Benedikt Geiger

The Thomson scattering diagnostic on the Helically Symmetric eXperiment (HSX) stellarator has been upgraded with a high-repetition-rate laser, enabling time-resolved measurements of electron temperature and density. The newly acquired InnoLas SpitLight EVO IV neodymium-doped yttrium aluminum garnet laser supports burst operation with 80 consecutive pulses at 400 Hz or four sets of ten pulses at 2 kHz, separated by a 25 ms cooldown period. The EVO IV also allows for continuous operation at 100 Hz. This newly accessible burst-mode operation enables the investigation of fast plasma phenomena on HSX, including plasma breakdown, magnetohydrodynamic activity, impurity injection behavior, and density profile evolution. To maximize beam energy, the laser was installed on an elevated optical table, eliminating the requirement for beam-steering periscope optics and reducing the optical path to include a single mirror interaction between the laser and the vacuum vessel. Beam polarization was adjusted using quarter- and half-waveplates, in conjunction with a Brewster exit window aligned to the magnetic axis. We characterized energy across the three operating modes, including continuous-mode warm-up behavior and differences between warm-rod and cold-rod operation in burst-mode, particularly regarding beam divergence caused by thermal lensing. We monitored per-pulse energy using a coherent energy monitor, which served as both a beam dump and a shot-to-shot diagnostic. Under the standard operational burst-mode of 400 Hz, we measured a mean of 852 mJ of through-vessel energy, corresponding to 89.0% of the available 957 mJ output energy.

This Department of Energy-Office of Fusion Energy Science-sponsored project at the University of Wisconsin-Madison (UW) has determined the characteristics, behavior and dynamics of turbulence and related instabilities in magnetically confined fusion plasmas at the DIII-D National Fusion Facility, operated by General Atomics in San Diego, CA. Our UW team has designed, developed, implemented and operated a suite of multifield, high-performance optical diagnostics at the DIII-D tokamak facility to remotely measure fluctuation characteristics in a wide range of tokamak plasmas. Major diagnostics in this suite include Beam Emission Spectroscopy (BES), Ultra-Fast Charge Exchange Recombination Spectroscopy (UF-CHERS), Charge eXchange Imaging (CXI), and the Beam Emission Manifold Fast Spectrometer (JrS), and a visible survey spectrometer. Measurements from these instruments have been used to study the L-H transition process, H-mode pedestal and ELM dynamics and ELM-suppression mechanisms, core turbulence properties, near-Scrape-Off-Layer turbulence, Alfven Eigenmodes, and Magnetohydrodynamic instabilities. Measurements have been obtained in a wide variety of operational scenarios, ranging from standing ELM’ing H-modes to hybrid scenarios, RMP-ELM suppressed H-modes, RI-modes, Negative Triangularity plasmas, ITER Baseline scenarios, and high-beta-poloidal plasmas, as several examples. A central element of this research has been comparison with and validation of gyrokinetic simulations and transport modes. Many UW graduate students have performed their PhD thesis research under this project on topics ranging from diagnostic development to plasma turbulence research. Our UW team has presented many Invited talks, contributed talks, and poster presentations at prestigious national and international conferences, such as the American Physical Society-Division of Plasma Physics and IAEA-Fusion Energy Conference, as well as specialized workshops. Our Team has also participated in and lead many plasma fusion committees and organizations. This UW-provided advanced fluctuation diagnostic capability has been available to and utilized by the full DIII-D National program, including many collaborators from other universities, multiple national laboratories, General Atomics, and other company collaborators.

Modern stellarator designs routinely attain high levels of magnetic-field quasi-symmetry through flux-surface shaping. Here, we examine different methods for characterizing stellarator flux-surface shapes in a manner analogous to flux-surface shaping in tokamaks. The methods considered use a Fourier analysis to define the shaping modes (e.g., elongation, triangularity, squareness, etc.) of equilibrium cross sections. Relative to an axisymmetric equilibrium, the additional degree of freedom in a non-axisymmetric equilibrium manifests as a rotation of each shaping mode about the magnetic axis. This analysis is performed on non-axisymmetric configurations with a high degree of quasi-symmetry and equilibria with varying quasi-symmetry quality from the quasi-symmetric Stellarator Repository database. One method in particular is shown to reduce shape complexity in quasi-symmetric equilibria by defining a set of cross sections that efficiently fill out an equilibrium volume. This is accomplished by defining a cross section as the set of points that occupy the shortest distance between the magnetic axis and an equilibrium flux surface across all quasi-symmetry contours. Using this method, we find empirically that an equilibrium geometry can be described with significantly fewer non-negligible shaping modes relative to other shape characterization methods. Moreover, the method reveals that quasi-symmetry quality is strongly correlated with equilibrium shapes that exhibit a highly constrained linear distribution of shaping modes, where an increase in shape complexity is proportional to an increase in shape rotation about the magnetic axis. It is therefore argued that this method provides a way to efficiently characterize the shape of quasi-symmetric equilibria in a manner analogous to how equilibrium shapes are described in tokamaks.

A synthetic reflectometer diagnostic has been developed to model the reflectometer used at the helically symmetric experiment (HSX) stellarator. The main purpose of the HSX reflectometer is to measure density fluctuations in order to study turbulence and coherent modes in HSX. A full-wave 2D synthetic diagnostic modeling the HSX reflectometer has been used to investigate its radial localization, characterize its sensitivities, and relate gyrokinetic simulations to physical measurements. The synthetic diagnostic results show that signal localization peaks slightly outboard of the cutoff surface, with the main localization lobe spanning between 15 % and 30 % of the minor radius. The poloidal and radial wavenumber sensitivities are k θ < 1.7 cm − 1 and k r < 6 cm − 1 , respectively, with minimal variation in k r sensitivity across probing regions and density profiles. Conversely, k θ sensitivity increases to > 2 cm − 1 in the core of the device, in accordance with an increase in local flux-surface curvature. Synthetic reflectometer signals scale linearly with density fluctuation amplitude over a large range of fluctuation levels. Multiple density fluctuation level estimators are tested to identify the optimal choice for use in HSX, with an equation from G.D. Conway Plasma Phys. Control. Fusion 1999 consistently performing best overall. Synthetic measurements of rescaled density fluctuations from a gyrokinetic simulation are then compared against experimental measurements, with coherent mode activity at 13 − 15 kHz and 22 kHz observed in both experimental and synthetic frequency spectra. Synthetic spectra overestimated experimental spectra at low frequencies and underestimated at high frequency.

Microtearing modes (MTMs) ( ω ∼ ω d e , k θ ρ s ∼ 0.1 , k r ρ s ∼ 0.3 − 1.0 ) are predicted to cause substantial electron thermal transport in the H-mode pedestal, limiting fusion performance on high-power devices. Localized 2D measurements of low-to-intermediate wavenumber density fluctuations in the edge of DIII-D H-mode plasmas suggest the presence of temporally intermittent or ‘bursting’ MTMs during the inter-ELM cycle in the steep gradient region. These measurements are obtained using a new intermediate radial resolution multichannel Charge eXchange Imaging (CXI) diagnostic that analyzes the intensity of the CVI emission at 529 nm. The mode is peaked near ρ = 0.97 with a radial full-width half maximum of 1.5–2.0 cm and a normalized density fluctuation amplitude peak of d n C n C ∼   5 % , peaking near 60 kHz in the lab frame. The mode additionally features a broad spectral width from 30 to 180 kHz and propagates in the electron diamagnetic direction in the plasma frame. CXI measurements taken during discharges with high density and current ramps provide evidence that MTMs become unstable at finite collisionality and remain at nearly the same location in ρ -space despite scanning of rational surface position. This indicates that the location of the peak in the electron diamagnetic frequency is a stronger driving force than individual rational surfaces.

A low-noise, high-speed optical detector module is characterized and successfully commissioned for the measurement of high-frequency, low-intensity beam emission on Wendelstein 7-X (W7-X). An ultra-narrow bandpass optical filter is employed to selectively transmit the desired emission line while suppressing broadband plasma background emissions. Carbon density fluctuations are investigated by observing the carbon C-VI emission line (n = 8 → 7, λ ∼ 529 nm), arising from charge exchange (CX) between the neutral beam atoms and the intrinsic carbon population. We present the characterization of the optical detector module and experimental measurements of carbon density fluctuations using available fibers on W7-X. The initial performance of the detector is presented in both active and passive CX measurements of intrinsic carbon density fluctuations. The low frequency dynamics of fluctuation is observed in response to the neutral beam and the pellet injection, demonstrating that the optical detector module is capable of providing a sufficient signal level with an adequate signal-to-noise ratio. In the upcoming OP2.4 campaign, this optical detector module will be adapted for use in a beam emission spectroscopy system by replacing the optical bandpass filter with one centered at 654 nm (90% transmission: 653–655.3 nm), which facilitates two-dimensional measurements of ion gyro-scale turbulence on W7-X.

We propose a quantum-enhanced plasma diagnostic based on squeezed states of light. Squeezed light can exhibit super-Poissonian photon statistics, leading to enhanced multiphoton absorption cross-sections compared to classical light. This effect enables improved sensitivity for two-photon excitation of high-energy atomic transitions such as ground-state excitation, and results in increased absorbed power and fluorescence in a plasma. We consider two methods of generating squeezed states and evaluate their advantages and limitations in the context of plasma absorption diagnostics. By comparing with and extending previous theoretical work, we predict an enhancement of the absorption signal by up to seven orders of magnitude at low intensities (10 ¹ W/m ² ), with diminishing enhancement persisting up to high intensities (10 ¹⁰ W/m ² ). These results suggest that squeezed-light sources offer a viable pathway toward quantum-enhanced plasma diagnostics.

Entangled two-photon absorption (ETPA) exhibits a quantum-enhanced two-photon absorption cross-section and a linear scaling with incident power that exceeds classical two-photon absorption (TPA) at low photon flux. Here, we assess the feasibility and applications of ETPA for active plasma spectroscopy. The ETPA-absorbed power for an Ar ⁺ species in a helicon plasma scenario is calculated to be as high as 0.6 nW cm ⁻¹ along the incident beam path for nondegenerate-entangled photon pairs that are near-resonant with an intermediate level. The ETPA absorption power exceeds classical TPA and Bremsstrahlung emission, a necessary condition for a feasible fluorescence measurement. Applications of ETPA plasma spectroscopy may include trace impurity detection, ground-state excitation, and continuous-wave pumping for high-bandwidth turbulence measurements. Possible benefits of plasma measurements are less harm to optical components with lower incident flux and reduced stray light that can contaminate optical diagnostics.

The Helically Symmetric Experiment (HSX) has demonstrated reduced neoclassical transport and flow damping with quasisymmetry, but the difference of turbulent transport between quasisymmetric and degraded-symmetry configurations has not been definitively assessed. Profile analysis presented here shows that anomalous transport at the mid-radius is larger with degraded quasisymmetry when temperature and density profiles are matched. An initial comparison ( T i / T e = 1 ) between the quasisymmetric and degraded symmetry configurations finds that trapped-electron mode (TEM) turbulence can support larger heat fluxes in the degraded symmetry configuration despite smaller linear growth rates. However, further simulations at the experimental temperature ratio ( T i / T e = 0.2 ) do not reproduce this effect. Experimental measurements of heat transport and density fluctuation amplitude are compared to nonlinear gyrokinetic simulations at the experimental temperature ratio. The heat flux and density fluctuation amplitude in simulation reproduce a substantial dependence on the density gradient, and the simulated heat flux matches measurements within experimental uncertainties, indicating that TEM turbulence is responsible for the anomalous transport at the steep density gradient in HSX.

A dual-band frequency-modulated reflectometry is employed on the Helically Symmetric eXperiment (HSX) stellarator. This system equips a fast PIN switch to alternate the frequency source between two voltage-controlled oscillators, providing an operational frequency range from 14.5 GHz to 25.5 GHz. A monostatic antenna geometry and an ellipsoidal mirror are implemented in the vessel of HSX, where the polarization of the transmitted microwave can be switched between O- and X-mode to accommodate the magnetic field and plasma density. Although the original system was designed for density fluctuation measurement, significant efforts have been undertaken to improve the system performance and to realize the density profile inversion. Recent improvements of the system reported here include calibration of the dispersion in the transmission line, optimization of the waveform, and implementation of the Choi-Williams time–frequency distribution for spectral analysis. In this paper, we present the optimization of the reflectometry system along with first experimental measurements of the density profile and observations of fluctuations during gas puffing experiments.