Plasma Equilibrium Research Articles

Dielectronic recombination studies of ions relevant to kilonovae and nonlocal thermodynamic equilibrium plasma

This study presents calculations of rate coefficients, resonance strengths, and cross sections for the dielectronic recombination (DR) of text Y text Sr text Te and text Ce — low-charge ions relevant to kilonovae and nonlocal thermodynamic equilibrium (non-LTE) plasmas. Using relativistic atomic structure methods, we computed DR rate coefficients under conditions typical of these environments. These DR rate coefficients and cross sections were calculated using the Flexible Atomic Code. The DR resonance features were identified by comparing theoretical resonance energies, estimated as the difference between National Institute of Standards and Technology excitation energies and Dirac binding energies, with dominant autoionizing states confirmed through an analysis of autoionization rates. Our results highlight the critical role of low-lying DR resonances in shaping rate coefficients at kilonova temperatures (∼ 10^4 K) and regulating charge-state distributions. Pronounced near-threshold DR resonances significantly influence the evolving ionization states and opacity of neutron star merger ejecta. Comparisons with previous studies emphasize the necessity of including high-n Rydberg states for accurate DR rate coefficients, especially for complex heavy ions with dense energy levels. Discrepancies with existing datasets underscore the need for refined computational techniques to minimize uncertainties. These results provide essential input for interpreting spectroscopic observations of neutron star mergers, including James Webb Space Telescope data. We also put forward suitable candidates for experimental studies, recognizing the challenges involved in such measurements. The data presented here have the potential to refine models of heavy-element nucleosynthesis, enhance plasma simulation accuracy, and improve non-LTE plasma modeling in astrophysical and laboratory settings.

Fast ion stabilization of tilt in large radius FRCs

The field reversed configuration (FRC) has been a curious case in plasma physics research in that early MHD analysis suggested FRCs should be grossly unstable, while experimental results contradicted that prediction. Later, this theory was able to resolve this contradiction by understanding that finite Larmor radius effects largely negated the MHD predictions. Similarly, previous theoretical studies of beam driven FRCs predicted that such system would be unstable to beam driven modes while, again, experimental results indicated the contradiction. In this paper, we reconcile the theoretical understanding of beam driven modes with experimental observations of stability in these systems. By self-consistently capturing fast ion generation from neutral beam injection and its impact on the plasma equilibrium, we show that low amplitude perturbations in the magnetic field, driven by betatron particles, modify the precession frequencies of the betatron particles such that the drive for compressional Alfvén waves in the thermal plasma is reduced. Finally, we are able to demonstrate, for the first time, stable beam driven FRC evolution at high S*/E in 3D kinetic simulations.

Effects of non-rigidity on fast plasma boundary control using in-vessel coils in JT-60SA

Abstract An effective fast plasma position control method using in-vessel poloidal field coils and capable of maintaining high-elongation plasma, and hence high vertical instability growth, was developed utilizing an MHD equilibrium simulation code “MECS.” First, the vertical instability was investigated. It was found that the plasma boundary moves faster than the plasma center due to vertical instability, indicating that boundary-focused control, here called ISO-FLUX scheme, is more effective by accounting for the plasma non-rigidity than schemes focused on the plasma vertical position. In JT-60SA, the ISO-FLUX scheme, in combination with a frequency separation technique, which serves to reduce high-frequency magnetic flux residuals at the control points around the plasma boundary, is employed in the control by in-vessel poloidal field coils. As a result, MECS simulations predict the stable operation of JT-60SA at a target plasma current of 5.5 MA with high elongation (κ ~ 1.94), even during poloidal beta collapse. These findings highlight the importance of considering non-rigid plasma displacement in fast plasma position control, offering valuable insights for real-time plasma equilibrium control in future nuclear fusion reactors.

Physics-informed neural networks for the modelling of interferometer-polarimetry in tokamak multi-diagnostic equilibrium reconstructions

Abstract Equilibrium reconstruction is crucial in nuclear fusion and plasma physics, as it enables the understanding of the distribution of fundamental plasma quantities within a reactor. Given that equilibrium reconstruction is an ill-posed problem, it is essential to constrain the algorithm with multiple diagnostics to achieve accurate results. Among these, the interferometer-polarimeter is one of the most valuable diagnostics for constraining equilibrium reconstruction, as it provides line-integrated information about the internal magnetic fields. However, the polarisation evolution of an electromagnetic wave traversing a magnetised plasma exhibits non-linear behaviour, making it challenging to incorporate polarimeter data into the reconstruction process. This difficulty often leads to the use of a linear approximation, known as the type-I approximation, in the inversion algorithm. Unfortunately, this approximation can significantly limit the accuracy of the reconstructions in many cases. In this work, we present a physics-informed neural network (PINN) algorithm for reconstructing plasma equilibrium using a multi-diagnostic approach that includes magnetics, Thomson scattering, and interferometer-polarimeter data. The PINN algorithm employs three models for reconstruction: the first uses the type-I approximation, the second uses the non-linear polarization equation under the cold-plasma approximation, and the third uses a comprehensive model that accounts for thermal effects, both relativistic and non-relativistic (defined as the hot plasma model). Parametric analyses conducted on synthetic cases demonstrate that the hot plasma model consistently yields the best results, while reconstructions using the type-I or cold plasma approximations are prone to systematic errors in the reconstructed plasma quantities. The PINN model has been tested on ITER-like plasma configurations with noisy measurements, showing that the inclusion of interferometer-polarimeter data significantly improves accuracy, achieving around 99.9%. Future work aims to transfer the algorithm to existing experimental nuclear fusion reactors and to integrate additional diagnostics for further enhancing the reliability and accuracy of the solutions.

Evaluation of Adequate Type of Non-Thermal Plasma for Treating Oily Sludge to Produce Refined Fuel

Although oily sludge is an industrial waste and difficult to separate, its calorific value can still reach 6000 cal/g, thus possessing significant recycling value. This study compares various types of non-thermal plasma for refining oily sludge. The pre-treatment technology utilized filtration combined with solvent extraction to extract the oil portion from the oily sludge. Subsequently, two types of non-thermal plasma, DC streamer discharge and dielectric plasma discharge, were used to crack and activate the oily sludge under different operating conditions. The fuel compositions and properties of the refined fuel treated by two types of non-thermal plasma were compared. The elemental carbon and oxygen of the oily sludge after treatment in a direct DBD plasma reactor for 8 min were 1.96 wt.% less and 1.38 wt.% higher than those of commercial diesel. The research results indicate that the pre-treatment process can effectively improve the refined fuel properties. After pre-treatment, the calorific value of the primary product from the oily sludge can reach 10,598 cal/g. However, the carbon residue of the oily sludge after pre-treatment remained as high as 5.58 wt.%, which implied that further refining processes are required. The streamer discharge plasma reactor used a tungsten needle tip as a high-voltage electrode, leading to a rather small treated range. Corona discharge and arc formation are prone to being produced during the plasma action. Moreover, the addition of quartz glass beads can form a protruding area on the surface of the oily sludge, generating an increase in the reacting surface of the oily sludge, and hence an enhancement of treatment efficiency, in turn. The direct treatment of DBD plasma can thus have a wider and more uniform operating range of plasma generation and a superior efficiency of plasma reaction. Therefore, a direct DBD type of non-thermal equilibrium plasma reactor is preferable to treat oily sludge among those three types of plasma reactor designs. Additionally, when the plasma voltage is increased, it effectively enhances fuel properties.

Plasma equilibrium in a magnetic field of co-axial current coils: A novel view

A new mode of operation of a so-called dipolar magnetic confinement apparatus and a novel approach to stationary magnetic plasma confinement with co-axial current coils, which can be suitable for fusion applications, are suggested.

Cross-species comparisons of plasma binding and considerations for data evaluation.

Cross-species comparisons of plasma binding and considerations for data evaluation.

Nonlinear Propagating Slow Waves in Cooling Coronal Magnetic Loops

We study the propagation of slow magnetosonic waves in coronal magnetic loops. In our study we take nonlinearity and loop cooling into account. We use the small beta approximation and neglect the effect of magnetic field perturbation on the wave propagation. In accordance with this we assume that the tube cross-section does not change. We also neglect the equilibrium plasma density variation along and across the tube. As a result the equations of magnetohydrodynamics reduce to purely one-dimensional gasdynamic equations that includes the effect of viscosity and thermal conduction. We assume that the perturbation amplitude is sufficiently small and use the reductive perturbation method to derive the generalised Burgers’ equation describing the evolution of initial perturbations. First we study a case with weak dissipation and drop the term describing it. When there is no cooling the evolution of the initial perturbation results in a gradient catastrophe. However strong cooling can prevent it. Then we solve the full equation numerically assuming that the temperature decreases exponentially. We fix the initial perturbation amplitude and then study the dependence of perturbation evolution on the cooling time. The main result that we obtain is that moderate cooling decelerates the wave damping. This effect is related to the fact that the dissipation coefficients are proportional to the temperature in 5/2 power. As a result they decrease fast because of plasma cooling. However strong cooling can cause perturbation damping on its own.

Validation and predictions of reduced models for stochastic electron transport in MAST and MAST-U

Abstract Magnetic stochastic perturbations can strongly influence cross-field transport in high β tokamak plasmas. The impact of stochastic magnetic fields on electron heat transport in MAST/MAST-U is studied over a range in collisionality. The physics guided semi-empirical Rechester-Rosenbluth and Rebut-Lallia-Walkins models are separately used to describe the stochastic field contribution to electron heat transport, and to supplement TGLF reduced model predictions of the transport from electrostatic turbulence. These combined models of anomalous transport are implemented in the JINTRAC code, and applied to transport simulations of the flat-top phase in MAST/MAST-U. The different ranges of validity of the stochastic transport models are briefly reviewed, focusing on the length-scales involved in the transport process. The principal relevant length-scales have been calculated using the plasma equilibrium characteristics, and used to determine the most appropriate stochastic transport model that is then applied in each shot. This analysis strongly suggests that stochasticity is an important transport mechanism in spherical tokamaks that should be included in ST plasma scenarios where strong electron heat transport is not described by other instabilities.

Study and analysis of ion cyclotron resonance heating scenarios for ADITYA-U Tokamak

Abstract This study provides a detailed analysis of ion cyclotron resonance heating (ICRH) scenarios for ADITYA-U Tokamak which is a crucial technique for core plasma heating in magnetically confined devices. The ICRH code LION is used to study the cyclotron resonance heating of Hydrogen minority ions in Deuterium plasma. The resonant heating of the minority hydrogen ions is analyzed for both fundamental and second harmonic frequencies which coincide with the second and fourth harmonics of Deuterium ions, respectively. The LION code, a full-wave solver based on the finite hybrid element method, enables detailed modeling of fast magnetosonic waves in the complex, axisymmetric geometry of the ADITYA-U Tokamak. A parametric study of power deposition both total and on individual species has been performed using several key parameters including wave frequency, toroidal wave number (k∥ ), electron temperature, and minority ion concentration. Additionally, we examine the impact of both circular and shaped plasma equilibrium conditions on the distribution of the absorbed wave power. Detailed simulations suggest that minority ion heating is quite effective in ADITYA-U plasma with a core density of 2 × 1019 m−3 and an electron temperature of 0.35 keV at lower toroidal wave number (1 to 8) and minority concentration of up to 15%. The second harmonic minority heating scheme is quite promising with significant power deposition (98%) on hydrogen ions in ADITYA-U tokamak.

Plasma response to resonant magnetic perturbations in HL-3: roles of plasma shape and pressure

Abstract Plasma response to the resonant magnetic perturbations (RMPs), envisaged for controlling the edge-localized mode (ELM) in the HL-3 tokamak under high pressure conditions, is investigated employing the MARS-F (Liu Y.Q. et al 2000 Phys. Plasmas 7 3681) and MARS-K (Liu Y.Q. et al 2008 Phys. Plasmas 15 112503) codes. Exploited mainly are influences of the plasma shape (upper and lower single-null, double-null and limiter shapes) and equilibrium pressure on the plasma response, following both the fluid and kinetic models of the plasma. Key physics quantities associated with the plasma response are examined, revealing that high equilibrium pressure drives significant amplification of the n=1 (n is the toroidal mode number) RMP field in the plasma edge region. The single-null plasma configurations accommodate more effective ELM control, reducing the required equilibrium pressure for triggering a strong resonant field amplification effect. As a result, a stronger edge-peeling type of the plasma response is identified with the single-null shape. For the double-null configuration, the slight up-down asymmetric pattern of the perturbed magnetic field originates from the toroidal plasma flow. The plasma response computed with the kinetic model is similar to that with the fluid model, independent of the plasma shaping. Similar but less pronounced response effects are found for the n=2 RMP.

Power Density and Thermochemical Properties of Hydrogen Magnetohydrodynamic (H2MHD) Generators at Different Pressures, Seed Types, Seed Levels, and Oxidizers

Hydrogen and some of its derivatives (such as e-methanol, e-methane, and e-ammonia) are promising energy carriers that have the potential to replace conventional fuels, thereby eliminating their harmful environmental impacts. An innovative use of hydrogen as a zero-emission fuel is forming weakly ionized plasma by seeding the combustion products of hydrogen with a small amount of an alkali metal vapor (cesium or potassium). This formed plasma can be used as a working fluid in supersonic open-cycle magnetohydrodynamic (OCMHD) power generators. In these OCMHD generators, direct-current (DC) electricity is generated straightforwardly without rotary turbogenerators. In the current study, we quantitatively and qualitatively explore the levels of electric conductivity and the resultant volumetric electric output power density in a typical OCMHD supersonic channel, where thermal equilibrium plasma is accelerated at a Mach number of two (Mach 2) while being subject to a strong applied magnetic field (applied magnetic-field flux density) of five teslas (5 T), and a temperature of 2300 K (2026.85 °C). We varied the total pressure of the pre-ionization seeded gas mixture between 1/16 atm and 16 atm. We also varied the seed level between 0.0625% and 16% (pre-ionization mole fraction). We also varied the seed type between cesium and potassium. We also varied the oxidizer type between air (oxygen–nitrogen mixture, 21–79% by mole) and pure oxygen. Our results suggest that the ideal power density can reach exceptional levels beyond 1000 MW/m3 (or 1 kW/cm3) provided that the total absolute pressure can be reduced to about 0.1 atm only and cesium is used for seeding rather than potassium. Under atmospheric air–hydrogen combustion (1 atm total absolute pressure) and 1% mole fraction of seed alkali metal vapor, the theoretical volumetric power density is 410.828 MW/m3 in the case of cesium and 104.486 MW/m3 in the case of potassium. The power density can be enhanced using any of the following techniques: (1) reducing the total pressure, (2) using cesium instead of potassium for seeding, and (3) using air instead of oxygen as an oxidizer (if the temperature is unchanged). A seed level between 1% and 4% (pre-ionization mole fraction) is recommended. Much lower or much higher seed levels may harm the OCMHD performance. The seed level that maximizes the electric power is not necessarily the same seed level that maximizes the electric conductivity, and this is due to additional thermochemical changes caused by the additive seed. For example, in the case of potassium seeding and air combustion, the electric conductivity is maximized with about 6% seed mole fraction, while the output power is maximized at a lower potassium level of about 5%. We also present a comprehensive set of computed thermochemical properties of the seeded combustion gases, such as the molecular weight and the speed of sound.

Two-Dimensional Mathematical Models of Strict Plasma Equilibrium in Galatea Magnetic Traps and Numerical Analysis of Stability

Two-Dimensional Mathematical Models of Strict Plasma Equilibrium in Galatea Magnetic Traps and Numerical Analysis of Stability

Beta limit of the stable interchange mode for a toroidal current dipole magnetic configuration

Abstract A free boundary plasma equilibrium solver is used in the dipole field of a ring current system. The solver employs multi-grid technology to effectively address the issue of slow solution speeds caused by changes in the plasma boundary. A power law pressure model is utilized to investigate the beta limit of the stable interchange mode. The stability of the interchange mode is influenced by beta, with high-beta pressure profiles tending to excite interchange instabilities at the plasma edge. Under the condition of a stable interchange mode, we investigated the effects of peak pressure position , steepness of the pressure gradient g, and plasma radius divided by the D-coil radius on the maximum beta βmax and the volume averaged beta 〈β〉 limit. βmax and 〈β〉 satisfy rapidly decaying power functions of g, such as βmax ~ g-3.94 and 〈β〉 ~ g-3.55. and 〈β〉 obey slowly increasing power functions of , such as βmax ~ 0.5 and 〈β〉 ~ 0.28. Additionally, βmax and 〈β〉 follow negative power functions of, i.e. βmax ~ -1.98 and 〈β〉 ~ -1.9. and do not significantly affect the trend with increasing g.

Linear MHD stability of 3D equilibrium formed after application of resonant magnetic perturbations

Abstract The three-dimensional magnetohydrodynamic code JOREK was utilized to perform a linear study on the HL-2A device. The primary objective of this investigation is to gain insight into how the Resonant Magnetic Perturbation (RMP) influences plasma equilibrium and, consequently, the behavior of the Edge Localized Modes (ELMs). A scan of the n = 1 (n is the toroidal mode number) RMP coil current from 1 to 4.9 kAt reveals a mode transition from n = 4 to n = 3 for the dominant toroidal mode number, after the RMP field exceeds a certain threshold. By comparing the changes in the electron density expansion diagrams at specified magnetic surface locations before and after the transition, it is found that the n = 1 periodic structure resulting from the application of RMP forms an n = 3 mode structure through mode linear coupling with natural ELMs (with the dominant mode number n = 4 ). This is a key reason for the change in the dominant mode number.

Plato: A High-Fidelity Library for Multicomponent Gases and Plasmas

This work presents plato (PLAsmas in Thermodynamic nOn-equilibrium), a high-fidelity library for the thermodynamics, transport, and collisional-radiative kinetics of equilibrium and nonequilibrium multicomponent gases and plasmas. plato is implemented in a modular and extensible fashion using Fortran 2003/2008 and can also be utilized in C and C++ codes. The theoretical framework of the library is based on nonequilibrium kinetic theory for dilute gases. A distinctive feature of plato is the availability of a hierarchy of physicochemical models of increasing complexity and accuracy, ranging from legacy multitemperature to grouping and/or collisional-radiative models. Application examples are presented and discussed to demonstrate the main features and capabilities of the library.

Reformulating polarized radiative transfer for astrophysical applications (I). A formalism allowing non-local Magnus solutions

The solar atmosphere is diagnosed by solving the polarized radiative transfer problem for plasmas in Non-Local Thermodynamical Equilibrium (NLTE). A key challenge in multidimensional NLTE diagnosis is to integrate the radiative transfer equation (RTE) efficiently, but current methods are local, limited to constant propagation matrices. The formalism presented in this paper lays the foundations to achieve an efficient non-local integration of the RTE based on the Magnus expansion. Our approach starts formulating the problem in terms of rotations represented in the Lorentz-Poincare group (Stokes formalism) and motivating the use of the Magnus expansion. Then, we combine a highly detailed algebraic characterization of the propagation matrix with Magnus to reformulate the homogenous solution to the RTE. Thus, we obtain a compact analytical evolution operator supporting arbitrary variations of the propagation matrix to first and second order in the Magnus expansion and showing the way to higher orders. Finally, we reformulate the inhomogeneous part to make it solvable with the Magnus expansion too, which gives rise to an interesting new object: the inhomogeneous evolution operator. This provides the first consistent and general formal solution of the RTE that furthermore is non-local, efficient, and accurate by design, with other peculiarity: it separates the integration part from the algebraic formal solution. Our framework is verified analytically and with a computational implementation that leads to a new family of numerical radiative transfer methods and suggests several applications, e.g. accelerating NLTE calculations with non-local radiative transfer. With cosmetic changes, our results apply to other universal physical problems sharing the Lorentz-Poincare algebra of the RTE and special relativity.

Integer charge states in hot dense plasmas using the quantum average-atom model

We present a quantum mechanical model to describe the integer charge states inside a plasma environment. We generalize the quantum average-atom model. The classical theory of fluctuations is used to select the integer charge states that need to be considered. We adapt what has been done to characterize the density effects of electronic configurations in hot dense plasmas. Illustrations are shown for an aluminum plasma in local thermodynamic equilibrium at solid density and at a temperature of 100 eV. Comparisons with experiment are done too. The electronic structure of each integer charge state differs noticeably from the electronic structure of the average-atom model. This can be of interest for opacity calculations using detailed configuration accounting, detailed level accounting, or superconfiguration accounting approaches. In particular, we take into account orbital relaxations that are frozen in the average-atom model.

Eddy current effect study on the HL-3 plasma equilibrium reconstruction

Eddy current effect study on the HL-3 plasma equilibrium reconstruction

A multi-ion non-equilibrium solver for ionised astrophysical plasmas with arbitrary elemental abundances

Context. While many astrophysical plasmas can be modelled successfully assuming ionisation and thermal equilibrium, in some cases this is not appropriate and a non-equilibrium approach is required. In nebulae around evolved stars, the local elemental abundances may also strongly vary in space and time. Aims. Here we present a non-equilibrium multi-ion module developed for the fluid-dynamics code PION, describing the physical processes included and demonstrating its capabilities with some test calculations. Methods. A non-equilibrium ionisation solver is developed that allows arbitrary elemental abundances for neutral and ionised (but not molecular) gas, for the elements H, He, C, N, O, Ne, Si, S, and Fe. Collisional ionisation and recombination, photoionisation and charge-exchange reactions are included, and ion-by-ion non-equilibrium radiative cooling is calculated based on the instantaneous ion fractions of each element. Element and ion mass-fractions are advected using passive scalars, operator-split from the microphysical processes. Results. The module is validated by comparing with equilibrium and non-equilibrium calculations in the literature. Effects of charge exchange on ion abundances in cooling plasmas are discussed. Application to modelling shocks and photo-ionised H II regions is demonstrated. The time-dependent expansion of a WR nebula is studied, including photoionisation and collisional processes, and spectral-line luminosities calculated for non-equilibrium and equilibrium plasma states. Conclusions. The multi-ion module enables simulation of ionised plasmas with spatially varying elemental abundances using self-consistent ion abundances and thermal evolution. This allows prediction of spectral lines in UV, optical, IR, and X-ray even in cases where the plasma is out of ionisation equilibrium.