Motional Stark Effect Research Articles

Motional Stark effect on bound-free spectra

Motional Stark effect on bound-free spectra

Measurement of Stark-split beam and carbon charge exchange emissions for simultaneous B-field and temperature/rotation analysis at DIII-D.

A set of two newly designed, single-channel Czerny-Turner spectrometers has been deployed at the DIII-D tokamak for measurements of the motional Stark effect (MSE) split beam emission and the C6+ (CVI) carbon charge exchange recombination (CER) emission at high spectral (δλ = 0.13nm) and temporal (1-5kHz) resolution. High throughput optics (f/# = 2.8) allow for good signal-to-noise at high time resolution using fast EMCCD detectors. The MSE emission allows for spectral fitting of the magnitude and direction of the local B-field, while the carbon emission yields local ion temperature and toroidal rotation information. To reduce so-called Doppler broadening of the MSE emission, a new channel-specific variable lens-masking approach has been developed. Experimental data collected from the 2023 DIII-D experimental campaign demonstrate the signal quality and instrument fidelity for both diagnostic measurements. Moreover, initial CER data analysis shows a clear evolution of the toroidal rotation during edge localized modes. Initial progress on the advanced MSE model, including a new validated ray-trace model of the DIII-D collection optics, is shown via sensitivity analysis.

Sensitivity of motional Stark effect on different beam energy components for radial electric field measurements in tokamak plasmas.

Measurement of the internal magnetic field is crucial for determining the equilibrium, stability, and current density of a plasma in a tokamak. A motional Stark Effect (MSE) diagnostic was developed to provide a measurement of the internal magnetic field in tokamaks by analyzing the emission from the interaction of the plasma particle with an injected neutral beam. The Stark effect causes the shifting and splitting of deuterium spectral lines due to the Lorentz electric field. However, it is difficult to accurately measure the internal magnetic field components since the radial electric field inherently formed inside the plasma is mixed with the Lorentz field. Under the circumstances in the Korea Superconducting Tokamak Advanced Research (KSTAR) device, one possible approach is to derive a radial electric field by measuring and comparing the polarization angles from the full and half-energy components of the neutral beam. To utilize the polychromatic MSE diagnostics in KSTAR, the half-energy component wavelength bands according to various magnetic field and beam energy combinations have been calculated, and the filter combinations required for those measurements have been selected. The Stokes-filter model used to evaluate the effect of multiple-ion-source neutral beam injection on the MSE measurements has been extended to infer the sensitivity of this approach to take the non-ideal bandpass filter effects into account.

MHD stability trends and improved performance of LHD inward-shifted configurations: The role of the neutral beam current drive and thermal plasma density

The aim of the present study is to analyze the effect of the neutral beam current drive (NBCD), thermal plasma density, and NBI operational regime on the stability of pressure gradient-driven modes (PGDM) and Alfvén eigenmodes (AE) in LHD inward-shifted configurations. The stabilization of n/m=1/2 PGDM (n toroidal mode and m poloidal mode) is observed in the discharge 167 800 during the co-NBCD phase. The iota profile evolution measured by motional stark effect diagnostic may indicate the iota profile up-shift caused by the co-NBCD can induce a non-resonant transition of the rational surface 1/2 before the mode stabilization. The evolution of the iota profile and continuum gaps in the discharge 167 805 during the ctr-NBCD phase leads to the stabilization of the AE, caused by the narrowing of the continuum gap as the iota profile down-shift. Opposite stability trends are identified for PGDM and AE stability with respect to the thermal plasma density. A larger thermal plasma density (larger thermal β) further enhances PGDM although the continuum gaps are narrower leading to configurations with stable AEs. The linear stability of AEs is analyzed using the gyro-fluid FAR3d code to reproduce the AE stability trends observed in the experiments with respect to the NBCD and thermal plasma density. The analysis of hypothetical scenarios dedicated to study different NBI operational regimes with respect to EP energy, and β and radial density profiles indicate off-axis NBI operation shows a higher EP β threshold to destabilize AEs compared to on-axis configuration. This is explained by the presence of a TAE gap in the inner plasma region, easily destabilized by an on-axis NBI injection. The control of the NBCD and thermal plasma in the discharge 167 800 shows a transitory stabilization of PGDM and AEs, as well as an improved discharge performance identified by an increment of the neutron fluxes.

The CXSFIT spectral fitting code: Past, present and future.

Magnetically confined plasma experiments generate a wealth of spectroscopic data. The first step toward extracting physical parameters is to fit a spectral model to the often complex spectra. The CXSFIT (Charge eXchange Spectroscopy FITting) spectral fitting code was originally developed for fitting charge exchange spectra on JET from the late 1980s onward and has been further developed over decades to keep up with the needs of the users. The primary use is to efficiently fit a large number of spectra with many constrained Gaussian spectral lines of which the physical parameters can be coupled in a user-friendly manner. More recent additions to the code include time-dependent couplings between parameters, flexible background subtraction, and a non-linear coupling scheme between fit parameters. The latter was a pre-requisite for implementing Zeeman and motional Stark effect multiplets in the library of spectral features. The ability to save and replay "fit recipes," even when multiple iterations are required, has ensured the traceability of the results and is one of the keys to the longevity and success of the code. The code is also in use on other tokamaks (AUG, ST-40) and to fit data from other spectroscopic diagnostics on JET. In this paper, we document the current capabilities and philosophy behind the structure of the code, including some of the algorithms used to calculate spectral features numerically efficiently. We also provide an outline of how CXSFIT could be transferred into a framework that would be able to meet the spectral fitting requirements of future devices, such as ITER.

Implementation of a real-time MSE system.

Motional Stark effect polarimetry is a key diagnostic for plasma fusion research since its usage on PBX-M. The MSE diagnostic measures the radial magnetic pitch angle profile in a plasma from a neutral beam by observation of Stark split D-alpha emission from atoms excited by collision with ions and electrons in the plasma. The pitch angle measurement is used with equilibrium reconstruction codes to determine the q-profile for studies of plasma stability, confinement, and transport. Historically, the algorithm was used in a post-processing fashion. The goal of our work was to apply this method in real time and pass the results to the plasma control system computer for real-time equilibrium reconstruction and control.

The motional Stark effect diagnostic for ITER.

An overview of the plans for the motional Stark effect (MSE) diagnostic installation on the International Thermonuclear Experimental Reactor (ITER) is presented. The MSE diagnostic uniquely provides spatially localized magnetic field measurements inside the plasma. These are used to constrain equilibrium reconstructions to determine q(r), the safety factor as a function of minor radius. Meeting the system requirements to deliver q-profiles and related quantities with the specified radial resolution of 20 points over the minor radius, 10ms time resolution, and better than 10% accuracy is challenging. MSE systems observe the D/H-α emission near 656.3nm from neutral beams. As the beam atoms traverse the magnetic field, B⃗, at high velocity, v⃗, they experience a Lorentz electric field, v⃗×B⃗, which causes the spectral emission to be split and polarized due to the Stark effect. Traditional MSE-LP (line polarization) measurements determine the direction of the magnetic field in the observation volume using polarimetric analysis of the detected light. The harsh conditions of ITER are expected to deposit thin films of contaminants on the first mirror, which would alter the polarization state of reflected light significantly. On ITER, the combination of high magnetic field strength and high energy beams makes the Stark spectrum resolution suitable for the determination of the magnetic field magnitude from the line shift, so this approach has been selected. Every aspect of the measurement system must be planned for the burning plasma environment and carefully analyzed ahead of time. Current status and plans for the system are presented.

Designing ITER motional Stark effect line shift (MSE-LS) spectrometers.

As a part of ITER beam aided diagnostics, the design of Motional Stark Effect (MSE) diagnostic observing the emission from the Balmer-α line is underway. The physics of Stark splitting shows that the Stark manifold is polarization dependent, and the energy splitting results in a line shift proportional to the electric field. Due to the challenges of maintaining the calibration of the plasma facing mirrors in ITER, the conventional MSE polarimetry measurement technique is replaced with a spectral approach that is deemed more favorable in the ITER environment. The MSE line shift (LS) diagnostic is designed to quantify the Lorentz electric field magnitude by measuring the Stark manifold using visible spectroscopy. In the presence of large magnetic fields and high energy heating beams of 1MeV, the expected Stark splitting is much larger than in typical devices. The MSE-LS design has unique challenges requiring careful consideration and modeling of its viewing geometry and photon budget. The MSE-LS approach on ITER is promising but has stringent demands on the allowable errors for the statistical and systematic fitting uncertainties. In this study, a full system model and numerical simulations of data for each sightline are completed. For a range of optical transmission fractions, photon noise analysis is conducted to determine the statistical uncertainties. This provides guidance on the spectrometer throughput, dispersion at the detector, optics, and other design choices. A conceptual design of a high throughput spectrometer with a volume phase transmission grating is presented.

Equilibrium reconstruction constrained by the consistency of current simulation on EAST

The attainment of a reliable equilibrium is a critical aspect of tokamak experiments and physics analysis. A common method for establishing a reliable equilibrium current involves reconstructing it from indirect measurements, such as those obtained from polarimeter-interferometers (POINT) and motional Stark effect (MSE) systems. However, uncertainties still exist in the reconstruction results. For the equilibrium reconstruction on the EAST tokamak, which is based on the POINT system, the primary sources of uncertainty are the limited scope of measurements and the sensitivity of the reconstruction process. This paper proposes an enhanced approach that utilizes current simulation as a constraint to maintain consistency between the initial equilibrium and the simulated results. The radio frequency waves driven current is identified as a particularly influential component due to its interaction with the q profiles of the equilibrium and the deposition region of the waves. Two specific discharges are presented to illustrate how a new equilibrium can be achieved, which enhances consistency between the equilibrium and the simulated current, taking into account the dependencies of various components.

Safety factor diagnostic for tokamak core plasma from three-dimensional reconstruction of pellet ablation trail.

Using a stereo camera system, a new diagnostic for the safety factor of the core plasma based on the pellet ablation trail is applied on the Experimental Advanced Superconducting Tokamak (EAST). In EAST discharge No. 128 874, a shattered pellet injection system is applied to inject a shattered neon pellet into the EAST. Since the strong magnetic field in tokamaks binds the ablated pellet material, the orientation of the pellet ablation trail is the same as the local magnetic field direction. Thus, from the three-dimensional reconstruction result of the pellet ablation trail, the local safety factor q can be obtained. The motional Stark effect (MSE) diagnostic is applied to determine the safety factor q profile in this shot. The determined safety factor q results for this new diagnostic are in quantitative agreement with those from the MSE diagnostic with the mean relative difference of only 6.8%, confirming the effectiveness of this new diagnostic of the safety factor.

Machine learning-based real-time kinetic profile reconstruction in DIII-D

Kinetic equilibrium reconstruction plays a vital role in the physical analysis of plasma stability and control in fusion tokamaks. However, the traditional approach is subjective and prone to human biases. To address this, the consistent automatic kinetic equilibrium reconstruction (CAKE) method was introduced, providing objective results. Nonetheless, its offline nature limits its application in real-time plasma control systems (PCSs). To address this limitation, we present RTCAKENN, a machine learning model that approximates 7 CAKE-level output profiles, namely pressure, inverse q, toroidal current density, electron temperature and density, carbon ion impurity temperature and rotation profiles, using real-time available inputs. The deep neural network consists of an encoder layer, where the scalars and interdependent inputs such as plasma boundary coordinates and motional Stark effect data are encoded using multi-layer perceptrons (MLPs), while profile inputs are encoded by 1D convolutional layers. The encoded data is passed through a MLP for latent feature extraction, before being decoded in the decoding layers, which consist of upsampling and convolutional layers. RTCAKENN has been implemented in the DIII-D PCS and our model achieves accuracy comparable to CAKE and surpasses existing real-time alternatives. Through clever dropout training, RTCAKENN exhibits robustness and can operate even in the absence of Thomson scattering data or charge exchange recombination data. It executes in under 8 ms in the real-time environment, enabling future application in real-time control and analysis.

Experimental evidence of magnetic flux pumping in ASDEX upgrade

In high-β scenarios with on-axis co-current electron cyclotron current drive, which normally lowers q 0 below unity, the absence of sawteeth suggests the involvement of an additional current redistribution mechanism beyond neoclassical current diffusion. This is supported by imaging motional Stark effect diagnostic measurements, which indicate that q 0 remains consistently around 1. This phenomenon is observed in the presence of a 1/1 mode, indicating its potential role in the current redistribution. It is shown that the mode’s ability to modify the central current and suppress sawteeth increases with plasma pressure. These findings align with a recent theoretical model, which predicts a pressure threshold for sawtooth avoidance by a 1/1 quasi-interchange mode and where this threshold increases with the strength of inward current diffusion. Moreover, the advantages of the flux pumping scenario for future machines are highlighted.

Fast forward modeling of neutral beam injection and halo formation including full Balmer-α emission prediction at W7-X

A full collisional-radiative (CR) neutral beam injection model based on Gaussian pencil (Gausscil) beams and a diffusive CR neutral halo model are presented. The halo is a neutral cloud around the neutral beam forming due to multiple charge exchange (CX) reactions. Both models do not rely on Monte-Carlo techniques and are thereby orders of magnitude faster than commonly used models. To model the neutral halo a system of coupled diffusion equations is solved numerically, enforcing mixed boundary conditions. From the equilibrium hydrogen neutral densities in the second excited energy state (n = 3), the Balmer-α emission intensity is calculated and the full spectrum is predicted, including effects as Doppler shifts and broadening due to the complex neutral beam geometry and the motional Stark effect (MSE) from the magnetic field. All forward models are implemented in the Minerva [1] Bayesian analysis framework to enable detailed multivariant inference from Balmer-α spectroscopy data. The modeled neutral beam and halo densities are successfully verified against calculations with a validated Monte-Carlo code for the W7-X beam and plasma geometry, especially proving the validity of the halo diffusion ansatz. A comparison of the predicted emission spectra with the experimental data proves the accuracy of the implemented model. All important parameters defining the neutral beams are inferred and compared to available reference values.

Numerical investigation of the 2/1 double tearing mode in EAST with the CLT code

The pressure crashes observed in shot No. 71326 in the Experimental Advanced Superconducting Tokamak are numerically investigated with the three-dimensional, toroidal, and full resistive-magnetohydrodynamics code (CLT). Based on the experimental observations, the pressure crash is caused by the nonlinear evolution of the m/n = 2/1 double tearing mode (DTM), where n and m are the toroidal and poloidal mode numbers, respectively. However, we find that the m/n = 2/1 DTM is stable based on the safety factor (q) profile from the equilibrium code EFIT, which indicates that the original q profile is somewhat inconsistent with the actual profile due to q measurement uncertainty. Since there is no motional Stark effect diagnostic for this shot, the local information of the magnetic field is missing, which leads to the largest contribution to the discrepancy. If other information is perfectly known and the q profile is the only uncertainty, then we could provide some information for the EFIT reconstruction by comparing our simulation results with electron cyclotron emission signals to constrain the uncertainty of the q profile to a much smaller region. The influence of plasma rotation and the two-fluids effect is also discussed.

A Bayesian formulation for perturbed current tomography in tokamaks

An initial investigation into the application of Bayesian inference to the reconstruction of the spatial distribution of current perturbations in tokamaks from diagnostic signals is presented. Previous work in Bayesian equilibrium current tomography is extended to the case of a complex phasor representation of harmonically time varying current distributions. A forward function to predict the response of magnetic diagnostics is constructed using only electrodynamics and not reduced models of ideal MHD. The extension of this forward function to incorporate a fully kinetic model of the plasma state is suggested. The response of soft x-ray diagnostics, and the motional Stark effect diagnostic to the current perturbations are also predicted and the integration of all diagnostics into a single estimate of the current perturbation is proposed. Simulations with synthetic diagnostics in simple geometry demonstrate that the perturbed current distribution can be reconstructed subject to prior assumptions regarding solution smoothness.

Reconstruction of tokamak plasma safety factor profile using deep learning

The motional Stark effect (MSE) diagnostic has been a standard measurement for the magnetic field line pitch angle in tokamaks that are equipped with neutral beams. However, the MSE data are not always available due to experimental constraints, especially in future devices without neutral beams. Here we develop a deep-learning based model (SGTC-QR) that can reconstruct the safety factor profile without the MSE diagnostic to mimic the traditional equilibrium reconstruction with the MSE constraint. The model demonstrates promising performance, and the sub-millisecond inference time is compatible with the real-time plasma control system.

Microwave ion source with dual helical antenna for diagnostics neutral beam of ALBORZ tokamak

An efficient ion source of the diagnostic neutral beam injection (DNBI) is designed and simulated for Alborz Tokamak, based on the microwave plasma source. The diagnostic neutral beam is designed for use in some diagnostics system such as charge-exchange recombination spectroscopy (CXRS), Rutherford Scattering (RS), and Motional Stark Effect (MSE) of Alborz Tokamak. In this work, a new helical antenna is designed and simulated for a microwave plasma source, to reach a plasma density of order8.23×1017m−3. The microwave plasma source is employed by the high-efficient ion beam accelerator. In this simulation, three-electrodes in different potentials of 20 kV, −2 kV, and grounded respectively, are used as extraction system of the ion beam source. According to our design, nine apertures grids are considered for the accelerator system. The simulation results show that, the system can extract an ion beam with energy and current of 20 keV and 60 mA respectively. The extracted ion beam consists of nine beamlets, where the beam waist and the current of each of them are calculated about 3 mm and 6.5 mA, respectively. The results of this work indicate that the ion beam with minimum divergence angle of 32 mrad can be generated by the proposed ion beam source.

On the frequency bifurcations of the MHD startup modes in NSTX

The observed bifurcations of the low frequency (<50 kHz) and low toroidal periodicity (n < 5) magnetohydrodynamic (MHD) activity often present in the initial part of the National Spherical Tokamak Experiment (NSTX) discharges can be explained by the evolution of the radial profile of the safety factor (q=rBϕ/RBθ) crossing multiple rational surfaces in the core. Important performance limiting instability mechanisms in the NSTX spherical tokamak are often linked to low frequency and low-n MHD activity. They are quite common in long-pulse NSTX plasmas. They can be present at the beginning of the plasma current flat-top, at the end of the discharge or during the whole duration, and they have been observed to deleteriously impact performance over a wide range of q95. An interesting feature observed in some NSTX discharges is the presence of a bifurcation in the frequency of the low n modes, as low as n = 1, that have frequencies comparable to the plasma core rotation divided by n. Equilibrium reconstructions constrained by magnetic diagnostics data and motional stark effect pitch angle radial profiles suggest that the observed bifurcations are linked to a fast evolving minimum value of q. 3D non-linear resistive MHD simulations show that these modes are ideal and exist as non-resonant before the correspondent rational surface enters the plasma.

Effect of collisions on motional Stark broadening of spectral lines

The shape of spectral lines in strongly magnetized plasmas is investigated theoretically in the framework of astrophysical research. Under certain conditions, the broadening of lines observed on white dwarf spectra is dominated by the so-called motional Stark effect, which occurs due to the Lorentz electric field v→×B→. If the plasma density is high enough, collisions between the emitter and perturbers change the atomic velocity v→ and the resulting motional Stark broadening is modified. We illustrate this modification through dedicated line shape calculations based on a stochastic model for the atomic velocity. A universal line shape formula, which is applicable to any isolated atomic line, is proposed for implementation in line shape codes.

Spatial heterodyne spectroscopy for fast local magnetic field measurements of magnetized fusion plasmas.

A novel spectroscopy diagnostic for measuring internal magnetic fields in high temperature magnetized plasmas has been developed. It involves spectrally resolving the Balmer-α (656nm) neutral beam radiation split by the motional Stark effect with a spatial heterodyne spectrometer (SHS). The unique combination of high optical throughput (3.7 mm2sr) and spectral resolution (δλ ∼ 0.1 nm) allows these measurements to be made with time resolution ≪1ms. The high throughput is effectively utilized by incorporating a novel geometric Doppler broadening compensation technique in the spectrometer. The technique significantly reduces the spectral resolution penalty inherent to using large area, high-throughput optics while still collecting the large photon flux provided by such optics. In this work, fluxes of order 1010s-1 support the measurement of deviations of <5 mT (ΔλStark ∼ 10-4 nm) in the local magnetic field with 50 µs time resolution. Example high time resolution measurements of the pedestal magnetic field throughout the ELM cycle of a DIII-D tokamak plasma are presented. Local magnetic field measurements give access to the dynamics of the edge current density, which is essential to understanding stability limits, edge localized mode generation and suppression, and predicting performance of H-mode tokamaks.