Low Internal Inductance Research Articles

Progress in extending high poloidal beta scenarios on DIII-D towards a steady-state fusion reactor and impact of energetic particles

To prepare for steady-state operation of future fusion reactors (e.g. the International Thermonuclear Experimental Reactor and China Fusion Engineering Test Reactor (CFETR)), experiments on DIII-D have extended the high poloidal beta (βP) scenario to reactor-relevant edge safety factor q95 ∼ 6.0, while maintaining a large-radius internal transport barrier (ITB) using negative magnetic shear. Excellent energy confinement quality (H98y2 > 1.5) is sustained at high normalized beta (βN ∼ 3.5). This high-performance ITB state with Greenwald density fraction near 100% and qmin ≥ 3 is achieved with toroidal plasma rotation Vtor ∼ 0 at ρ ≥ 0.6. This is a key result for reactors expected to have low Vtor. At high βP (≥1.9), large Shafranov shift can stabilize turbulence leading to a high confinement state with a low pedestal and an ITB. At lower βP (<1.9), negative magnetic shear in the plasma core contributes to turbulence suppression and can compensate for reduced Shafranov shift to continue to access a large-radius ITB and excellent confinement with low Vtor, consistent with the results of gyrofluid transport simulations. These high-βP cases are characterized by weak/no Alfvén eigenmodes (a.e.) and classical fast-ion transport. At high density, the fast-ion deceleration time decreases and Δβfast is lower; these reduce a.e. drive. The reverse-shear Alfvén eigenmodes are weaker or stable because the negative magnetic shear region is located at higher radius, away from the peaked fast-ion profile. Resistive wall modes can be a limitation at simultaneous high βN, low internal inductance, and low rotation. Analysis suggests that additional off-axis external current drive could provide a more stable path at reduced q95. Based on a DIII-D high-βP plasma with large-radius ITB, two scenarios are proposed for CFETR Q = 5 steady-state operation with ∼1 GW fusion power: a lower- ( ∼ 0.66) and a higher- ( ∼ 0.75) case. Using a Landau closure model, multiple energetic particle (EP) effects on the a.e. stability are analyzed modifying the growth rate of the a.e.s triggered by the neutral-beam-injection EPs and alpha particles, although the stabilizing/destabilizing effect is weak for the cases analyzed. The stabilizing effects of the combined EP species β, energy, and density profile in CFETR need further investigation.

Dependence of the internal inductance on the radial distance between the primary and secondary X-point surfaces in the EAST tokamak

In view of their advantage in long-pulse high-performance operations, low internal inductance scenarios are being developed and tested for the EAST and other tokamaks. Dependence of the internal inductance on several main plasma configuration parameters are statistically analyzed. It is found that the internal inductance of the plasma is closely related to the radial distance between the primary and secondary X-point surfaces on the outer mid-plane as well as the poloidal field of the last closed flux surface. Moreover, is also related to the distribution of the fast electrons driven by the injected lower-hybrid waves, which is partially responsible for the observed relation between and the internal inductance. The results here should therefore be helpful as a guide for future experiments on internal inductance control and long-pulse operations of the EAST and other tokamaks, as well as for detailed theoretical study of the underlying physics.

Coreless AFPM Pulsed Alternator With Low Internal Inductance

The linear induction launcher consists of two parts: the barrel section and the projectile section. The barrel contains of a long coaxial sectionalized group of coils that are energized by a capacitor bank or generator sets. This paper deals with the design, implementation, and experimental test of a coreless axial-flux permanent magnet (AFPM) pulsed alternator with a flywheel system as an energy source for linear induction coil launchers. The proposed coreless AFPM generator has a low internal inductance and resistance of stator windings without compensation windings when compared with the conventional iron core machines. This paper describes the coreless AFPM generator configuration and shows the simulation findings.

Non-inductively driven tokamak plasmas at near-unity βt in the Pegasus toroidal experiment

A major goal of the spherical tokamak (ST) research program is accessing a state of low internal inductance ℓi, high elongation κ, and high toroidal and normalized beta (βt and βN) without solenoidal current drive. Local helicity injection (LHI) in the Pegasus ST [Garstka et al., Nucl. Fusion 46, S603 (2006)] provides non-solenoidally driven plasmas that exhibit these characteristics. LHI utilizes compact, edge-localized current sources for plasma startup and sustainment. It results in hollow current density profiles with low ℓi. The low aspect ratio (R0/a∼1.2) of Pegasus allows access to high κ and high normalized plasma currents (IN=Ip/aBT&amp;gt;14). Magnetic reconnection during LHI provides auxiliary ion heating. Together, these features provide access to very high βt plasmas. Equilibrium analyses indicate that βt up to ∼100% is achieved. These high βt discharges disrupt at the ideal no-wall β limit at βN∼7.

Scenario development during commissioning operations on the National Spherical Torus Experiment Upgrade

The National Spherical Torus Experiment Upgrade (NSTX-U) will advance the physics basis required for achieving steady-state, high-beta, and high-confinement conditions in a tokamak by accessing high toroidal fields (1 T) and plasma currents (1.0–2.0 MA) in a low aspect ratio geometry (A = 1.6–1.8) with flexible auxiliary heating systems (12 MW NBI, 6 MW HHFW). This paper describes the progress in the development of L- and H-mode discharge scenarios and the commissioning of operational tools in the first ten weeks of operation that enable the scientific mission of NSTX-U. Vacuum field calculations completed prior to operations supported the rapid development and optimization of inductive breakdown at different values of ohmic solenoid current. The toroidal magnetic field (BT0 = 0.65 T) exceeded the maximum values achieved on NSTX and novel long-pulse L-mode discharges with regular sawtooth activity exceeded the longest pulses produced on NSTX (tpulse > 1.8 s). The increased flux of the central solenoid facilitated the development of stationary L-mode discharges over a range of density and plasma current (Ip). H-mode discharges achieved similar levels of stored energy, confinement (H98y,2 > 1) and stability (βN/βN-nowall > 1) compared to NSTX discharges for Ip ⩽ 1 MA. High-performance H-mode scenarios require an L–H transition early in the Ip ramp-up phase in order to obtain low internal inductance (li) throughout the discharge, which is conducive to maintaining vertical stability at high elongation (κ > 2.2) and achieving long periods of MHD quiescent operations. The rapid progress in developing L- and H-mode scenarios in support of the scientific program was enabled by advances in real-time plasma control, efficient error field identification and correction, effective conditioning of the graphite wall and excellent diagnostic availability.

Noninductively Driven Tokamak Plasmas at Near-Unity Toroidal Beta.

Access to and characterization of sustained, toroidally confined plasmas with a very high plasma-to-magnetic pressure ratio (β_{t}), low internal inductance, high elongation, and nonsolenoidal current drive is a central goal of present tokamak plasma research. Stable access to this desirable parameter space is demonstrated in plasmas with ultralow aspect ratio and high elongation. Local helicity injection provides nonsolenoidal sustainment, low internal inductance, and ion heating. Equilibrium analyses indicate β_{t} up to ∼100% with a minimum |B| well spanning up to ∼50% of the plasma volume.

Design and Analysis of a Two-Phase Two-Axis-Compensated Compulsaor

As power supplies, compulsators are popular choices for electromagnetic railguns. In this paper, a two-phase two-axis-compensated compulsator (2P2AC compulsator) with lower internal inductance and higher power density was designed and analyzed. Two-phase armature windings are allocated on the stator, and discharge pulse currents to the load via a rectifier. This arrangement decouples the machine speed from the pulsewidth, thus enables a higher tip speed. Two sets of windings with electrical orthogonal displacement are allocated on the rotor. The bigger one is the field winding that freewheels via a diode and provides the direct-axis compensation during the discharge process, while the smaller one is the short-circuit compensating winding providing the quadrature-axis compensation. The effect of the composition of the d- and q-axis compensation is equivalent to a passive compensation using a continuous conductive shield, which compresses the flux for all rotor positions. Compared with the passive compensation, this arrangement has no conductive path to couple with the field winding due to the orthogonal displacement, thus speeding up the charging process. This paper presents the design methodology of the 2P2AC compulsator, along with its system performance of driving railgun load.

ITER-like current ramps in JET with ILW: experiments, modelling and consequences for ITER

Since the ITER-like wall in JET (JET-ILW) came into operation, dedicated ITER-like plasma current (Ip) ramp-up (RU) and ramp-down (RD) experiments have been performed and matched to similar discharges with the carbon wall (JET-C). The experiments show that access to H-mode early in the Ip RU phase and maintaining H-mode in the Ip RD as long as possible are instrumental to achieve low internal plasma inductance (li) and to minimize flux consumption. In JET-ILW, at a given current rise rate similar variations in li (0.7–0.9) are obtained as in JET-C. In most discharges no strong W accumulation is observed. However, in some low density cases during the early phase of the Ip strong core radiation due to W influx led to hollow electron temperature (Te) profiles. In JET-ILW Zeff is significantly lower than in JET-C. W significantly disturbs the discharge evolution when the W concentration approaches 10−4; this threshold is confirmed by predictive transport modelling using the CRONOS code. Ip RD experiments in JET-ILW confirm the result of JET-C that sustained H-mode and elongation reduction are both instrumental in controlling li.

Recent progress towards an advanced spherical torus operating point in NSTX

Progress in the development of integrated advanced ST plasma scenarios in NSTX (Ono et al 2000 Nucl. Fusion 40 557) is reported. Recent high-performance plasmas in NSTX following lithium coating of the plasma facing surfaces have achieved higher elongation and lower internal inductance than previously. Analysis of the thermal confinement in these lithiumized discharges shows a stronger plasma current and weaker toroidal field dependence than in previous ST confinement scaling studies; the ITER-98(y, 2) scaling expression describes these scenarios reasonably well. Analysis during periods free of MHD activity has shown that the reconstructed current profile can be understood as the sum of pressure driven, inductive and neutral beam driven currents, without requiring any anomalous fast-ion transport. Non-inductive fractions of 65–70%, and βP > 2, have been achieved at lower plasma current. Some of these low-inductance discharges have a significantly reduced no-wall βN limit, and often have βN at or near the with-wall limit. Coupled m/n = 1/1 + 2/1 kink/tearing modes can limit the sustained β values when rapidly growing ideal modes are avoided. A βN controller has been commissioned and utilized in sustaining high-performance plasmas. ‘Snowflake’ divertors compatible with high-performance plasmas have been developed. Scenarios with significantly larger aspect ratios have also been developed, in support of next-step ST devices. Overall, these NSTX plasmas have many characteristics required for next-step ST devices.

Demonstration of 300 kA CHI-startup current, coupling to transformer drive and flux savings on NSTX

Discharges formed by transient coaxial helicity injection (CHI) in the National Spherical Torus Experiment (NSTX) have attained peak currents of 300 kA for the first time. CHI-started discharges are coupled to induction, and ramped up to over 1 MA. Up to an additional 400 kA of toroidal current is produced, compared with discharges with the same inductive drive without CHI. These CHI-inductively coupled discharges demonstrate flux savings over standard NSTX inductive-only discharges, requiring significantly less transformer flux to reach 1 MA of toroidal current, as well as exhibiting higher elongation and lower internal inductance. These results indicate the potential for substantial current generation capability by CHI in NSTX and in future toroidal devices.

Equilibrium and global MHD stability study of KSTAR high beta plasmas under passive and active mode control

The Korea Superconducting Tokamak Advanced Research, KSTAR, is designed to operate a steady-state, high beta plasma while retaining global magnetohydrodynamic (MHD) stability to establish the scientific and technological basis of an economically attractive fusion reactor. An equilibrium model is established for stability analysis of KSTAR. Reconstructions were performed for the experimental start-up scenario and experimental first plasma operation using the EFIT code. The VALEN code was used to determine the vacuum vessel current distribution. Theoretical high beta equilibria spanning the expected operational range are computed for various profiles including generic L-mode and DIII-D experimental H-mode pressure profiles. Ideal MHD stability calculations of toroidal mode number of unity using the DCON code shows a factor of 2 improvement in the wall-stabilized plasma beta limit at moderate to low plasma internal inductance. The planned stabilization system in KSTAR comprises passive stabilizing plates and actively cooled in-vessel control coils (IVCCs) designed for non-axisymmetric field error correction and stabilization of slow timescale MHD modes including resistive wall modes (RWMs). VALEN analysis using standard proportional gain shows that active stabilization near the ideal wall limit can be reached with feedback using the midplane segment of the IVCC. The RMS power required for control using both white noise and noise taken from NSTX active stabilization experiments is computed for beta near the ideal wall limit. Advanced state-space control algorithms yield a factor of 2 power reduction assuming white noise while remaining robust with respect to variations in plasma beta.

Overview of results from the National Spherical Torus Experiment (NSTX)

The mission of the National Spherical Torus Experiment (NSTX) is the demonstration of the physics basis required to extrapolate to the next steps for the spherical torus (ST), such as a plasma facing component test facility (NHTX) or an ST based component test facility (ST-CTF), and to support ITER. Key issues for the ST are transport, and steady state high β operation. To better understand electron transport, a new high-k scattering diagnostic was used extensively to investigate electron gyro-scale fluctuations with varying electron temperature gradient scale length. Results from n = 3 braking studies are consistent with the flow shear dependence of ion transport. New results from electron Bernstein wave emission measurements from plasmas with lithium wall coating applied indicate transmission efficiencies near 70% in H-mode as a result of reduced collisionality. Improved coupling of high harmonic fast-waves has been achieved by reducing the edge density relative to the critical density for surface wave coupling. In order to achieve high bootstrap current fraction, future ST designs envision running at very high elongation. Plasmas have been maintained on NSTX at very low internal inductance li ∼ 0.4 with strong shaping (κ ∼ 2.7, δ ∼ 0.8) with βN approaching the with-wall β-limit for several energy confinement times. By operating at lower collisionality in this regime, NSTX has achieved record non-inductive current drive fraction fNI ∼ 71%. Instabilities driven by super-Alfvénic ions will be an important issue for all burning plasmas, including ITER. Fast ions from NBI on NSTX are super-Alfvénic. Linear toroidal Alfvén eigenmode thresholds and appreciable fast ion loss during multi-mode bursts are measured and these results are compared with theory. The impact of n > 1 error fields on stability is an important result for ITER. Resistive wall mode/resonant field amplification feedback combined with n = 3 error field control was used on NSTX to maintain plasma rotation with β above the no-wall limit. Other highlights are results of lithium coating experiments, momentum confinement studies, scrape-off layer width scaling, demonstration of divertor heat load mitigation in strongly shaped plasmas and coupling of coaxial helicity injection plasmas to ohmic heating ramp-up. These results advance the ST towards next step fusion energy devices such as NHTX and ST-CTF.

Current profile tailoring using localized electron cyclotron heating in highly elongated TCV plasmas

Radially localized electron cyclotron heating (ECH) at the 2nd harmonic (X2) is used to tailor the current profile through the modification of the temperature, and hence conductivity, profiles. The optimal conditions for current profile broadening are investigated and applied to decrease the plasma internal inductance at constant plasma current. Highly elongated plasmas are thus created at low current, where they are vertically unstable with peaked Ohmic current profiles, using active current profile broadening by far off-axis X2 ECH to ensure the vertical stability of the plasma. Central 3rd harmonic (X3) ECH is also applied and its impact on the current profile is described. The magnetohydrodynamic activity and in particular the replacement of the sawtooth by a multi-harmonics mode, resonant on the q = 1 surface and observed at high density and low internal inductance, is investigated.

Access to sustained high-beta with internal transport barrier and negative central magnetic shear in DIII-D

High values of normalized β (βN∼4) and safety factor (qmin∼2) have been sustained simultaneously for ∼2s in DIII-D [J.L. Luxon, Nucl. Fusion 42, 64 (2002)], suggesting a possible path to high fusion performance, steady-state tokamak scenarios with a large fraction of bootstrap current. The combination of internal transport barrier and negative central magnetic shear at high β results in high confinement (H89P&amp;gt;2.5) and large bootstrap current fraction (fBS&amp;gt;60%) with good alignment. Previously, stability limits in plasmas with core transport barriers have been observed at moderate values of βN (&amp;lt;3) because of the pressure peaking which normally develops from improved core confinement. In recent DIII-D experiments, the internal transport barrier is clearly observed in the electron density and in the ion temperature and rotation profiles at ρ∼0.5 but not in the electron temperature profile, which is very broad. The misalignment of Ti and Te gradients may help to avoid a large local pressure gradient. Furthermore, at low internal inductance ∼0.6, the current density gradients are close to the vessel and the ideal kink modes are strongly wall-coupled. Simultaneous feedback control of both external and internal sets of n=1 magnetic coils was used to maintain optimal error field correction and resistive wall mode stabilization, allowing operation above the free-boundary β limit. Large particle orbits at high safety factor in the core help to broaden both the pressure and the beam-driven current profiles, favorable for steady-state operation. At plasma current flat top and β∼5%, a noninductive current fraction of ∼100% has been observed. Stability modeling shows the possibility for operation up to the ideal-wall limit at β∼6%.

Aspect ratio scaling of ideal no-wall stability limits in high bootstrap fraction tokamak plasmas

Recent experiments in the low aspect ratio National Spherical Torus Experiment (NSTX) [M. Ono et al., Nucl. Fusion 40, 557 (2000)] have achieved normalized beta values twice the conventional tokamak limit at low internal inductance and with significant bootstrap current. These experimental results have motivated a computational re-examination of the plasma aspect ratio dependence of ideal no-wall magnetohydrodynamic stability limits. These calculations find that the profileoptimized no-wall stability limit in high bootstrap fraction regimes is well described by a nearly aspect ratio invariant normalized beta parameter utilizing the total magnetic field energy density inside the plasma. However, the scaling of normalized beta with internal inductance is found to be strongly aspect ratio dependent at sufficiently low aspect ratio. These calculations and detailed stability analyses of experimental equilibria indicate that the nonrotating plasma no-wall stability limit has been exceeded by as much as 30% in NSTX in a high bootstrap fraction regime.

β-Limiting MHD instabilities in improved-performance NSTX spherical torus plasmas

Global magnetohydrodynamic (MHD) stability limits in the National Spherical Torus Experiment (NSTX) have increased significantly recently due to a combination of device and operational improvements. First, more routine H-mode operation with broadened pressure profiles allows access to higher normalized β and lower internal inductance. Second, the correction of a poloidal field coil induced error-field has largely eliminated locked tearing modes during normal operation and increased the maximum achievable β. As a result of these improvements, peak β values have reached (not simultaneously) βT = 35%, βN = 6.4, ⟨βN⟩ = 4.5, βN/li = 10, and βP = 1.4. High βP operation with reduced tearing activity has allowed a doubling of discharge pulse-length to just over 1 s with sustained periods of βN≈6 above the ideal no-wall limit and near the with-wall limit. Details of the β-limit scalings and β-limiting instabilities in various operating regimes are described.

Control of the resistive wall mode in advanced tokamak plasmas on DIII-D

Resistive wall mode (RWM) instabilities are found to be a limiting factor in advancedtokamak regimes with low internal inductance. Even small amplitude modes can affect therotation profile and the performance of these ELMing H mode discharges. Although completestabilization of the RWM by plasma rotation has not yet been observed, several dischargeswith increased beam momentum and power injection sustained good steady state performancefor record durations. The first investigation of active feedback control of the RWM hasshown promising results: the leakage of radial magnetic flux through the resistive wall canbe successfully controlled and the duration of the high beta phase can be prolonged. Theresults provide a comparative test of several approaches to active feedback control, andare being used to benchmark the analysis and computational models of active control.

MHD beta limits for advanced scenarios on JET

Ideal MHD limits to beta and bootstrap fraction are computed for pressure profiles similar to those of JET discharges with both internal and H mode transport barriers. Several non-monotonic current profiles are tested, and the pressure profile is constrained so that no negative current drive is required in steady state. Calculations are made both with and without an ideally conducting wall. The main result is that, for such peaked pressure profiles, the limits to beta and bootstrap fraction improve at low internal inductance, in particular when wall stabilization is taken into account. The highest limits to beta, and often also to normalized beta, occur for the maximum plasma current. There is also a weak dependence on qmin, for which three favourable regions have been identified. A highly advantageous region is found at qmin ≃ 1.6, where the limits to β* are 7.0% with, and 4.8% without, wall stabilization. The corresponding limits are 68 and 50%, respectively, for the bootstrap fraction and 4.0 and 2.9 for the normalized beta. These equilibria have low internal inductance, li = 0.62. For higher inductance, an optimum occurs when qmin ≃ 1.2, where the limit to β* is 5.3% with a wall and 4.7% without. The corresponding bootstrap fractions are about 46 and 38%, respectively. A third type of equilibrium that is interesting for steady state operation has qmin ≃ 2.1 and low inductance. Here the β* limits are lower, 4.9 and 3.4%, but the bootstrap fractions are higher, 77 and 60%.

Systematic study of toroidicity-induced Alfvén eigenmodes at low-q discharges in JT-60U

Toroidicity-induced Alfvén eigenmodes (TAE) were studied systematically in low-q discharges in JT-60U. Low-n TAE modes appeared outside the q = 1 surface at a low internal inductance (li), while high-n multiple TAE modes appeared inside the q = 1 surface at high internal inductance. In addition, the low-n multiple TAE modes were observed outside the q = 1 surface in very low-li plasmas , while the bi-directional TAE modes were observed inside the q = 1 surface in high-li and relatively high electron density plasmas . The high-n multiple TAE modes observed inside the q = 1 surface are much more harmful for energetic ion confinement than the low-n TAE modes observed outside the q = 1 surface.

Parametric representation of a superconducting high-current generator

An equivalent circuit model of a superconducting high-current brushless generator, the rotating-spot flux pump, is derived. The idealized version of the flux pump consists of a superconducting strip and a reciprocating magnet. This configuration has been used to make the mathematics manageable. Various design parameters describing the performance of the flux pump are derived. These derivations are used to determine the equivalent circuit model of the flux pump. The internal inductance of the pump associated with the switching loss is estimated from the surface current distribution on the superconducting sheet. The inductive transfer effects taking place in the pump are discussed, and a numerical example is given to provide an idea of the order of magnitude of the design parameters. The results of the calculations point to the advantages of the low internal inductance of the flux pump and of the current switching occurring as late as possible in the pumping cycle.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>