Bootstrap Current Modeling in M3D-C1�¹Saurabh Saxena, ¹Nathaniel Ferraro, ²Mike F. Martin, �¹ Princeton Plasma Physics Laboratory, �² Thea Energy�

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What is Bootstrap Current?

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What is Bootstrap Current?

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¹Neuner et al. (2021)

Importance of Bootstrap Current

TOKAMAKS

• Reduces reliance on external current sources: Enables more efficient and self-sustaining operation.

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• Essential to understand magnetohydrodynamic (MHD) equilibrium: It contributes to the plasma current and thereby to confinement.

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• Essential for steady-state operation: Makes long-duration fusion reactions more feasible.

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STELLARATORS

• Can strongly affect the rotational transform of the magnetic field in the plasma

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• Essential to understand magnetohydrodynamic (MHD) equilibrium & stability

Mano et al (2012)

Liu et al (2023)

Helander et al (2011); Neuner et al., (2021)

Bootstrap Current Modelling in M3D-C1

• In quasisymmetric (QS) stellarators and at the edge of tokamaks, bootstrap current often comprises the bulk of the electric current density.

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• This study expands the modeling capabilities of M3D-C1, an extended-MHD code, by implementing self-consistent physics models for bootstrap current.

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• Two analytical frameworks:
• a generalized Sauter model (¹Sauter et. al. 1999)
• a revised Sauter-like model (²Redl et. al 2021)

And for stellarator configurations we use the isomorphism described by ³Landreman et. al. (2022).

M3D-C1

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• M3D-C1 is a high fidelity extended MHD code⁴
• It implements a comprehensive two-fluid, two-temperature MHD model of the plasma that can include impurities and sources.
• Capability for stellarator configurations was recently implemented⁵

The extended-MHD equations are solved using a split-implicit time stepping scheme.

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⁴Jardin et al (2012)

⁵Zhou et al (2021)

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Bootstrap Current Modelling in M3D-C1

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¹Sauter and ²Redl Models

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¹Sauter et. al. 1999

²Redl et. al 2021

Isomorphism

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²Redl et. al 2021

³Landreman et. al. (2022).

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Treatment of Gradients in M3D-C1

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Workflow

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neo_input.nc

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Validation Cases

Adelle’s Case

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Tokamak

Hager & Chang (2016)

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01: Tokamak Case

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Tokamak

Hager & Chang (2016)

The case chosen for benchmarking is the CIRC1 case from Hager & Chang (2016):

• Tight aspect ratio case

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• Grad-Shafranov equilibrium with circular plasma boundary

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• Density & Temperature profiles are tanh-type pedestals

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01: Tokamak Case

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Tokamak

Hager & Chang (2016)

• M3D-C1’s Sauter model agrees well with NEO 2D’s Sauter with a 2.5% difference at the peak

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• M3D-C1’s Sauter results and Hager & Chang’s (2016) XGCa are almost identical.

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• M3D-C1’s Redl profile agrees well with NEO 3D and SFINCS profiles

R0 = 0.11;

R1 = 1.76;

Rmaxis=1.1067

¹Hager & Chang (2016).

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Validation Cases

Adelle’s Case

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Tokamak

Hager & Chang (2016)

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02: Quasi-Axisymmetric Stellarator

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¹Landreman et. al. (2022).

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02: Quasi-Axisymmetric Stellarator

Optimized QA Stellarator

QA Stellarator

¹Landreman et. al. (2022).

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¹Landreman et. al. (2022)

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Time Evolution

Optimized QA

¹Landreman et. al. (2022).

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Time Evolution

Optimized QA

¹Landreman et. al. (2022).

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With Bootstrap Model

Without Bootstrap Model

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Summary

• Two analytical models for the bootstrap current have been implemented in M3D-C1:
• a generalized Sauter model (¹Sauter et. al. 1999)
• a revised Sauter-like model (²Redl et. al 2021)

For stellarator geometries the isomorphism described by ³Landreman et. al. (2022) is employed.

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• The new implementation is benchmarked against neoclassical codes such as NEO, XGCa, and SFINCS.

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• M3D-C1 is now capable of self-consistently calculating the kinetic contributions to plasma current in both tokamaks and QS stellarators.

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• Ongoing:
• Impact of bootstrap current on the time evolution of optimized QA stellarator and NCSX configurations.

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Thank You

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