-SS cylindrical vessel up to a 0.3 m level was heated by a concentrically inserted heater pin of 12.5 mm O.D. and 54 mm active length. The parallel magnetic field to the vessel was imposed by a superconducting magnet. The experiment covered the ranges of the lithium temperature: 320～510°C, the heat flux: 10～40 W/cm², the transverse B: 0～1.2 T (Ha = 0～2,730) and the parallel B= 0～3T (Ha = O～6,860).

The temperature fluctuation is enhanced by imposing a weak magnetic field of B = 0.1 ～ 0.3 T for both parallel and transverse fields and almost completely suppressed with increasing to B = 1 T in the case of the transverse field but its low frequency component still remains large, becoming oscillatory, up to B = 3 T in the case of parallel field. The heat transfer shows a similar trend to the temperature fluctuation. It increases singularly by a weak B especially in the perpendicular sector to the transverse magnetic field and decreases with increasing B. In the case of parallel magnetic field, the heat transfer increases in a weak field of B = 0.1 ～ 0.5 T, the same as in the transverse magnetic field, but it does not decrease so much in a strong field of B = 1～3 T, presenting a rather higher value than in B = 0 T.     

Simulation of runaway electron generation and diffusion during major disruptions in the HL-2A tokamak

The generation and diffusion of runaway electrons (REs) during major disruptions in the HL-2A tokamak has been studied numerically. The diffusion caused by the magnetic perturbation is especially addressed. The simulation results show that the strong magnetic perturbation (δB/B ∼ 1.0 × 10⁻³) can cause a significant loss of REs due to the radial diffusion and restrain the RE avalanche effectively. The results also indicate that the REs are generated initially in the plasma core during disruptions, and that the toroidal electric field does not exhibit a centrally hollow phenomenon. In addition, it is found that the toroidal effects have little impact on the generation of RE and the evolution of toroidal electric field.     

A Theoretical Study of MHD Power Generation, (I)

This paper deals with an analysis of the current and electric field distributions in the entrance and exit regions of a linear MHD power generator, for the case where the working fluid (gas) exhibits the Hall effect. For simplicity, the following assumptions are adopted:

1. The MHD power generator is of constant-velocity-type.

2. The problem is two dimensional.

3. The electrical conductivity and the Hall parameter of the fluid and the magnetic field are constant and uniform in the region of interest.

4. The seeding material is injected uniformly at the entrance plane.

Solutions are presented in closed form for several values of the Hall parameter, ωπ. They show that the electric potential in the entrance plane assumes an extreme value between the electrodes, and that the length of the “entrance region” is of the same order as the distance between the electrodes. The influence of electric field distortion at the entrance on the current and electric field distributions is negligible beyond this region. The electric field distortion occurs in the exit region also, resulting in “end loss” which is approximately proportional to σ ^eff ωτ.     

Ion Extraction Characteristics from Photoionized Plasma by Radio-Frequency Resonance Method

In order to raise ion extraction efficiency in laser isotope separation, we have developed a radio-frequency (rf) resonance method. Then, to confirm feasibility of this method to a photoionized plasma, we experimentally studied the ion extraction characteristics.

When the rf frequency was swept under a weak magnetic field (5mT), the plasma-sheath resonance was found to occur at about 12MHz which was almost the same value as the theoretical one. Moreover, it was confirmed that the ion extraction time at the resonance frequency became the minimum.

When the magnetic field strength decreased from 5mT to zero, the ion extraction time became long. From the simulation results, this was because the plasma potential decreased with the magnetic field strength. Therefore, a magnetic field strength of more than 1mT was required to obtain a sufficient ion extraction efficiency.

To obtain the same extraction time as when applying a ?3kV dc voltage in the electrostatic method, the rf resonance method needed a voltage more than 70V_rms, in which the dc bias was ?1kV. Therefore, we confirmed that this method is feasible for the ion extraction from the photoionized plasma.     

Charge and Mass Considerations for Plasma Velocity Measurements in Rotating Plasmas

Velocity of hydrogen plasmas rotating due to imposed E × B fields at the Maryland Centrifugal Experiment (MCX) (Ellis et al., Phys Plasmas 12:055704, 2005), where E is the electric field in the radial direction and B the magnetic field in the axial direction of a cylindrical configuration, has traditionally been measured using Doppler shifts of atomic spectra from impurity elements such as carbon. Ideally, the gyrocenter of trace particles rotates at the bulk plasma velocity, regardless of the charged state or trace particle mass. However, for sufficiently large applied |E/B| (or equivalently, a sufficiently large ratio of bulk plasma rotation frequency and particle gyrofrequency), charged particles may have gyroradii that depart significantly from quasi-circular orbits drifting about the B field axis. This effect is investigated numerically with a single particle code that includes scattering, as well as experimentally at MCX. Numerical findings are compared to experimentally measured Doppler shifts of singly inonized helium and oxygen, and doubly ionized carbon atoms.     

A Theoretical Study of MHD Power Generation, (II)

The electric potential drop near the electrode surfaces in MHD power generators is studied theoretically by considering a simple model, in which the current flows in the direction normal to the electrode surfaces. In order to simplify the situation so as to permit analytic solution, the idea of a “boundary layer” near the electrodes is introduced, and the problem is treated entirely macroscopically, wherein the following assumptions are made:

1. The electrical conductivity is constant.

2. The Hall effect and the induced magnetic field can be neglected.

3. The behavior of the flow in the boundary layer may be described by equations for laminar flow.

4. The temperature variation in the boundary layer perpendicular to the electrode surfaces may be neglected.

The theory predicts that the magnitude of the electric potential drop near the electrode is of the order of 10 V in typical MHD power generators.     

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.     

Heliotron E Results and Large Helical Project

Heliotron E(H-E) experiment was started in 1980. Until 1987 high power heating experiments for improving plasma parameters have almost finished. H-E firstly demonstrated that ECR heated plasmas are usable for target plasmas of NBI or ICRF heating to obtain high density and high temperature currentless plasmas. The highest electron temperature is 1.5keV and ion temperature is 1.6keV and both are realized in the low density regime of <n> (average density) ≤10¹³cm^?3.

H-E also showed that the currentless plasmas have no major disruption and quasi-steady plasmas are confined with controlling impurity ions by titanium gettering and carbon coating.

H-E also obtained <β> (average β) –2%, which is the highest value realized in helical systems, with <n–8×l0¹³cm^?3 and Te(0)–T_i(0)–350 eV at B₀ (magnetic field at the magnetic axis) =0.94 T. In the high β experiments pressure-driven instabilities were observed for peaked pressure profiles and sometimes relaxation oscillations similar to the tokamak internal disruptions were observed.

In the ECRH plasmas neoclassical transport is dominant in the region inside the half radius. However, global confinement time τ_E follows the scaling law τ_E ∝<n>^0.66P_heat ^?0.53 which is different from the neoclassical scaling law. Here P_heat denotes the net heating power.

Based on the H-E results, a new large helical system design study has started in 1986. The plasma parameters entering the regime of <n>τ_E<T> (2–3)× 10¹⁹m^?3?S?keV is investigated, which is about one tenth of fusion plasma condition. From the transport code studies and empirical scaling law based on the H-E results, R=(4×5)m, ā=(50–60)cm and B_o=4T are required to satisfy the above condition with P_heat=20MW. The design study to fix the magnetic field configuration is progressing. Expected one is l=2 and m=10 with additional poloidal coils, where m is a toroidal period number. The magnetic field is produced by superconducting coil and long pulse operation will be tested, if continuous heating is available.     

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.     

Redistribution of Gaseous Phase of Liquid Metal Two-Phase Flow in a Strong Magnetic Field

In the previous paper, the authors pointed out the motion of bubble or gaseous phase in the direction to the both side walls due to the pinch effect caused by the induced magnetic field in the liquid metal two-phase flow under the strong magnetic field. In the present paper, to clarify the existence of the pinch effect experimentally, an experimental study was performed.

Firstly the distributions of the void fraction in the cross section perpendicular to the flow were measured at three locations in the flow direction for the various strength of the applied magnetic field. Secondly a magnetic field was superposed on the induced magnetic field by the outer coil to disturb the pinch effect by the cancel of the induced magnetic field with the superposed one, resulting in the evident redistribution of the void-fraction profile obtained above.

From these experiments it is concluded that the pinch effect will play an important role to redistribute the bubble or gaseous phase in the liquid metal two-phase flow under the strong magnetic field and that the effect is more promoted with increasing magnetic interaction number defined as a ratio of the electromagnetic force to the inertia of the fluid.     

Cracked beam under influence of dynamic electromagnetic force

This paper is concerned with both numerical analysis and experiment on the fracture phenomena related to the electromagnetic force, considering an edge-cracked beam which carries a transient current I and is placed in a uniform and steady magnetic field B₀.As for the numerical study, isoparametric quarter point elements are used to treat the singularities at the crack tip both for the stress and the current density. Also some discussions are presented on the application of nonlinear fracture mechanics to the present problem, the temperature increase at the crack tip and the skin effect of the electric current.     

Effects of Magnetic Field and Ion Velocity on SPT Plasma Sheath Characteristics

The distribution of magnetic field in Hall thruster channel has significant effect on its discharge process and wall plasma sheath characteristics. By creating physical models for the wall sheath region and adopting two-dimensional particle in cell simulation method, this work aims to investigate the effects of magnitude and direction of magnetic field and ion velocity on the plasma sheath characteristics. The simulation results show that magnetic field magnitudes have small impact on the sheath potential and the secondary electron emission coefficient, magnetic azimuth between the magnetic field direction and the channel radial direction is proportional to the absolute value of the sheath potential, but inversely proportional to the secondary electron emission coefficient. With the increase of the ion incident velocity, secondary electron emission coefficient is enhanced, however, electron density number, sheath potential and radial electric field are decreased. When the boundary condition is determined, with an increase of the sinmlation area radial scale, the sheath potential oscillation is aggravated, and the stability of the sheath is reduced.     

B2SOLPS0.5.2D Code Simulations of SOL Flows and Drifts Effects in the Edge Plasma of Small Size Divertor Tokamak

The B2SOLPS0.5.2D code can completely derive measured target asymmetries in edge plasma of small size divertor tokamak (SSDT). SOL flow measurements by the code have been performed in L-mode plasma at various poloidal locations in small size divertor tokamak. The main results of simulations suggest that, the following results: (1) SOLPS0.5.2D simulation predicts J_r^(\textdia) ×B_T J_{r}^{{({\text{dia}})}} \times B_{T} J_r^(\textdia) J_{r}^{{({\text{dia}})}} is diamagnetic current, B _T is normal toroidal magnetic field) force due to the presence of large up-down pressure asymmetries is one of the reasons responsible for observed target asymmetries. (2) The shear of plasma toroidal rotation which is contributed for ITB formation and transition to improved confinement regime is formed near separatrix. The role of centrifugal effect in target asymmetries and SOL flow has been investigated.     

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.     

Development of Analytical Method for DC Electromagnetic Flow Coupler Including End Effects

To develop an analytical method for a DC electromagnetic flow coupler, an electric circuit analog has been considered. The adopted analog consists of an infinite series of the lumped parameter circuit of the flow coupler cross section and allows an analysis of end effects which appear outside the inlet and outlet of the flow ducts. The ordinary differential equation of the second order was derived for the current distributions from the circuit equations of the present analog. The present method predicted very well the current distributions of the analytical solutions obtained by Birtzvalk et al. for the coupler with infinite width and length.

Further, the overall efficiency of the typical flow coupler evaluated by the present method gave a similar dependence on the flow ratio to that of Hughes & Alexion, although differences appeared in the results of the pressure rise and drop in the coupler's two ducts. From the current distributions obtained, these differences were attributed to the electrical coupling of the pump and the generator ducts in the fringing magnetic field which was considered by the present method, but not by Hughes & Alexion. Finally, the current flow patterns are given with an improved distribution of the external magnetic field including the wall effect.     

Experimental Measurement of Asymmetric Fluctuations of Poloidal Magnetic Field in Damavand Tokomak at Different Plasma Currents

Toroidal and Poloidal magnetic fields have an important effect on the tokomak topology. Damavand Tokomak is a small size tokomak characterized with k?=?1.2, B _t?=?1T, R ₀?=?36?cm, maximum plasma current is about 35?KA with a discharge time of 21?ms. In this experimental work, the variation of poloidal magnetic field on the torodial cross section is measured and analyzed. In order to measure the polodial magnetic field, 18 probes were installed on the edge of tokomak plasma with ?θ?=?18°, while a limiter was installed inside the torus. Plasma current, I _p, induces a polodial magnetic field, B _p, smaller than the torodial magnetic field B _t. Magnetic lines B produced as a combination of B _t and B _p, are localized on the nested toroidal magnetic surfaces. The presence of polodial magnetic field is necessary for particles confinement. Mirnov oscillations are the fluctuations of polodial magnetic field, detected by magnetic probes. Disrupted instability in Tokomak typically starts with mirnov oscillations which appear as fluctuations of polodial magnetic field and is detected by magnetic probes. Minor disruptions inside the plasma can contain principal magnetic islands and their satellites can cause the annihilation of plasma confinement. Production of thin layer of turbulent magnetic field lines cause minor disruption. Magnetic limiter may cause the deformation of symmetric equilibrium configuration and chaotic magnetic islands reveal in plasma occurring in thin region of chaotic field lines close to their separatrix. The width of this chaotic layer in the right side of poloidal profile of Damavand Tokomak is smaller than the width in the left side profile because of Shafranov displacement. Ergodic region in the left side of profile develops a perturbation on the magnetic polodial field lines, B _p, that are greater in magnitude than that in the right side, although the values of B _p on the left side are smaller than that on the right side of the profile. The Left side of profile is close to the principal magnetic axis and the right side is away from Z axis of Tokamak.     

Internal Magnetic Field Measurements in the TCSU RMF Current Drive Experiment

Detailed magnetic measurements of Field-reversed configurations (FRC) from the Translation Confinement Sustainment Upgrade (TCSU) experiment are presented. A two-axis probe inserted transversely at the axial midplane provides 24 independent measurements of B _z (r) and B _x (r). Two single-axis 29 channel probes provide axial profiles at the plasma edge. The B _x (r) field profiles, oriented to measure B_θ from the rotating magnetic field (RMF), provide details about RMF penetration into the FRC. B _z (r) profiles, when combined with the high beta nature of the FRC, interferometric density measurements, and assuming uniform temperature, yield radial density and pressure profiles. Time evolution of these profiles gives insight into plasma dynamics and the n = 1 (wobble) and n = 2 instabilities. Data from 123 and 172 kHz RMF frequencies is presented.     

Three-Dimensional Numerical Calculations on Liquid-Metal Magnetohydrodynamic Flow in Magnetic-Field Inlet-Region

Three-dimensional numerical calculations have been performed on liquid-metal magnetohydrodynamic (MHD) flow through a rectangular channel in the inlet region of the applied magnetic field, including a region upstream the magnetic field section. The continuity equation, the momentum equation including the Lorentz force term and the induction equation have been solved numerically. The induction equation is derived from Maxwell's equations and Ohm's law in electromagnetism. The discretization of the equations is carried out by the finite difference method, and the solution procedure follows the MAC method. Along the flow axis (i.e. the channel axis), the pressure decreases slightly as normal non-MHD flow, increases once, thereafter decreases sharply and finally decreases as fully-developed MHD flow. The sharp decrease in the pressure, resulting in a large pressure drop, in the inlet region is due to increase in the induced electric current in this region comparing with that in the fully-developed region. In the inlet region, the flow velocity distribution changes from a parabolic profile of a laminar non-MHD flow to a flat profile of a fully-developed MHD flow.     

A Practical Method for Evaluating the Neutron Dose Equivalent Rate

A practical method applicable to field monitoring with survey instruments is presented, which permits evaluation of the dose equivalent rate for neutrons, the spectrum of which is unknown but with energy ranging from epithermal to fast. The detectors employed consist of a BF₃ proportional counter with paraffin moderators 6.5 cm and I.Ocm thick, sheathed in 0.5 mm thick Cd, and a scintillation (ZnS and plastic) counter.

The dose equivalent rate Z)(mrem/hr) of neutrons with a broad spectrum is determined from the equation D=D_B+D_S , where D _B is dose equivalent rate determined from the effective neutron flux and the effective neutron energy through the counting rates obtained with the BF₃ proportional counter with paraffin moderators, and Ds the dose measured with the scintillation counter, the sensitivity of which is nearly proportional to the dose equivalent rate for neutrons above 2 MeV.

The error in evaluating the dose equivalent rate by the present method has been calculated to be at most 60% for typical neutron spectra, in the energy range from epithermal to 10 MeV.