arXiv subjects

Matthew Pharr

Publications and source records attributed to Matthew Pharr.

6 recordsLinked to original sources

arXiv2026

Coordinate-invariant flux-surface Fourier analysis in tokamaks

The Fourier spectra of resonant quantities in tokamaks depend on the choice of magnetic coordinates, and an area weighting of the Fourier integrand preserves the resonant coefficients on rational surfaces. That result constrains only the resonant interior; the coordinate dependence of the external Fourier spectrum, which determines the coupling to Resonant Magnetic Perturbation (RMP) coils and error-field penetration, was left untreated. This paper shows that pairing a square-root-area weighted vacuum field perturbation with a full-area-weighted resonant field yields a coupling matrix C whose singular values are invariant under coordinate transformations and whose right singular vectors reconstruct to a consistent real-space field pattern across coordinate systems, completing the coordinate-invariance picture for the plasma-3D-field coupling paradigm. GPEC calculations confirm the analytic result and show that improperly weighted coupling matrices can produce dominant modes whose overlap with the vacuum field perturbation differs by a factor of $2--3$ between coordinate systems for strongly shaped, low aspect ratio equilibria, with the discrepancy growing with inverse aspect ratio. The same coordinate dependence afflicts alternative formulations such as the three-mode metric or zeroing the $q=2$ resonant field without proper weighting. The result applies to any tool computing Fourier spectra of resonant or external quantities on flux surfaces.

physics.plasm-ph↗

arXiv2026

Compact Experimental Negative TriAngUlarity Reactor (CENTAUR): A design study for a compact, affordable breakeven tokamak

This work presents the compact experimental negative triangularity reactor (CENTAUR), a low overnight cost, high-field tokamak, breakeven reactor design, achieving a predicted total fusion power of 40MW and scientific energy gain of 1.3. Ballooning stability calculations confirm that the device's pedestal is within the first stability regime, which is consistent with the expected ELM-free operation associated with negative triangularity (NT) plasmas. The geometry of the NT divertor allows for high fraction of radiated power (13.5$\%$) between the separatrix and plasma facing components. Heat transport modeling based on simulations of the edge region show heat loads into plasma facing components well below material limits. The magnet system employs rare-earth barium copper oxide (REBCO) high-temperature superconductors in 18 toroidal field coils, an hourglass-shaped central solenoid, and six poloidal field coils to support high-field ($B_0=10.9$ T) plasma confinement, shaping, and current drive. Neutronics analysis shows that a 12 cm $B_4C$ shield keeps superconducting magnet heating below the 33~K quench limit during 10 s, 40 MW DT pulses. With this shielding, the modeled fluence indicates HTS components can survive more than ten times the 3000-pulse design lifetime. Iteration of economic analysis in tandem with the technical design process allows CENTAUR to achieve its overnight cost goal of $\$$2B determined using a custom costing model that predicts a total overnight cost of $1.6$B$\pm0.2$B.

physics.plasm-ph↗

arXiv2026

Quantifying resonant drive in resistive perturbed tokamak equilibria

Resonant drive in tokamaks is routinely quantified using a variety of different metrics that target different aspects of a resonant response to an external perturbation. Two of the most direct metrics, $\Delta_{mn}$ and $b_{pen}$, are widely used but their relative behavior was previously uncharacterized. This work examines how these metrics representing the shielding current and penetrated field relate in resistive perturbed tokamak equilibria using asymptotically matched solutions with a resistive MHD inner layer model in GPEC. $b_{pen}$ scales with Lundquist number as $S^{-2/3}$ until saturation at low $S$, and $\Delta_{mn}$ remains consistent with its ideal definition but is affected by global kink structure. Both metrics are shown to yield closely similar dominant coupling modes within the same resistive model. However, the resistive physics shifts this dominant mode spectrum to lower poloidal mode numbers $m$ in a low-rotation ITER equilibrium. This alteration is predicted to be observable in experiment in the form of optimal relative phasings of resonant magnetic perturbation coils.

physics.plasm-ph↗

arXiv2025

Electromagnetic System Conceptual Design for a Negative Triangularity Tokamak

Negative triangularity (NT) tokamak configurations have several key benefits including sufficient core confinement, improved power handling, and reduced edge pressure gradients that allow for edge-localized mode (ELM) free operation. We present the design of a compact NT device for testing sophisticated simulation and control software, with the aim of demonstrating NT controllability and informing power plant operation. The TokaMaker code is used to develop the basic electromagnetic system of the $R_0$ = 1 m, $a$ = 0.27 m, $B_t$ = 3 T, $I_p$ = 0.75 MA tokamak. The proposed design utilizes eight poloidal field coils with maximum currents of 1 MA to achieve a wide range of plasma geometries with $-0.7 < \delta < -0.3$ and $1.5 < \kappa < 1.9$. Scenarios with strong negative triangularity and high elongation are particularly susceptible to vertical instability, necessitating the inclusion of high-field side and/or low-field side passive stabilizing plates which together reduce vertical instability growth rates by $\approx$75%. Upper limits for the forces on poloidal and toroidal field coils are predicted and mechanical loads on passive structures during current quench events are assessed. The 3 T on-axis toroidal field is achieved with 16 demountable copper toroidal field coils, allowing for easy maintenance of the vacuum vessel and poloidal field coils. This pre-conceptual design study demonstrates that the key capabilities required of a dedicated NT tokamak experiment can be realized with existing copper magnet technologies.

physics.plasm-ph↗

arXiv2024

Error Field Predictability and Consequences for ITER

ITER coil tolerances are re-evaluated using the modern understanding of coupling to least-stable plasma modes and an updated center-line-traced model of ITER's coil windings. This reassessment finds the tolerances to be conservative through a statistical, linear study of $n=1$ error fields (EFs) due to tilted, shifted misplacements and nominal windings of central solenoid and poloidal field coils within tolerance. We also show that a model-based correction scheme remains effective even when metrology quality is sub-optimal, and compare this to projected empirical correction schemes. We begin with an analysis of the necessity of error field correction (EFC) for daily operation in ITER using scaling laws for the EF penetration threshold. We then consider the predictability of EF dominant mode overlap across early planned ITER scenarios and, as measuring EFs in high power scenarios can pose risks to the device, the potential for extrapolation to the ITER Baseline Scenario (IBS). We find that carefully designing a scenario matching currents proportionally to those of the IBS is far more important than plasma shape or profiles in accurately measuring an optimal correction current set.

physics.plasm-ph↗

arXiv2022

A non-local magneto-curvature instability in a differentially rotating disk

A global mode is shown to be unstable to non-axisymmetric perturbations in a differentially rotating Keplerian disk containing either vertical or azimuthal magnetic fields. In an unstratified cylindrical disk model, using both global eigenvalue stability analysis and linear global initial-value simulations, it is demonstrated that this instability dominates at strong magnetic field where local standard MRI becomes stable. Unlike the standard MRI mode, which is concentrated in the high flow shear region, these distinct global modes (with low azimuthal mode numbers) are extended in the global domain and are Alfv\'en continuum driven unstable modes. As its mode structure and relative dominance over MRI is inherently determined by the global spatial curvature as well as the flow shear in the presence of magnetic field, we call it the magneto-curvature (magneto-spatial-curvature) instability. Consistent with the linear analysis, as the field strength is increased in the nonlinear simulations, a transition from a MRI-driven turbulence to a state dominated by global non-axisymmetric modes is obtained. This global instability could therefore be a source of nonlinear transport in accretion disks at higher magnetic field than predicted by local models.

astro-ph.HE↗