Boiling of Potassium in Vertical Tube under Transverse Magnetic Field

The experimental study was conducted to examine the applicability of boiling potassium two-phase flow to the blanket cooling of fusion power reactors. A high flux heater pin of 44mm heating length and 6.5mm O. D. with eight thermocouples of 0.5mm O. D. was inserted from the bottom of a vertical channel which was made of a 4m long, 14.9mm I.D. and 17.5mm O. D. stainless steel tube and placed in a D.C. magnet of 50cm long poles. The experimental conditions were the heat flux: 0~67W/cm², the magnetic field strength: 0~1.8T, the Ar cover gas pressure: 1.0bar, the potassium level above heater: 1.8m, and the temperature of upper unheated section: 400°C.

In the absence of magnetic field, boiling occurred intermittently, repeating the cycles between superheating with moderate temperature fluctuation and desuperheating with condensing shock pulses. When a weak magnetic field was applied, the temperature fluctuation was enhanced by natural convection, the incipient boiling superheat was reduced, and the boiling pattern became continuous. With increasing the magnetic field strength, the fluctuation was suppressed and the incipient boiling superheat increased but tended to level off around 1.5 T. Violent incipient boiling caused by a large superheat inherent in liquid metals was mitigated by magnetohydrodynamic interaction under a transverse magnetic field of 1.0T or larger, and subsequently followed by continuous saturation boiling with small fluctuation. No burn-out of the heater pin occurred in spite of symptom of dryout within the experimental range: q=67W/cm² and B=1.5T.     

Heat Transfer and Temperature Fluctuation of Lithium Flowing under Transverse Magnetic Field

For providing background information on the liquid metal cooling of fusion reactors, the MHD effects on heat transfer of flowing lithium was experimentally studied with an emphasis on temperature fluctuations. The test section was constituted of a 15.8 mm I.D., 1.65 mm thick, 316-SS tubing and a 7.6 mm O.D. heater pin with nine 0.5 mm thermocouples. The experiment covered the range of B=0–1.0 T, U=0.2–4.0m/s, T=320–390°C and q=0–68 W/cm². The results are summarized as follows:

(1) With increasing magnetic flux density B, Nusselt number Nu decreases to a value of flat flow velocity model: 6.38 but rises in B=0.1–0.4T. (2) The RMS of temperature fluctuation has strong dependence on B and presents a peak near B=0.25T. (3) The singular rise of Nu is inferred to result from enhanced turbulence due to steepening of radial gradient of velocity near the wall as a result of MHD effect. (4) The transit velocity estimated from temperature cross-correlation in the parallel sector coincides with the mean velocity when B=0 but deviates toward a lower value with applying B. (5) Local flow velocity is decelerated in the magnetically-parallel sectors and accelerated in the perpendicular.     

Influence of Transverse Magnetic Field on Heat Transport Characteristics of Potassium Heat Pipe

The influence of a transverse magnetic field on the heat transport characteristics of a potassium heat pipe was experimentally studied in the range of field strength 0~0.6 T. The wick was constituted of a multilayer mesh screen, and the adiabatic section, to which the magnetic field was applied, was made up of a concentric double-wall rectangular tube, with the inner wall completely separating the vapor and liquid flows.

The magnetic field was applied perpendicularly to the heat pipe, upon which the axial temperature distribution of the heat pipe was observed to be affected, and the heat transport rate to be reduced with increasing field strength.

The effect of the magnetic field on the heat transport rate is analyzed in terms of the liquid pumping ability of the wick and of the magnetohydrodynamic (MHD) effect on the liquid flow through the wick. The MHD effect on the flow through wick is shown to be expressible by a formula similar to that for flow between parallel plates.

The heat transport rate measured in magnetic field are compared with values calculated assuming that the wick pumping ability was not influenced by the magnetic field but that it was the MHD effect on the liquid flow through the wick that affected the heat transport. The calculated results well explained the experimental data.     

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.     

MHD flow past a vertical oscillating plate

The motion of a semi-infinite incompressible, viscous electrically conducting fluid, caused by the oscillation of a plane vertical plate under the action of a transverse magnetic field, has been studied on taking into account the presence of free convection currents. Closed form solutions to velocity and penetration distance through which the leading edge effect propagates have been derived on neglecting the transient part. In case of air, it has been observed that the velocity profiles lie on left or right hand side of η-axis according as G < 0 (heating of the plate) or G > 0 (cooling of the plate). There may occur instability in case of air for ωt = 0. With increasing magnetic field, the transition from conduction to convection is enhanced.     

Numerical simulation of MHD effects on convective heat transfer characteristics of flow of liquid metal in annular tube

A numerical study is conducted in an annular duct formed by a SS316 circular tube with electrically conducting walls and a coaxial heater pin, with liquid Lithium as the working fluid for magnetic field ranging from 0 to 1 T. The Hartmann and Stuart number of the study ranges from 0 to 700 and 0 to 50 respectively. The Reynolds number of the study is 10⁴.It was shown that the convective heat transfer and hence the Nusselt number decreases near the walls perpendicular to the magnetic field due to reduction in turbulent fluctuations with increase of magnetic field. It was observed that the Nusselt number value increases near the walls parallel to the magnetic field as the mean velocity increase near the walls. A singular rise was observed near both the walls near Stuart number ～10 which is due to the increase of turbulence levels in the process of changing from turbulent to electromagnetically laminarized flow.When a very low Reynolds number ～300 is used, the reduction in Nusselt number near the perpendicular walls is less. This shows that the reduction in Nusselt number near the perpendicular walls for the high Reynolds number study is due to the reduction in turbulent fluctuations. The Nusselt number was found to increase near the parallel walls as the mean velocity increases near the walls.When an insulating duct is used the Nusselt number near the parallel walls did not increase for the case with insulating walls as in the case with conducting walls showing the contribution of the ‘M’ shaped velocity profile in the Nusselt number increase near the parallel walls. The Nusselt number near the perpendicular walls was found to decrease at a higher rate in case of insulating walls than that of the study with conducting walls.     

Antisymmetric RMF Current Drive in FRCs

A major concern for Rotating Magnetic Field (RMF) current drive of an FRC is that a transverse magnetic field tends to open the field lines, thus compromising confinement. In recent FRC current drive experiments it was found that thermal confinement is much improved when an antisymmetric RMF is applied, rather than the usual symmetric RMF. A field line tracking analysis showed that with a combination of partial penetration and antisymmetric RMF, the field lines remain closed for larger ratios of B _ω/B _e than was previously thought. In this paper the analysis is extended to more fully understand the boundaries of when and where the field lines are expected to remain closed when antisymmetric RMF current drive is applied to an FRC.     

MHD flow past a semi-infinite flat plate with heat transfer

Exact numerical solutions to the boundary layer similarity equations of MHD flow and heat transfer past a semi-infinite flat plate of an incompressible viscous fluid have been presented. The velocity of the fluid U and the magnetic field H₀ at a distance from the plate are both assumed to be uniform and parallel to the plate which is considered as isothermal. Velocity, magnetic and temperature fields have been shown graphically whereas the numerical values of ƒ′(0) and {−θ′(0)} are entered in tables. We observe that both ƒ′(0) and {−θ′(0)} decrease with increasing S (magnetic field parameter) and increase with increasing λ (ratio of magnetic diffusivity and viscous diffusivity).     

A new facility for studying plasma interacting with flowing liquid lithium surface

A new facility to study plasmas interacting with flowing liquid lithium surface was designed and is constructing in Sichuan University. The integrated setup includes the liquid lithium circulating part and linear high density plasma generator. The circulating part is consisted of main loop, on-line monitor system, lithium purification system and temperature programmed desorption system. In our group a linear high density plasma generator was built in 2012. Three coils were mounted along the vessel to produce an axial magnetic field inside. The magnetic field strength is up to 0.45 T and work continuously. Experiments on plasmas interacting with free flowing liquid lithium surface will be performed.     

Measurement of the correlation spectrum of electrostatic potential fluctuations in an ECRH Helimak plasma

Measurements of the length and time scales of turbulent potential fluctuations were carried out on the MIT Versatile Toroidal Facility (VTF). Plasmas were produced by ECRF heating in a novel toroidal configuration which we have termed the Helimak. The configuration consists of a toroidal fieldB of approximately 800 gauss and a vertical fieldB _z of typically 10 gauss, produced by a Helmholtz coil.T _e is approximately 10 eV. The density exhibited a peaked profile havingn _max 2×10¹⁰ cm^–3 and a density gradient scale length of 10 cm. The fluctuation experiments were conducted using a mobile vertical array of eight Langmuir probes. At major radii outside the density peak, the vertical correlation lengths _c of fluctuations were found to be on the order of 5–10 cm for fluctuation frequencies below 3–8 kHz, and on the order of 1–2 cm at higher frequencies. At major radii on the inner slope of the density peak, a new feature appears in the spatial coherence function consisting of a second peak at a probe separation which scales linearly with vertical field. This observation indicates that these fluctuations have a correlation length on the order of 2R ₀600 cm in the direction parallel to the helical magnetic field lines.     

Study and optimization of boronization in Alcator C-Mod using the Surface Science Station (S3)

A Surface Science Station (S³) on the Alcator C-Mod tokamak is used to study and optimize the location and rate of boron film deposition in situ during electron cyclotron (EC) discharge plasmas using 2.45 GHz radio-frequency (RF) heating and a mixture of helium and diborane (B₂D₆) gasses. The radial profile of boron deposition is measured with a pair of quartz microbalances (QMB) on S³, the faces of which can be rotated 360° including orientations parallel and perpendicular to the toroidal magnetic field B_T ～0.1 T. The plasma electron density is measured with a Langmuir probe, also on S³ in the vicinity of the QMBs, and typical values are ～1 × 10¹⁶ m^?3. A maximum boron deposition rate of 0.82 μg/cm²/min is obtained, which corresponds to 3.5 nm/min if the film density is that of solid boron. These deposition rates are sufficient for boron film applications between tokamak discharges. However the deposition does not peak at the EC resonance as previously assumed. Rather, deposition peaks near the upper hybrid (UH) resonance, ～5 cm outboard of the EC resonance. This has implications for RF absorption, with the RF waves being no longer damped on the electrons at the EC resonance. The previously inferred radial locations of critical erosion zones in Alcator C-Mod also need to be re-evaluated. The boron deposition profile versus major radius follows the ion flux/density profile, implying that the boron deposition is primarily ionic. The application of a vertical magnetic field (B_V ～0.01 T) was found to narrow the plasma density and boron deposition profiles near the UH resonance, thus better localizing the deposition. A Monte Carlo simulation is developed to model the boron deposition on the different QMB/tokamak surfaces. The model requires a relatively high boron ion gyroradius of ～5 mm, indicating a B⁺¹ ion temperature of ～2 eV, to match the deposition on QMB surfaces with different orientation to B_T. Additionally, the boron ion trajectories become de-magnetized at high neutral gas throughput (～0.5 Pa m³ s^?1) and pressure (～2 Pa) when the largest absolute deposition rates are measured, resulting in deposition patterns, which are independent of surface orientation to B_T in optimized conditions.     

Computational studies of thermoelectric MHD driven liquid lithium flow in metal trenches

The LiMIT system (Lithium/Metal Infused Trenches) is an innovative plasma-facing component for tokamak divertors, recently proposed at the University of Illinois. Thanks to the coupling of two metals having different Seebeck coefficients, the device is able to generate internal thermoelectric currents as a response to an incoming heat flux from the plasma. One of the two metals is liquid lithium and the second metal is a solid composing the trenches (tungsten, or molybdenum, or stainless steel, etc.). Together with the high toroidal magnetic field, the liquid lithium is propelled by a JxB electrodynamic force inside the solid trenches. In the present work we present a numerical characterization of the device. The diffusion–advection of heat is solved together with the Navier–Stokes equations forced by the JxB electrodynamic force, comprising the thermoelectric contribution. We report parametric plots to show the influence of the toroidal magnetic field and of the plasma heat flux. It is found that the average flow velocity of the liquid lithium peaks at a critical magnetic field, always lower than 1.0 T, and then decreases with an inverse law in the range of tokamak-relevant fields. The flow velocity of the lithium increases with a square-root law versus an increasing heat flux. The heat transfer coefficient of the cooling channels is parametrically investigated, revealing that coefficients higher than >4000 W/m² K are needed for the device in order to withstand heat fluxes of 10 MW/m².     

Equilibrium and stability of plasma in axially symmetric toroidal systems

Conclusions In the case when the magnetic surfaces have circular normal cross sections in the neighborhood of a magnetic axis (=1), the stability criterion reduces to a limitation on the ratio of the current density to the magnetic field on the magnetic axis j₀R/B₀<2. On the assumption of a uniform axial current, this criterion is equivalent to the Shafranov-Kruskal stability condition RB (a)/aB(a)<1/m for the first mode of oscillation m=1. If the current density falls off on going away from the magnetic axis, the stability criterion when written in the form of the Shafranov-Kruskal condition will correspond to m>1. For example, in the case of the parabolic current density distribution j=j₀ (1–₂/a ²), it turns out that m=2.To investigate the effect of the ellipticity of the magnetic surface cross sections, a study was made of the two cases when the external magnetic surface had an elliptical or semielliptical cross section. As can be seen from Figs. 2 and 4, the limiting value of j₀R/B₀ decreases rapidly when the semi-axis ratio is decreased below unity and decreases more smoothly when is increased above unity: (=l _z/l _r).In the case when toroidal aspects of the problem are very strongly expressed, when the external boundary of the plasma has a semi-elliptical cross section with a semi-axis ratio =1/2 (which corresponds to =1), the limiting ratio of the axial current in the plasma to the current in the windings of the solenoid producing the axial magnetic field amounts to J/I1/3, which corresponds to a ratio of plasma pressure to magnetic pressure 1/2.To investigate the effect of the toroidal geometry on the stability, we also investigated the case of a plasma torus in which the external magnetic surface was of rectangular cross section. As can be seen from Fig. 6, in the case when the axial magnetic field decreases on moving away from the magnetic axis (b/a>0) the limiting value of the ratio N=j₀R/B₀ is reduced somewhat with increasing toroidality, this reduction in N being associated with a corresponding increase in .In summary, as far as the conditions of hydromagnetic stability for a prescribed magnetic field are concerned, an increase in toroidality should lead to an increase in the limiting plasma current and pressure.Translated from Atomnaya Énergiya, Vol. 24, No. 5, pp. 453–459, May, 1968.     

Experimental Studies on Heat Transfer by Natural Convection and Pool Boiling of Sodium in a Strong Magnetic Field

This report deals with an experiment on the heat transfer of liquid sodium, with particular reference to the effects brought by the application of a magnetic field on pool boiling. The test section, a heater pin of 6.5 mm diameter, was inserted vertically into the center of a sodium tank. The heating surface of the pin was parallel to the magnetic field as well as to the direction of gravity.

Under conditions of natural convection in a magnetic field, a sharp rise of the heating surface temperature was always seen to occur at some point when the heat flux was gradually increased, accompanied by the onset of sharp temperature oscillations.

The surface superheat required for the initiation of boiling decreased with increasing intensity of the applied magnetic field, reached a minimum, then increased again.

The surface temperature fluctuations in nucleate boiling was higher under magnetic field than when free of such influence. The critical heat flux for burn-out was not appreciably affected by magnetic field.     

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.     

Zero Flux Eigenvalues of Relaxed Axisymmetric Compact Tokamaks (CT’s)

Compact toroidal configuration is of simpler construction than the conventional tokamak and has important advantages due to the novel physics properties of low aspect ratio. In this paper we are developing a numerical program to study the magnetic dynamo or relaxation of CT’s characterized by arbitrary tight aspect ratio. It is shown that the numerical method (Collocation Method), used here, works quite well to calculate numerically the lowest zero flux eigenvalues μ of Taylor’s relaxed plasma state equation [(?)\vec] ×[(B)\vec] = m[(B)\vec] \vec{\nabla } \times \vec{B} = \mu \vec{B} for an axisymmetric tokamaks of circular cross section. An excellent fulfillment of the toroidal flux vanishing boundary condition \iint B_? \textdr\textdz = 0 \iint {B_{\emptyset } {\text{d}}r{\text{d}}z = 0} along the whole boundary for such tokamaks are achieved. Dependence of μ on the aspect ratio is also obtained. Several runs of the program for various wave numbers k showed that μ is very insensitive to the choice of k. Besides, the poloidal magnetic field topologies inside the tokamak are well represented.     

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.     

Effect of a transverse magnetic field on a toroidal discharge in a strong longitudinal magnetic field

The effect of a transverse magnetic field on a toroidal discharge in a strong longitudinal magnetic field was studied. It was found that, for a definite value of the pinch displacement caused by the 1/c [I,B], force, the oscillations on the oscillograms of the electrical characteristics of the discharge had minimum amplitude, while the mean plasma conductivity reached a maximum. It was shown that the effect of the transverse component of the magnetic field could, in general, be explained from the concept of the equilibrium of the plasma pinch inside the conducting sheath.Translated from Atomnaya Énergiya, Vol. 17, No. 3, pp. 177–184, September, 1964.     

Pressure Drop of Liquid Mercury MHD Power Generators

This paper deals with experimental studies of performance characteristics of both constant-area (34×7×295 mm) and diverging-area (23×7 to 43×7×295 mm) MHD power generators with liquid mercury as working fluid, with particular reference to the pressure drop created in the inlet and outlet ducts as well as inside the generator channel, and comparisons are made with various theoretical results. Discussions are presented on the following aspects. In respect of the constant-area channel, pressure drop in laminar and turbulent flow inside the channel, transition Reynolds number for given Hartmann number, pressure drop in the inlet duct and eddy current created near the end of electrode, output electrical power. For diverging channel, applied magnetic field intensity required for zero pressure drop inside the channel, pressure distribution inside the channel, output electrical power in the case of zero pressure drop. The experimental conditions were as follows: Re10<⁵ and Ha<60.     

Gravitational flow of a thin film of liquid metal in a strong magnetic field

The influence of a poloidal magnetic field of the spherical Tokamak on super thin (h ≈ 0.1 mm) film flow of liquid metal driven by gravity over the surface of the cooled divertor plate is addressed. The experimental setup developed at the Institute of Physics, University of Latvia (IPUL) is described, which makes it possible to drive and visualize such liquid metal flows in the solenoid of the superconducting magnet “Magdalena”. As applied to the above setup, the magnetic field effect on the operation of the capillary system of liquid metal flow distribution (CSFD) is evaluated by using molten metal (lithium or eutectic InGaSn alloy) with a very small linear flowrate q ≤ 1 mm²/s, spread uniformly across the substrate. The magnetic field effect on the main parameters of the fully developed film flow is estimated for the above-mentioned liquid metals.An approximation technique has been proposed to calculate the development of the gravitational film flow. A non-linear differential second order equation has been derived, which describes the variation of the film flow thickness over the substrate length versus the flowrate q, magnetic field B and the substrate sloping α.Results of InGaSn film flow observations in a strong (B = 4 T) poloidal magnetic field are presented. Analysis of the video records evidences of experimental realization of a stable stationary film flow at width-uniform supply of InGaSn.