Justin Ball

ARC: A compact, high-field, fusion nuclear science facility and demonstration power plant with demountable magnets

The affordable, robust, compact (ARC) reactor is the product of a conceptual design study aimed at reducing the size, cost, and complexity of a combined fusion nuclear science facility (FNSF) and demonstration fusion Pilot power plant. ARC is a ∼200–250 MWe tokamak reactor with a major radius of 3.3 m, a minor radius of 1.1 m, and an on-axis magnetic field of 9.2 T. ARC has rare earth barium copper oxide (REBCO) superconducting toroidal field coils, which have joints to enable disassembly. This allows the vacuum vessel to be replaced quickly, mitigating first wall survivability concerns, and permits a single device to test many vacuum vessel designs and divertor materials. The design point has a plasma fusion gain of Qp ≈ 13.6, yet is fully non-inductive, with a modest bootstrap fraction of only ∼63%. Thus ARC offers a high power gain with relatively large external control of the current profile. This highly attractive combination is enabled by the ∼23 T peak field on coil achievable with newly available REBCO superconductor technology. External current drive is provided by two innovative inboard RF launchers using 25 MW of lower hybrid and 13.6 MW of ion cyclotron fast wave power. The resulting efficient current drive provides a robust, steady state core plasma far from disruptive limits. ARC uses an all-liquid blanket, consisting of low pressure, slowly flowing fluorine lithium beryllium (FLiBe) molten salt. The liquid blanket is low-risk technology and provides effective neutron moderation and shielding, excellent heat removal, and a tritium breeding ratio ≥ 1.1. The large temperature range over which FLiBe is liquid permits an output blanket temperature of 900 K, single phase fluid cooling, and a high efficiency helium Brayton cycle, which allows for net electricity generation when operating ARC as a Pilot power plant.

Intrinsic momentum transport in up–down asymmetric tokamaks

Recent work has demonstrated that breaking the up–down symmetry of tokamak flux surfaces removes a constraint that limits intrinsic momentum transport, and hence toroidal rotation, to be small. We show, through MHD analysis, that ellipticity is most effective at introducing up–down asymmetry throughout the plasma. We detail an extension to GS2, a local δf gyrokinetic code that self-consistently calculates momentum transport, to permit up–down asymmetric configurations. Tokamaks with tilted elliptical poloidal cross-sections were simulated to determine nonlinear momentum transport. The results, which are consistent with the experiment in magnitude, suggest that a toroidal velocity gradient, (∂uζi/∂ρ)/vthi, of 5% of the temperature gradient, (∂Ti/∂ρ)/Ti, is sustainable. Here vthi is the ion thermal speed, uζi is the ion toroidal mean flow, ρ is the minor radial coordinate normalized to the tokamak minor radius, and Ti is the ion temperature. Though other known core intrinsic momentum transport mechanisms scale poorly to larger machines, these results indicate that up–down asymmetry may be a feasible method to generate the current experimentally measured rotation levels in reactor-sized devices.

Conditions for up-down asymmetry in the core of tokamak equilibria

A local magnetic equilibrium solution is sought around the magnetic axis in order to identify the key parameters defining the magnetic-surfaces up-down asymmetry in the core of tokamak plasmas. The asymmetry is found to be determined essentially by the ratio of the toroidal current density flowing on axis to the fraction of the external fields odd perturbation that manages to propagate from the plasma boundary into the core. The predictions are tested and illustrated with experimentally relevant numerical equilibria. Hollow current-density distributions, and hence reverse magnetic shear, are seen to be crucial to bring into the core asymmetry values that are usually found only near the plasma edge.

Poloidal tilting symmetry of high order tokamak flux surface shaping in gyrokinetics

A poloidal tilting symmetry of the local nonlinear

Intuition for the radial penetration of flux surface shaping in tokamaks

\delta f

Effect of the Shafranov shift and the gradient of β on intrinsic momentum transport in up-down asymmetric tokamaks

gyrokinetic model is demonstrated analytically and verified numerically. This symmetry shows that poloidally rotating all the flux surface shaping effects with large poloidal mode number by a single tilt angle has an exponentially small effect on the transport properties of a tokamak. This is shown using a generalization of the Miller local equilibrium model to specify an arbitrary flux surface geometry. With this geometry specification we find that, when performing an expansion in large flux surface shaping mode number, the governing equations of gyrokinetics are symmetric in the poloidal tilt of the high order shaping effects. This allows us to take the fluxes from a single configuration and calculate the fluxes in any configuration that can be produced by tilting the large mode number shaping effects. This creates a distinction between tokamaks with mirror symmetric flux surfaces and tokamaks without mirror symmetry, which is expected to have important consequences for generating toroidal rotation using up-down asymmetry.

Turbulent momentum transport due to the beating between different tokamak flux surface shaping effects

Using analytic calculations, the effects of the edge flux surface shape and the toroidal current profile on the penetration of flux surface shaping are investigated in a tokamak. It is shown that the penetration of shaping is determined by the poloidal variation of the poloidal magnetic field on the surface. This fact is used to investigate how different flux surface shapes penetrate from the edge. Then, a technique to separate the effects of magnetic pressure and tension in the Grad?Shafranov equation?is presented and used to calculate radial profiles of strong elongation for nearly constant current profiles. Lastly, it is shown that more hollow toroidal current profiles are significantly better at conveying shaping from the edge to the core.

The engineering design of ARC: A compact, highfield, fusion nuclear science facility and demonstration power plant

Tokamaks with up–down asymmetric poloidal cross-sections spontaneously rotate due to turbulent transport of momentum. In this work, we investigate the effect of the Shafranov shift on this intrinsic rotation, primarily by analyzing tokamaks with tilted elliptical flux surfaces. By expanding the Grad–Shafranov equation in the large aspect ratio limit we calculate the magnitude and direction of the Shafranov shift in tilted elliptical tokamaks. The results show that, while the Shafranov shift becomes up–down asymmetric and depends strongly on the tilt angle of the flux surfaces, it is insensitive to the shape of the current and pressure profiles (when the geometry, total plasma current, and average pressure gradient are kept fixed). Next, local nonlinear gyrokinetic simulations of these MHD equilibria are performed with GS2, which reveal that the Shafranov shift can significantly enhance the momentum transport. However, to be consistent, the effect of (i.e. the radial gradient of β) on the magnetic equilibrium was also included, which was found to significantly reduce momentum transport. Including these two competing effects broadens the rotation profile, but leaves the on-axis value of the rotation roughly unchanged. Consequently, the shape of the β profile has a significant effect on the rotation profile of an up–down asymmetric tokamak.

Nonlinear gyrokinetic simulations of intrinsic rotation in up-down asymmetric tokamaks

Introducing up?down asymmetry into the tokamak magnetic equilibria appears to be a feasible method to drive fast intrinsic toroidal rotation in future large devices. In this paper we investigate how the intrinsic momentum transport generated by up?down asymmetric shaping scales with the mode number of the shaping effects. Making use the gyrokinetic tilting symmetry (Ball et al 2016 Plasma Phys. Control. Fusion 58 045023), we study the effect of envelopes created by the beating of different high-order shaping effects. This reveals that the presence of an envelope can change the scaling of the momentum flux from exponentially small in the limit of large shaping mode number to just polynomially small. This enhancement of the momentum transport requires the envelope to be both up?down asymmetric and have a spatial scale on the order of the minor radius.

Optimized up–down asymmetry to drive fast intrinsic rotation in tokamaks

The affordable, robust, compact (ARC) reactor conceptual design study aims to reduce the size, cost, and complexity of a combined fusion nuclear science facility (FNSF) and demonstration fusion pilot power plant. ARC is a 200 MWe tokamak reactor with a major radius of 3.3 m, a minor radius of 1.1 m, and an on-axis magnetic field of 9.2 T. ARC is designed to use rare earth barium copper oxide (REBCO), a type of high-temperature superconductor (HTS), for its toroidal field coils. The use of HTS technology offers many advantages over traditional superconductors when applied to tokamak designs. REBCO superconductors in particular have orders of magnitude higher critical current density than traditional superconductors such as Nb3Sn at local fields greater than 20 T, enabling much higher fields to be used in the tokamak. The large allowable temperature range (up to ~90 K) of HTS allows the use of coolants other than helium and makes possible the design of joints in the toroidal field coils. This allows the vacuum vessel to be replaced quickly, lowering first wall survivability concerns and reducing the cost and operational implications of vessel failure during the experimental phase of the reactor. External current drive for ARC is provided by two inboard (high-field side) RF launchers using 25 MW of lower hybrid and 13.6 MW of ion cyclotron fast wave power. The resulting efficient current drive provides a robust, steady state core plasma far from disruptive limits. ARC uses an all-liquid blanket, consisting of low pressure, slowly flowing fluorine lithium beryllium (FLiBe) molten salt. The liquid blanket is low-risk technology and provides effective neutron moderation and shielding, excellent heat removal, and a tritium breeding ratio ≥ 1.1. The large temperature range over which FLiBe is liquid permits blanket operation at ~900 K with single phase fluid cooling and a high-efficiency Brayton cycle, allowing for net electricity generation when operating ARC as a pilot power plant. When coupled with a demountable compact reactor design, the immersion blanket allows the vacuum vessel to be a replaceable component, eliminating the need for complex sector maintenance. The modular design of ARC allows a single machine to initially serve as an experiment and then transition to a demonstration commercial reactor.