arXiv subjects

S. J. Frank

Publications and source records attributed to S. J. Frank.

10 recordsLinked to original sources

arXiv2026

Design of a Doppler backscattering diagnostic for the Wisconsin HTS Axisymmetric Mirror (WHAM)

The Wisconsin HTS Axisymmetric Mirror (WHAM) is a compact high-field magnetic mirror. In such magnetic mirrors, cross-field transport is dominated by the flute instability (Endrizzi et al., 2023). To investigate density fluctuations associated with the flute instability, we designed a Doppler backscattering (DBS) diagnostic for WHAM, to be installed at the midplane port window. The diagnostic uses a two-channel tunable Ka-band (26.5--40 GHz) source and X-mode polarization. The azimuthal launch angle is set mechanically by rotating the external quasioptical assembly. As such, the system is reconfigurable during dedicated setup periods. Using the \textit{Scotty} beam-tracing code (Hall-Chen et al., 2022), we show that the proposed DBS system can measure density fluctuations with perpendicular wavenumbers $1 \leq k_\perp \leq 3~\mathrm{cm}^{-1}$ over radial locations $0.7 \leq ρ\leq 0.9$, where $ρ$ is the normalized radial coordinate. This is achieved with probe frequencies between 28 and 38.5 GHz, an elevation launch angle of $0^\circ$, and azimuthal launch angles in the range $1^\circ$--$3^\circ$. The selected configurations have low mismatch angle at cutoff, $|θ_{m,c}|<1^\circ$. The quasioptical system uses a Ka-band horn and a biconvex ultra-high molecular weight polyethylene lens, and satisfies the port-access constraints in WHAM. The planned microwave system has a monostatic, homodyne architecture based on two phase-coupled Ka-band microwave channels. These two channels will be for the transmitted signal and coherent local oscillator (LO) for IQ downconversion, respectively. As the two phase-coupled channels can be independently tuned or swept with a controlled frequency offset, the same microwave chain can also support profile-reflectometry measurements using cutoff-delay information.

physics.plasm-ph↗

arXiv2026

Nonlinear anisotropic equilibrium reconstruction in axisymmetric magnetic mirrors

Magnetic equilibrium reconstruction is a crucial simulation capability for interpreting diagnostic measurements of experimental plasmas. Equilibrium reconstruction has mostly been applied to systems with isotropic pressure and relatively low plasma $β= 2μ_0p/B^2$. This work extends nonlinear equilibrium reconstruction to high-$β$ plasmas with anisotropic pressure and applies it to the Wisconsin High Temperature Superconducting Axisymmetric Magnetic Mirror experiments to infer the presence of sloshing ions. A novel basis set for the plasma profiles and machine learning algorithm using scalable constrained Bayesian optimization allow accurate nonlinear reconstructions with uncertainty quantification to be made more quickly with fewer experimental diagnostics and improves the robustness of reconstructions at high $β$. In addition to WHAM and other mirrors, such reconstruction techniques are potentially attractive in high-performance devices with constrained diagnostic capabilities such as fusion power plants.

physics.plasm-ph↗

arXiv2025

First implementation of AXUV-based analysis and macro-instability diagnostics on WHAM

Absolute extreme ultraviolet (AXUV) diode arrays are widely used in fusion experiments for time-resolved measurements of plasma radiation. We report the first implementation of an AXUV-based analysis framework on the Wisconsin High-Temperature Superconducting (HTS) Axisymmetric Mirror (WHAM). A single, precisely calibrated 20-channel AXUV assembly measures line-integrated plasma emission with $ 100~\mathrm{kHz}$ temporal resolution and $\sim1~\mathrm{cm}$ spatial accuracy across the mid-plane. The data were processed to obtain plasma's statistical moments, yielding time-resolved measurement of the centroid displacement $Φ(t)$ and effective radius $R(t)$. From the joint covariance of these quantities, we define a macroscopic instability parameter $χ(t)$, that quantifies large-scale plasma motion and profile evolution directly from AXUV observables. The parameter $χ$ serves as a compact indicator of global macroscopic instability, decreasing with increasing end-plate bias and exhibiting strong anti-correlation with diamagnetic flux during confinement transitions. These results demonstrate that a single AXUV array can provide quantitative, real-time assessment of macroscopic plasma instabilities, constituting the first demonstration of such capability in a magnetic mirror plasma. Future extensions to multiple arrays will further enhance spatial coverage and enable full-mode tracking in axisymmetric mirror configurations and related fusion devices.

physics.plasm-ph↗

arXiv2025

Confinement performance predictions for a high field axisymmetric tandem mirror

This paper presents Hammir tandem mirror confinement performance analysis based on Realta Fusion's first-of-a-kind model for axisymmetric magnetic mirror fusion performance. This model uses an integrated end plug simulation model including, heating, equilibrium, and transport combined with a new formulation of the plasma operation contours (POPCONs) technique for the tandem mirror central cell. Using this model in concert with machine learning optimization techniques, it is shown that an end plug utilizing high temperature superconducting magnets and modern neutral beams enables a classical tandem mirror pilot plant producing a fusion gain Q > 5. The approach here represents an important advance in tandem mirror design. The high fidelity end plug model enables calculations of heating and transport in the highly non-Maxwellian end plug to be made more accurately. The detailed end plug modelling performed in this work has highlighted the importance of classical radial transport and neutral beam absorption efficiency on end plug viability. The central cell POPCON technique allows consideration of a wide range of parameters in the relatively simple near-Maxwellian central cell, facilitating the selection of more optimal central cell plasmas. These advances make it possible to find more conservative classical tandem mirror fusion pilot plant operating points with lower temperatures, neutral beam energies, and end plug performance requirements than designs in the literature. Despite being more conservative, it is shown that these operating points have sufficient confinement performance to serve as the basis of a viable fusion pilot plant provided that they can be stabilized against MHD and trapped particle modes.

physics.plasm-ph↗

arXiv2024

MANTA: A Negative-Triangularity NASEM-Compliant Fusion Pilot Plant

The MANTA (Modular Adjustable Negative Triangularity ARC-class) design study investigated how negative-triangularity (NT) may be leveraged in a compact, fusion pilot plant (FPP) to take a ``power-handling first" approach. The result is a pulsed, radiative, ELM-free tokamak that satisfies and exceeds the FPP requirements described in the 2021 National Academies of Sciences, Engineering, and Medicine report ``Bringing Fusion to the U.S. Grid". A self-consistent integrated modeling workflow predicts a fusion power of 450 MW and a plasma gain of 11.5 with only 23.5 MW of power to the scrape-off layer (SOL). This low $P_\text{SOL}$ together with impurity seeding and high density at the separatrix results in a peak heat flux of just 2.8 MW/m$^{2}$. MANTA's high aspect ratio provides space for a large central solenoid (CS), resulting in ${\sim}$15 minute inductive pulses. In spite of the high B fields on the CS and the other REBCO-based magnets, the electromagnetic stresses remain below structural and critical current density limits. Iterative optimization of neutron shielding and tritium breeding blanket yield tritium self-sufficiency with a breeding ratio of 1.15, a blanket power multiplication factor of 1.11, toroidal field coil lifetimes of $3100 \pm 400$ MW-yr, and poloidal field coil lifetimes of at least $890 \pm 40$ MW-yr. Following balance of plant modeling, MANTA is projected to generate 90 MW of net electricity at an electricity gain factor of ${\sim}2.4$. Systems-level economic analysis estimates an overnight cost of US\$3.4 billion, meeting the NASEM FPP requirement that this first-of-a-kind be less than US\$5 billion. The toroidal field coil cost and replacement time are the most critical upfront and lifetime cost drivers, respectively.

physics.plasm-ph↗

arXiv2022

A quasi-local inhomogeneous dielectric tensor for arbitrary distribution functions

Treatments of plasma waves usually assume homogeneity, but the parallel gradients ubiquitous in plasmas can modify wave propagation and absorption. We derive a quasilocal inhomogeneous correction to the plasma dielectric for arbitrary distributions by expanding the phase correlation integral and develop a novel integration technique that allows our correction to be applied in many situations and has greater accuracy than other inhomogeneous dielectric formulas found in the literature. We apply this dielectric tensor to the lower-hybrid current drive problem and demonstrate that inhomogeneous wave damping does not affect the lower-hybrid wave's linear damping condition, and in the non-Maxwellian problem damping and propagation should remain unchanged except in the case of waves with very large phase velocities.

physics.plasm-ph↗

arXiv2022

Radiative pulsed L-mode operation in ARC-class reactors

A new ARC-class, highly-radiative, pulsed, L-mode, burning plasma scenario is developed and evaluated as a candidate for future tokamak reactors. Pulsed inductive operation alleviates the stringent current drive requirements of steady-state reactors, and operation in L-mode affords ELM-free access to $\sim90\%$ core radiation fractions, significantly reducing the divertor power handling requirements. In this configuration the fusion power density can be maximized despite L-mode confinement by utilizing high-field to increase plasma densities and current. This allows us to obtain high gain in robust scenarios in compact devices with $P_\mathrm{fus} > 1000\,$MW despite low confinement. We demonstrate the feasibility of such scenarios here; first by showing that they avoid violating 0-D tokamak limits, and then by performing self-consistent integrated simulations of flattop operation including neoclassical and turbulent transport, magnetic equilibrium, and RF current drive models. Finally we examine the potential effect of introducing negative triangularity with a 0-D model. Our results show high-field radiative pulsed L-mode scenarios are a promising alternative to the typical steady state advanced tokamak scenarios which have dominated tokamak reactor development.

physics.plasm-ph↗

arXiv2022

Verifying raytracing/Fokker-Planck lower-hybrid current drive predictions with self-consistent full-wave/Fokker-Planck simulations

Raytracing/Fokker-Planck (FP) simulations used to model lower-hybrid current drive (LHCD) often fail to reproduce experimental results, particularly when LHCD is weakly damped. A proposed reason for this discrepancy is the lack of "full-wave" effects, such as diffraction and interference, in raytracing simulations and the breakdown of raytracing approximation. Previous studies of LHCD using non-Maxwellian full-wave/FP simulations have been performed, but these simulations were not self-consistent and enforced power conservation between the FP and full-wave code using a numerical rescaling factor. Here we have created a fully-self consistent full-wave/FP model for LHCD that is automatically power conserving. This was accomplished by coupling an overhauled version of the non-Maxwellian TORLH full-wave solver and the CQL3D FP code using the Integrated Plasma Simulator. We performed converged full-wave/FP simulations of Alcator C-Mod discharges and compared them to raytracing. We found that excellent agreement in the power deposition profiles from raytracing and TORLH could be obtained, however, TORLH had somewhat lower current drive efficiency and broader power deposition profiles in some cases. This discrepancy appears to be a result of numerical limitations present in the TORLH model and a small amount of diffractional broadening of the TORLH wave spectrum. Our results suggest full-wave simulation of LHCD is likely not necessary as diffraction and interference represented only a small correction that could not account for the differences between simulations and experiment.

physics.plasm-ph↗

arXiv2020

Disruption Avoidance via RF Current Condensation in Magnetic Islands Produced by Off-Normal Events

As tokamaks are designed and built with increasing levels of stored energy in the plasma, disruptions become increasingly dangerous. It has been reported that 95% of the disruptions in the Joint European Torus (JET) tokamak with the ITER-like wall are preceded by the growth of large locked islands, and these large islands are mostly produced by off-normal events other than neoclassical tearing modes. This paper discusses the use of RF current drive to stabilize large islands, focusing on nonlinear effects that appear when relatively high powers are used to stabilize large islands. An RF current condensation effect can concentrate the RF driven current near the center of the island, increasing the efficiency of the stabilization. A nonlinear shadowing effect can hinder the stabilization of islands if the aiming of the ray trajectories does not properly consider the nonlinear effects.

physics.plasm-ph↗

arXiv2020

Generation of Localized Lower-Hybrid Current Drive By Temperature Perturbations

Despite high demonstrated efficiency, lower-hybrid current drive (LHCD) has not been considered localized enough for neoclassical tearing mode (NTM) stabilization in tokamaks. This assessment must be reconsidered in view of the RF current condensation effect. We show that an island with a central hot spot induces significant localization of LHCD. Furthermore, in steady state tokamaks where a significant amount of current is provided by LHCD, passive stabilization of NTMs may occur automatically, particularly as islands become large, without requiring precise aiming of the wave power.

physics.plasm-ph↗