Solenoid Flux Research Articles

Safety factor profile control with reduced central solenoid flux consumption during plasma current ramp-up phase using a reinforcement learning technique

Safety factor profile control via active feedback control of electron temperature profile during a plasma current ramp-up phase of a DEMO reactor is investigated to minimize the magnetic flux consumption of a central solenoid (CS) for wide range of q profiles. It is shown that q profiles with positive, weak and reversed magnetic shear can be obtained with the resistive flux consumption less than 60% of the empirical estimation which is calculated using the Ejima constant of 0.45. For the optimization of the target electron temperature profile and feedback gain to control electron heating power, reinforcement learning technique is introduced. One important feature of the system trained by reinforcement learning is that it can optimize the target electron temperature adaptive to the present status of a plasma. This adaptive feature of the reinforcement learning enables to control q profiles even in the case that an effective charge profile is randomly modified and it is not measured directly.

Simulation of plasma current ramp-up with reduced magnetic flux consumption in JT-60SA

Current ramp-up with reduced central solenoid (CS) flux consumption in JT-60SA has been investigated using an integrated modeling code suite (TOPICS) with a turbulent model (CDBM). The plasma current can be ramped-up from 0.6 MA to 2.1 MA with no additional CS flux consumption if the plasma current is overdriven by neutral-beam-driven and bootstrap current. A time duration required for the current ramp-up without CS flux consumption becomes as long as 150 s in the scenario we have examined. In order to achieve a current overdrive condition from 0.6 MA, the current drive by a lower energy neutral beam (85 keV) is effective. A higher energy neutral beam (500 keV) cannot be used in this early phase with a low central electron density (~2 × 1019 m−3) due to large shine through loss, while it can be effectively used in the later phase. Therefore, the main current driver should be switched from the lower energy neutral beam to the higher energy neutral beam during the current ramp-up phase. As a result of an intensive auxiliary heating, plasma beta (the ratio of the plasma pressure to the magnetic pressure) becomes high. Ideal MHD instabilities of such high beta plasmas have been investigated using a linear ideal MHD stability analysis code (MARG2D). External kink modes which might affect the core plasma can be stabilized during the current ramp-up if there is a perfectly conducting wall at the location of the stabilizing plate and the vacuum vessel of JT-60SA and the plasma has a broader pressure profile with the H-mode pedestal and the internal transport barrier.

Non-inductive plasma start-up on NSTX and projections to NSTX-U using transient CHI

Transient coaxial helicity injection (CHI) in the National Spherical Torus Experiment (NSTX) has generated toroidal current on closed-flux surfaces without the use of the central solenoid. When induction from the central solenoid was added, CHI initiated discharges in NSTX achieved 1 MA of plasma current using 65% of the solenoid flux of standard induction-only discharges. In addition, the CHI-initiated discharges have lower density and a low normalized internal plasma inductance of 0.35, as desired for achieving advanced scenarios. Transient CHI will be used for non-inductive plasma start-up on the upgrade to NSTX (NSTX-U) that is now under construction. It will have numerous improvements that significantly enhance CHI start-up capability. The TSC code is now starting to be used for full discharge simulation, which includes solenoid-less start-up with CHI and subsequent non-inductive current ramp-up using neutral beams. These results suggest that the increased injector flux capability of NSTX-U should allow CHI start-up at more than the 400 kA level and that the new tangential neutral beam system on NSTX-U should be able to ramp the current to the 1 MA levels.

Conceptual design for the superconducting magnet system of a pulsed DEMO reactor

A methodology has been developed to consistently investigate, taking into account main reactor components, possible magnet solutions for a pulsed fusion reactor aiming at a large solenoid flux swing duration within the 2–3h range. In a conceptual approach, investigations are carried out in the equatorial plane, taking into account the radial extension of the blanket-shielding zone, of the toroidal field magnet system inner leg and of the central solenoid for estimation of the pulsed swing.Design criteria are presented for the radial extension of the superconducting magnets, which is mostly driven by the structures (casings and conductor jacket). Typical available cable current densities are presented as a function of the magnetic field and of the temperature margin.The magnet design criteria have been integrated into SYCOMORE, a code for reactor modeling presently in development at CEA/IRFM in Cadarache, using the tools of the EFDA Integrated Tokamak Modeling task force.Possible solutions are investigated for a 2GW fusion power reactor with different aspect ratios.The final adjustment of the DEMO pulsed reactor parameters will have to be consistently done, considering all reactor components, when the final goals of the machine will be completely clarified.

Experimental demonstration of tokamak inductive flux saving by transient coaxial helicity injection on national spherical torus experiment

Discharges initiated by transient coaxial helicity injection in National Spherical Torus Experiment have attained peak toroidal plasma currents up to 300 kA. When induction from the central solenoid is then applied, these discharges develop up to 300 kA additional current compared to discharges initiated by induction only. CHI initiated discharges in NSTX have achieved 1 MA of plasma current using only 258 mWb of solenoid flux whereas standard induction-only discharges require about 50% more solenoid flux to reach 1 MA. In addition, the CHI-initiated discharge has lower plasma density and a low normalized internal plasma inductance of 0.35, as needed for achieving advanced scenarios in NSTX.

Overview of physics results from NSTX

In the last two experimental campaigns, the low aspect ratio NSTX has explored physics issues critical to both toroidal confinement physics and ITER. Experiments have made extensive use of lithium coatings for wall conditioning, correction of non-axisymmetric field errors and control of n = 1 resistive wall modes (RWMs) to produce high-performance neutral-beam heated discharges extending to 1.7 s in duration with non-inductive current fractions up to 0.7. The RWM control coils have been used to trigger repetitive ELMs with high reliability, and they have also contributed to an improved understanding of both neoclassical tearing mode and RWM stabilization physics, including the interplay between rotation and kinetic effects on stability. High harmonic fast wave (HHFW) heating has produced plasmas with central electron temperatures exceeding 6 keV. The HHFW heating was used to show that there was a 20–40% higher power threshold for the L–H transition for helium than for deuterium plasmas. A new diagnostic showed a depletion of the fast-ion density profile over a broad spatial region as a result of toroidicity-induced Alfvén eigenmodes (TAEs) and energetic-particle modes (EPMs) bursts. In addition, it was observed that other modes (e.g. global Alfvén eigenmodes) can trigger TAE and EPM bursts, suggesting that fast ions are redistributed by high-frequency AEs. The momentum pinch velocity determined by a perturbative technique decreased as the collisionality was reduced, although the pinch to diffusion ratio, Vpinch/χϕ, remained approximately constant. The mechanisms of deuterium retention by graphite and lithium-coated graphite plasma-facing components have been investigated. To reduce divertor heat flux, a novel divertor configuration, the ‘snowflake’ divertor, was tested in NSTX and many beneficial aspects were found. A reduction in the required central solenoid flux has been realized in NSTX when discharges initiated by coaxial helicity injection were ramped in current using induction. The resulting plasmas have characteristics needed to meet the objectives of the non-inductive start-up and ramp-up program of NSTX.

MAST Upgrade centre column design and analysis

The MAST-U (Mega-Amp Spherical Tokamak Upgrade) experiment is now being designed and will involve significant advances over the existing MAST machine, including increasing the toroidal field from 0.52 to 0.78 Tesla, the solenoid flux swing from 0.9 to 1.7 volt-seconds and the pulse length from 0.5 to 5 seconds (at 0.54 Tesla toroidal field). To meet these and other enhancements, the existing MAST centre column sub-assembly will be completely replaced in MAST-U. This sub-assembly comprises (a) the centre rod which forms the inner legs of the TF circuit, (b) the solenoid which fits closely over the centre rod, (c) the “air side” coils which are for plasma shaping – one within the bore of the centre rod (Pc) and one outside the solenoid (Px), (d) the two stainless steel crowns which are keyed and bonded to the ends of the centre rod for torsional support and (e) axial supports for the solenoid and airside coils. This paper describes the detailed design of the centre rod and the solenoid magnets and the means to manage the increased twisting torque on the centre rod (138 kNm in MAST-U compared with 58 kNm on MAST) due to the interaction of these two magnets.

Reduction of low-Z impurities during plasma start-up

Reduction of low-Z impurities is essential during the plasma start-up in tokamaks. For plasma start-up using the method of Coaxial Helicity Injection (CHI) it has been found that conventional wall conditioning methods have been inadequate to generate a plasma with acceptably low levels of low-Z impurities. NSTX has now used a new combination of techniques to improve CHI start-up performance. These are the use of high-current discharge cleaning of the lower divertor surfaces, which function as the CHI electrodes, to remove loosely bound impurities, controlling the poloidal magnetic field to avoid plasma wall contact and the use of evaporated lithium coatings of the electrodes and other plasma-facing surfaces. Together, these techniques have enabled significant improvement in NSTX CHI performance leading to a saving of central solenoid flux and the first observation of electron temperatures during CHI exceeding the oxygen radiation barrier temperature.

Feedback control of the lower hybrid power deposition profile on Tore Supra

The Tore Supra facility is well suited to study ITER relevant topics such as the real-time control of plasma current and the sustaining of steady-state discharges. This work describes a tool that was recently developed and implemented on Tore Supra to control in real time, by means of the direct knowledge of the suprathermal electron local emission profile, the width of the lower hybrid power deposition profile. This quantity can be considered to some extent equivalent to the width of the plasma current density profile in case of fully non-inductive discharges. This system takes advantage of an accurate hard x-ray diagnostics, of an efficient lower hybrid additional heating and of a reliable real-time communication network. The successful experiments carried out to test the system employed, as actuators, the parallel refractive index n// and the total power PLH. The control of the suprathermal electron local emission profile through n// was also integrated with the feedback control of the total plasma current IP with PLH and of the loop voltage Vloop with the central solenoid flux. These results demonstrate that the system is robust, reliable and able to counterbalance destabilizing events. This tool can be effectively used in the future in fully non-inductive discharges to improve the MHD stability and to maintain internal transport barriers or lower hybrid enhanced performance modes. The real-time control of the lower hybrid power deposition profile could also be used in conjunction with the electron-cyclotron radiofrequency heating for synergy studies.

Discussion About the Size of a Future Fusion Demonstration Reactor: The Impact of the Toroidal Magnetic Field

In parallel to ITER preparation, power plant conceptual studies have been carried out in Europe as a guideline for the main design parameters of a fusion demonstration reactor, the construction of which is scheduled to start twenty years hence. A key component of this fusion demonstration reactor is the superconducting magnetic system, which represents in ITER 30% of the investment cost. A high toroidal confinement field Bt, can help to moderate the major radius of the tokamak, and thereby the investment cost of the machine. Two versions of such a demonstration reactor, with different values of Bt will be compared in terms of volume, radial extension for the toroidal field magnet inner leg, central solenoid available flux swing and investment cost.

Plasma formation in START and MAST spherical tokamaks

Different methods of plasma formation have been studied in spherical tokamaks (ST). In inductive methods, breakdown and formation of ST plasma are achieved through the application of an electric field produced by a rapid change of currents in poloidal field coils, in the central solenoid or by using internal electrodes. In non-inductive methods, breakdown and formation of ST plasma are achieved by the application of radio frequency (RF) power, neutral beam injection or other ionization and current drive techniques. A combination of these methods is often used. Inductive methods utilizing flux from the central solenoid have limited performance as there is limited space for the central solenoid in STs, so methods not using the central solenoid flux are of special interest. In this paper we discuss different methods developed and used on the START and MAST STs at Culham; in particular, direct induction and electron cyclotron resonance preionization assisted formation are discussed in detail. These experiments have been performed at different RF frequencies and results of these studies are compared with the theory. Other methods, for example, the merging–compression and the double-null merging, are mentioned and prospects of different formation methods for future STs are discussed.

Experimental demonstration of plasma startup by coaxial helicity injection

Experimental results on the transfer of a coaxial-helicity-injection (CHI) produced discharge to inductive operation are reported. CHI assisted plasma startup is more robust than inductive only operation and reduces volt-seconds consumption. After handoff to inductive operation, the initial 100 kA of CHI produced current drops to 50 kA, then ramps up to 180 kA, using only 30 mVs, about 40% higher than that produced by induction alone. Results show that initiation of CHI discharges at lower densities produce higher levels of coupling current. Coupling a CHI produced discharge to induction from a precharged central solenoid has produced record currents of 290 kA using only 52 mWb of central solenoid flux. CHI discharges can also be generated while the central transformer is in the process of being precharged, during which period it induces a negative loop voltage on the CHI discharge. These significant results were obtained on the Helicity Injected Torus-II (HIT-II) [T.R. Jarboe, Fusion Technol. 15, 7 (1989)] spherical torus experiment (major/minor radius of 0.3/0.2 m and elongation of 1.5).

Next-step-targeted experiments on the Mega-Amp Spherical Tokamak

Since its first physics campaign, the principal parameters on MAST (Mega-Amp Spherical Tokamak) [A. Sykes et al., Nuclear Fusion 41, 1423 (2001)] have been brought up towards their design values. Considerable advances have been made in a range of physics areas of direct relevance to the International Thermonuclear Experimental Reactor (ITER) [ITER Physics Basis, Nuclear Fusion 39, 2175 (1999)]. In this paper, results on H-mode access, global confinement and pedestal studies are presented and compared with conventional aspect ratio tokamak scalings. Physics and engineering requirements relevant to next step spherical tokamak devices are discussed, in particular the plasma formation, current ramp-up and sustainment, and plasma exhaust. Results of first experiments directly targeting these issues are presented: Plasma current up to 0.5 MA has been produced without use of the central solenoid flux, and current ramp-up and sustainment without use of the central solenoid flux has been demonstrated. Experiments on neutral beam heating and current drive (CD) demonstrate up to 50% bootstrap current fraction and good CD efficiency, and divertor power loading has been found to be tolerable and have a favorable outboard asymmetry.

First results from MAST

MAST is one of the new generation of large, purpose-built spherical tokamaks (STs)now becoming operational, designed to investigate the properties of the ST in large, collisionless plasmas. The first six months of MAST operations have been remarkably successful. Operationally, both merging-compression and the more usual solenoid induction schemes have been demonstrated, the former providing over 400 kA of plasma current with no demand on solenoid flux. Good vacuum conditions and operational conditions, particularly after boronization in trimethylated boron, have provided plasma current of over 1 MA with central plasma temperatures (ohmic) of order 1 keV. The Hugill and Greenwald limits can be exceeded and H mode achieved at modest additional NBI power. Moreover, particle and energyconfinement show an immediate increase at the L-H transition, unlike the case of START, where this became apparent only at the highest plasma currents. Halo currents are small, with low toroidal peaking factors, in accordance with theoretical predictions, and there is evidence of a resilience to the major disruption.

Inductive plasma current start-up by the outer vertical field coil in a spherical tokamak

Plasma current-start up induced by an outer vertical field coil is studied during the ignition access phase in a spherical tokamak reactor. We have illustrated the concept that the plasma current of ~50 MA could be induced by the outer vertical field coil in the proposed spherical tokamak with the help of the small central solenoid flux of ±5 V s and the strong heating power less than 100 MW for the internal inductance of i~0.4-0.8 without the help of bootstrap current and non-inductive current drive power. The required condition to achieve this operation scenario is that the flux produced by the equilibrium vertical field is larger than the inductive flux. Current start-up operation is achieved by adding the small ohmic heating solenoid flux for the flux waveform adjustment because the flux from the outer vertical field coil cannot solely induce the desired plasma current waveform in the case of the preprogramming of the heating power.

Effect of Coulomb repulsion and magnetic frustration on persistent currents in the Hubbard model

The interplay between Coulomb repulsion and magnetic frustration and its effect on persistent currents in the Hubbard model are studied. We consider a system of tight-binding electrons confined to a cylindrical geometry subject to a solenoid flux threading its center and a magnetic field perpendicular to the face. Here, the magnetic field introduces frustration, the flux per plaquette in units of flux quantum, $f=p/q$ with p and q being relative prime integer. Mean-field calculations show that the on-site Coulomb repulsion decreases the persistent current by opening a gap at the Fermi level. The suppressive role of the Coulomb interaction is influenced by the frustration, which depends on the parity of q for the half-filled case. For odd q, the persistent current is suppressed by the frustration, but the opposite is true for even q; i.e., the frustration reduces the interaction effect and enhances the persistent current.

The design and operation of the SPHEX spheromak

We describe the design and operation of the SPHEX spheromak device and present an overview of its behaviour. The plasma is formed by ejection from a magnetized Marshall gun, and can be sustained as long as the gun is energized. The plasma is divided into the annulus comprising the closed toroidal flux, linked with the open flux forming the central column. The column current is driven directly by the central gun electrode, and the toroidal current in the annulus is driven indirectly by a mechanism associated with a coherent n = 1 oscillation of the column. The configuration exemplifies the operation of the process of relaxation to a state of minimum magnetic energy, which leads to magnetic configurations similar to those observed; to sustain these configurations requires some mechanism of toroidal current drive. Associated with this is the amplification of the poloidal flux, which is typically a factor of about five larger than the flux generated by the gun solenoid; the constancy (to a first approximation) of this factor plays a controlling role in spheromak behaviour. In standard operating conditions there is a `hard' limit, set by the solenoid flux, on the current carried by the column; any current driven by the external circuit above this apparently does not emerge from the gun. Evidence is presented that the column current is carried largely (> 50%) by accelerated ions with energy up to the gun voltage ( for a typical gun current of 60 kA). These ions are poorly magnetized and can escape across the magnetic field to the wall, a likely mechanism for the observed `loss' of current. Hydrogen is the normal operating gas: other gases ( and He) have been used, but the current drive is found to be less effective than in , with lower toroidal current maintained in the annulus.

The Modeling and Simulation of a Proportional Solenoid Valve

A nonlinear dynamic model of a high speed direct acting solenoid valve is presented. The valve consists of two subsystems; a proportional solenoid and a spool assembly. These two subsystems are modeled separately. The solenoid is modeled as a nonlinear resistor/inductor combination, with inductance parameters that change with displacement and current. Empirical curve fitting techniques are used to model the magnetic characteristics of the solenoid, enabling both current and magnetic flux to be simulated. The spool assembly is modeled as a spring/mass/damper system. The inertia and damping effects of the armature are incorporated in the spool model. The solenoid model is used to estimate the spool force in order to obtain a suitable damping coefficient value. The model accurately predicts both the dynamic and steady-state response of the valve to voltage inputs. Simulated voltage, current, and displacement results are presented, which agree well with experimental results.

On Aharonov-Bohm Effect in Multiconnected Superconductor

is zero in the whole particle localization region {P}, is known as the AharonovBohm effect. The AB-effect is the consequence of the main axiom of quantum mechanics, asserting the single-valuedness of the particle wave function Ψ(r) when r rounds a closed curve in {P} [1]. Numerous experiments were realized during the period 1960-1980 to reveal the AB-effect because of its big importance in physics foundations understanding. In most of these experiments the electron microscopy technique was used. Meanwhile, it has been already noted in [1] that superconduction are the objects in which the AB-effect leads to non-trivial consequences. In fact, the effect was observed, when one placed a long narrow solenoid into the coil of SQUID and varied the current Is through the solenoid. As the Josephson current Ic of SQUID depends on the phase shift Δ0 between electron waves, passed through the upper and the lower halves of coil and Δθ is determined by the vector potential of solenoid, the increase in I s produces the periodical change of Ic (Is ), although H = 0 for any Is [2]. One can abandon, in principle, current feed wires of the coil and observe Ic oscillations, measuring its magnetic field Hind alterations. Namely, it was shown in [3] that the sum of the coil flux Φi nd and the solenoid flux

Flux quantization in a hollow superconducting cylinder with a solenoid inside a cavity

The behavior of a hollow superconducting cylinder with a long solenoid inside a cavity is considered within the framework of the Ginzburg-Landau theory. The general form is found of the thermodynamic potential of the system, which describes its behavior under the influence of the solenoid's field. It is shown that the magnetic field appears inside a cavity, when the solenoid's flux is not zero. The total flux in the system changes by jumps, due to the effect of flux quantization. The dependence of the superconducting order parameter on the solenoid's flux is found, the phase diagram of the superconducting states is analyzed. The hysteresis transitions in the system are investigated, as well as oscillations of the critical temperature and of the specific heat of the cylinder. The connection with the paper of G. Kunstatter, M. Revzen, and L. E. H. Trainor ( Ann. Phys. (N.Y.) 145 (1983), 329), where the corresponding problem was first touched upon, is discussed.