TokaMaker: An open-source time-dependent Grad-Shafranov tool for the design and modeling of axisymmetric fusion devices

Hansen, C.; Stewart, I.G.; Burgess, D.; Pharr, M.; Guizzo, S.; Logak, F.; Nelson, A.O.; Paz-Soldan, C.

doi:10.1016/j.cpc.2024.109111

Cited by 5 publications

(5 citation statements)

References 40 publications

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“…The asymmetric effect of the plates located near the upper and lower outboard corners reflects the fact that the magnetic flux cannot change drastically near the limiting point of the equilibrium [25]. Conductors near the X-point have the effect of 'squeezing' the perturbed flux towards the opposite side of the plasma, where it is more free to vary, thus destabilizing the equilibrium further.…”

Section: Passive Plate Positioningmentioning

confidence: 99%

“…To investigate the effect of plasma properties and conducting structures on vertical stability, the open-source TokaMaker code [25] is used to generate plasma equilibria over a large parameter space. TokaMaker is a new 2D free-boundary Grad-Shafranov equilibrium solver with both static and time dependent capabilities.…”

Section: Effect Of Plasma Geometry and Equilibrium Profilesmentioning

confidence: 99%

“…In this study, we determine the dependence of vertical instability growth rates on plasma and machine properties in order to gauge the feasibility of favorable passive stability in NT reactor scenarios. In section 2, we begin by using the TokaMaker code [25,26] to assess various vertical stability trends for free-boundary NT equilibria in conformal wall geometries. Vacuum vessel shape is discussed in section 3, where we find that reduced growth rates in non-conformal wall geometries do not compensate for decreased vertical gaps in compact reactors, and are therefore not the ideal resolution to the NT vertical stability question.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Assessment of vertical stability for negative triangularity pilot plants

Guizzo,

Nelson,

Hansen

et al. 2024

Plasma Phys. Control. Fusion

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Negative triangularity (NT) tokamak configurations may be more susceptible to magneto-hydrodynamic instability, posing challenges for recent reactor designs centered around their favorable properties, such as improved confinement and operation free of edge-localized modes. In this work, we assess the vertical stability of plasmas with NT shaping and develop potential reactor solutions. When coupled with a conformal wall, NT equilibria are confirmed to be less vertically stable than equivalent positive triangularity (PT) configurations. Unlike PT, their vertical stability is degraded at higher poloidal beta. Furthermore, improvements in vertical stability at low aspect ratio do not translate to the NT geometry. NT equilibria are stabilized in PT vacuum vessels due to the increased proximity of the plasma and the wall on the outboard side, but this scenario is found to be undesirable due to reduced vertical gaps which give less spatial margin for control recovery. Instead, we demonstrate that informed positioning of passively conducting plates can lead to improved vertical stability in NT configurations on par with stability metrics expected in PT scenarios. An optimal setup for passive plates in highly elongated NT devices is presented, where plates on the outboard side of the device reduce vertical instability growth rates to 16% of their baseline value. For lower target elongations, integration of passive stabilizers with divertor concepts can lead to significant improvements in vertical stability. Plates on the inboard side of the device are also uniquely enabled in NT geometries, providing opportunity for spatial separation of vertical stability coils and passive stabilizers.

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Section: Passive Plate Positioningmentioning

confidence: 99%

Section: Effect Of Plasma Geometry and Equilibrium Profilesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Assessment of vertical stability for negative triangularity pilot plants

Guizzo,

Nelson,

Hansen

et al. 2024

Plasma Phys. Control. Fusion

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“…Calculation of the natural instability growth rates of tokamak equilibria is generally a tractable problem, as long as an accurate description of the machine in question is available [15,17]. In this work we use a collection of calculations known as GSPert, which are included in the TokSys code suite, to compute the open-loop growth rates (γ) of the n = 0 vertical instability for SPARC discharges [15,16].…”

Section: Passive Stability Of Sparc Dischargesmentioning

confidence: 99%

“…In support of experimental endeavors to establish reliable vertical control of tokamak plasmas, several modeling suites have been developed that can accurately capture the interplay between the plasma state, the vessel geometry and the coil power supplies [15][16][17][18][19]. Since the physics governing VDEs is relatively well understood [20][21][22][23][24], it is possible to use these codes to predict the expected stability margins for future devices with fairly good accuracy.…”

Section: Introductionmentioning

confidence: 99%

Implications of vertical stability control on the SPARC tokamak

Nelson,

Garnier,

Battaglia

et al. 2024

Nucl. Fusion

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To achieve its performance goals, SPARC plans to operate in equilibrium configurations with a strong elongation of κ areal ∼ 1.75 , which in turn will destabilize the n = 0 vertical instability. However, SPARC also features a relatively thick conducting wall that is designed to withstand disruption forces, leading to lower vertical instability growth rates than usually encountered. In this work, we use the TokSyS framework to survey families of accessible shapes near the SPARC baseline configuration, finding maximum growth rates in the range of γ ≲ 100 s−1. The addition of steel vertical stability plates has only a modest ( ∼ 25 % ) effect on reducing the vertical growth rate and almost no effect on the plasma controllability when the full vertical stability system is taken into account, providing flexibility in the plate conductivity in the SPARC design. Analysis of the maximum controllable displacement on SPARC is used to inform the power supply voltage and current limit requirements needed to control an initial vertical displacement of 5% of the minor radius. From the expected spectra of plasma disturbances and diagnostic noise, requirements for filter latency and vertical stability coil heating tolerances are also obtained. Small modifications to the outboard limiter location are suggested to allow for an unmitigated vertical disturbance as large as 5% of the minor radius without allowing the plasma to become limited. Further, investigations with the 3D COMSOL code reveal that strategic inclusion of insulating structures within the VSC supports are needed to maintain sufficient magnetic response. The workflows presented here help to establish a model for the integrated predictive design for future devices by coupling engineering decisions with physics needs.

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Interplay of the magnetic and current density field topologies in axisymmetric devices for magnetic confinement fusion

Firpo

2024

J. Plasma Phys.

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In magnetic confinement fusion devices close to axisymmetry, such as tokamaks, a key element is the winding profile of the magnetic field lines, or its inverse, the safety profile $q=q_{\boldsymbol {B}}$ . A corresponding profile, $q_{\boldsymbol {J}}$ , can be defined for the current density field lines. Ampère's law relates any mode of current perturbation $\delta \boldsymbol {J}_{m,n}$ with a mode of magnetic perturbation $\delta \boldsymbol {B}_{m,n}$ . It is shown that the knowledge of the pair $(q_{\boldsymbol {B}},q_{\boldsymbol {J}})$ allows us then to characterize the resonant, or non-resonant, nature of the modes for both the magnetic and current density field lines. The expression of $q_{\boldsymbol {J}}$ in the flux coordinate is derived. Including this calculation in real-time Grad–Shafranov equilibrium reconstruction codes would yield a comprehensive view of the magnetics. The monitoring of the pair $(q_{\boldsymbol {B}},q_{\boldsymbol {J}})$ would then allow us to investigate the role played by the resonant modes for the current density, that are current filamentary modes, in the plasma small-scale turbulence. By driving the magnetic and current density profiles apart so that the images of $q_{\boldsymbol {B}}$ and $q_{\boldsymbol {J}}$ are disjoint, these filamentary modes would not impact the magnetic field topology, being not associated with magnetic islands but with non-resonant magnetic modes. It remains to be explored to what extent such a configuration, where the spectrum of tiny current density filaments produces a spectrum of magnetic modes that has practically no effect on heat transport, is beneficial.

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TokaMaker: An open-source time-dependent Grad-Shafranov tool for the design and modeling of axisymmetric fusion devices

Cited by 5 publications

References 40 publications

Assessment of vertical stability for negative triangularity pilot plants

Assessment of vertical stability for negative triangularity pilot plants

Implications of vertical stability control on the SPARC tokamak

Interplay of the magnetic and current density field topologies in axisymmetric devices for magnetic confinement fusion

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