JOREK is a massively parallel fully implicit non-linear extended magneto-hydrodynamic (MHD) code for realistic tokamak X-point plasmas. It has become a widely used versatile simulation code for studying large-scale plasma instabilities and their control and is continuously developed in an international community with strong involvements in the European fusion research programme and ITER organization. This article gives a comprehensive overview of the physics models implemented, numerical methods applied for solving the equations and physics studies performed with the code. A dedicated section highlights some of the verification work done for the code. A hierarchy of different physics models is available including a free boundary and resistive wall extension and hybrid kinetic-fluid models. The code allows for flux-surface aligned iso-parametric finite element grids in single and double X-point plasmas which can be extended to the true physical walls and uses a robust fully implicit time stepping. Particular focus is laid on plasma edge and scrape-off layer (SOL) physics as well as disruption related phenomena. Among the key results obtained with JOREK regarding plasma edge and SOL, are deep insights into the dynamics of edge localized modes (ELMs), ELM cycles, and ELM control by resonant magnetic perturbations, pellet injection, as well as by vertical magnetic kicks. Also ELM free regimes, detachment physics, the generation and transport of impurities during an ELM, and electrostatic turbulence in the pedestal region are investigated. Regarding disruptions, the focus is on the dynamics of the thermal quench (TQ) and current quench triggered by massive gas injection and shattered pellet injection, runaway electron (RE) dynamics as well as the RE interaction with MHD modes, and vertical displacement events. Also the seeding and suppression of tearing modes (TMs), the dynamics of naturally occurring TQs triggered by locked modes, and radiative collapses are being studied.
Tiani Wahyu Utami, Nur Chamidah, T. Saifudin
et al.
Dengue hematrocit fever (DHF) is a health problem in Indonesia, which tends to cause an increase in the number of sufferers and is becoming more widespread. Semarang City is an endemic region in Indonesia. Platelet and hematocrit modeling are required to diagnose DHF. The independent variables in this model were hemoglobin (Hb) level and examination time, whereas platelets and hematocrit were the dependent variables. This study used secondary data obtained from the Roemani Hospital in Semarang, Indonesia. The study included 13 patients who met the criteria for Grade 2 DHF, and their blood samples were collected once daily for 6 days during their hospitalization to form longitudinal data. This study aimed to model hematocrit and platelet counts using semiparametric bi-response regression with local polynomial estimators. The GCV method was used to select the optimal combination of bandwidth and polynomial order. The results obtained for platelets were a polynomial order of 2 and a bandwidth of 0.1, while hematocrit was selected with a polynomial order of 1 and a bandwidth of 0.8. Platelet and hematocrit modeling using the semiparametric bi-response regression applied to the in-sample data resulted in a coefficient of determination (R²) of 90.12%. The model results can be used to predict platelets and hematocrit with high accuracy, yielding an MAPE of 4.84%. Based on the analysis results, the increase in Hb and hematocrit has a unidirectional relationship (both increase) and is in the opposite direction to the number of platelets, which usually decreases (thrombocytopenia). Platelet dynamics in patients with Grade 2 DHF who were hospitalized for 6 days showed that on the 3rd or 4th day, the patient experienced thrombocytopenia and an increase in hematocrit above normal, which is a sign of plasma leakage; therefore, it is necessary to be aware that this patient's condition requires more intensive care to stabilize platelets and hematocrit.
Abstract A high-frame-rate camera with microsecond-level time resolution was used to make systematic investigations of plasma self-organization and spoke dynamics during individual HiPIMS pulses. The plasma was imaged for a range of argon pressures (0.25–2 Pa) and peak discharge currents (10–400 A) using an Al target. The experiments revealed that plasma evolves through three characteristic stages as the discharge current increases. In stage I, which is present from the current onset and up to ∼25 A, spokes are azimuthally long and rotate in the −Ez × B direction. The spoke behavior is similar to the one observed in DCMS discharges. The number of spokes depends on pressure and the current growth rate. At the lowest pressure (0.25 Pa) a single spoke is present in discharge, while at higher pressures (1–2 Pa) two spokes are most often observed. The spoke velocity depends on the number of spokes, current growth rate and pressure. A single spoke rotates with velocities in the 4–15 km s−1 range, while two spokes rotate in the 1–9 km s−1 range depending on the pressure and growth rate. Following stage I, the plasma undergoes a complex reorganization that is characterized by aperiodic spoke patterns and irregular dynamics. In stage II spokes are less localized, they merge, split and propagate either in the retrograde or prograde direction. After chaotic plasma reorganization, more ordered spoke patterns begin to form. Spokes in stage III are azimuthally shorter, typically exhibit a triangular shape and rotate in the Ez × B direction. In general, the spoke dynamics is less complicated and is only influenced by the pressure. Spokes rotate faster at higher pressures than at lower ones; velocities range from 9 km s−1 at 0.25 Pa to 6 km s−1 at 2 Pa. The spoke velocity in stage III is largely unaffected by the discharge current or number of spokes. Stage III can be further divided into sub-stages, which are characterized by different current growth rates, spoke sizes and shapes. In general, the spoke evolution is highly reproducible for pulses with similar discharge current waveforms.
AbstractThe scattering dynamics of electron capture in ‐H(1 s) scattering under dense semi‐classical plasma (DSCP) environments has been investigated theoretically. Coupled multi‐channel two‐body Lippmann‐Schwinger equations have been solved by retaining +H(1 s) and p + Ps(1 s) channels to calculate the cross sections (CS) of the electron capture process at intermediate and high incident energies. The effective interaction of the plasma charged particles is modelled by a pseudopotential which is a function of two parameters, namely the plasma screening strength and the de Broglie wavelength. A detailed study is made to explore the changes in the CSs of the above‐mentioned process with respect to the variation in the plasma screening strength and de Broglie wavelength. Significant changes are found to take place, when the screening strength and the de Broglie wavelength are varied. Specifically, the sharp minimum in the differential CS moves toward the forward direction with increasing de Broglie wavelength at a given screening strength.
Daniel W. Crews, Iman A. M. Datta, Eric T. Meier
et al.
The Kadomtsev pinch, namely the Z-pinch profile marginally stable to interchange modes, is revisited in light of observations from axisymmetric MHD modeling of the FuZE sheared-flow-stabilized Z-pinch experiment. We show that Kadomtsev's stability criterion, cleanly derived by the minimum energy principle but of opaque physical significance, has an intuitive interpretation in the specific entropy analogous to the Schwarzschild-Ledoux criterion for convective stability of adiabatic pressure distributions in the fields of astrophysics, meteorology, and oceanography. By analogy, the Kadomtsev profile may be described as magnetoadiabatic in the sense that plasma pressure is polytropically related to area-averaged current density from the ideal MHD stability condition on the specific entropy. Further, the non-ideal stability condition of the entropy modes is shown to relate the specific entropy gradient to the ideal interchange stability function. Hence, the combined activity of the ideal interchange and non-ideal entropy modes drives both the specific entropy and specific magnetic flux gradients to zero in the marginally stable state. The physical properties of Kadomtsev's pinch are reviewed in detail and following from this the localization of pinch confinement, i.e., pinch size and inductance, is quantified by the ratio of extensive magnetic and thermal energies. In addition, results and analysis of axisymmetric MHD modeling of the FuZE Z-pinch experiment are presented where pinch structure is found to consist of a near-marginal flowing core surrounded by a super-magnetoadiabatic low-beta sheared flow.
In fusion plasmas, where electron temperatures $T_e$ range from keV to hundreds of keV, Bremsstrahlung radiation constitutes a significant energy loss mechanism. While various thermal average fitting formulas exist in the literature, their accuracy is limited, particularly for $T_e \leq 20$ keV with error $>10\%$. Additionally, non-relativistic fitting formulas become invalid for $T_e \geq 50$ keV. The accurate calculation of Bremsstrahlung radiation is important for fusion gain study, especially of advanced fuels fusion. In this work, we develop new but still simple fitting formulas that are valid for electron temperatures ranging from small ($\lesssim0.1$ keV) to extreme relativistic range, with errors of less than 1\% even for high atomic number ions (e.g., $Z=30$), which could be sufficient for fusion plasma applications. Both electron-ion (e-i) and electron-electron (e-e) Bremsstrahlung radiations are considered. Both polynomial fitting with truncated ($t=k_BT_e/m_ec^2\leq10$) and one-fit-all formulas are provided. Additionally, we offer fitting formulas for e-i and e-e specifically for electron energies, which could prove useful in non-Maxwellian Bremsstrahlung radiation studies.
Magnetic reconnection, a fundamental plasma process, is pivotal in understanding energy conversion and particle acceleration in astrophysical systems. While extensively studied in two-dimensional (2D) configurations, the dynamics of reconnection in three-dimensional (3D) systems remain under-explored. In this work, we extend the classical tearing mode instability to 3D by introducing a modulation along the otherwise uniform direction in a 2D equilibrium, given by $g(y)$, mimicking a flux tube-like configuration. We perform linear stability analysis (both analytically and numerically) and direct numerical simulations to investigate the effects of three-dimensionality. Remarkably, we find that a tearing-like instability arises in 3D as well, even without the presence of guide fields. Further, our findings reveal that the 3D tearing instability exhibits reduced growth rates compared to 2D by a factor of $\int g(y)^{1/2} dy~/\int dy$, with the dispersion relation maintaining similar scaling characteristics. We show that the modulation introduces spatially varying resistive layer properties, which influence the reconnection dynamics.
A rigorous treatment of light-matter interactions typically requires an interacting quantum field theory. However, most applications of interest are handled using classical or semiclassical models, which are valid only when quantum-field fluctuations can be neglected. This approximation breaks down in scenarios involving large light intensities or degenerate matter, where additional quantum effects become significant. In this work, we address these limitations by developing a quantum kinetic framework that treats both light and matter fields on equal footing, naturally incorporating both linear and nonlinear interactions. To accurately account for light fluctuations, we introduce a photon distribution function that, together with the classical electromagnetic fields, provides a better description of the photon fluid. From this formalism, we derive kinetic equations from first principles that recover classical electrodynamical results while revealing couplings that are absent in the corresponding classical theory. Furthermore, by addressing the Coulomb interaction in the Hartree-Fock approximation, we include the role of fermionic exchange exactly in both kinetic and fluid regimes through a generalized Fock potential. The latter provides corrections not only to the electrostatic forces but also to the plasma velocity fields, which become significant in degenerate conditions.
Bowen Zhu (朱博文), Hao Wang (王灏), Jian Wu (吴坚)
et al.
We designed a new artificial neural network called Exposed latent state neural ordinary differential equation with physics (ExpNODE-p) by modifying the neural ordinary differential equation (NODE) framework to successfully predict the time evolution of the two-dimensional mode profile in nonlinear saturated stage. Starting from the magnetohydrodynamic equations, simplifying assumptions were applied based on physical properties and symmetry considerations of the energetic-particle-driven geodesic acoustic mode (EGAM) to reduce complexity. Our approach embeds known physical characteristics directly into the neural network architecture by exposing latent differential states, enabling the model to capture complex features in the nonlinear saturated stage that are difficult to describe analytically. ExpNODE-p was evaluated using a dataset generated from first-principles simulations of the EGAM instability, focusing on the nonlinear saturated stage where the mode properties (e.g. frequency) are quite difficult to capture. Compared to state-of-the-art models such as ConvLSTM, ExpNODE-p achieved superior performance in both accuracy and training efficiency for multi-step predictions. Additionally, the model exhibited strong generalization capabilities, accurately predicting mode profiles outside the training dataset and capturing detailed features and asymmetries inherent in the EGAM dynamics. Our results establish ExpNODE-p as a powerful tool for creating fast, accurate surrogate models of complex plasma phenomena, opening the door to applications that are computationally intractable with first-principles simulations.
The development of real-time control strategies for key discharge parameters, such as densities, fluxes, and energy distributions, is of fundamental interest to many plasma sources. Over the last decade, multi-harmonic ‘tailored’ voltage waveforms have been successfully employed to achieve enhanced control of key parameters in a wide range of radio-frequency (RF) plasma sources through application of the electrical asymmetry effect (EAE). More recently, the analogous magnetic asymmetry effect (MAE) has been numerically and experimentally demonstrated to achieve a notable degree of control in parallel plate RF plasma sources. The MAE is achieved via selectively magnetising the charged species adjacent to one electrode, altering the charge flux to the surface and enforcing a DC self-bias to maintain quasineutrality. This study addresses the degree of control achieved by the MAE in a non-planar geometry via 2D fluid/kinetic simulations of a magnetised RF capacitively coupled plasma source employing two different magnetic topologies. The simultaneous application of the EAE and MAE is then presented for the same geometry, demonstrating a degree of non-linear behaviour dependant upon the applied magnetic topology. Control of the DC self-bias voltage ηdc is demonstrated for a single 600 Vpp , 13.56 MHz discharge in both ‘convergent’ (maximum on-axis field strength) and ‘divergent’ (minimum on-axis field strength) magnetic topolgies. MAE induced modulations of ηdc = 0.13 Vpp and ηdc = 0.03 Vpp are achieved for each magnetic topology, respectively, for magnetic field strengths between 50 and 1000 G. Simultaneous application of an EAE and MAE is achieved through a multi-harmonic ‘peak’-type tailored voltage waveform employing varying harmonic phase offsets between 0∘ ⩽ θ ⩽ 360∘ . The degree to which the DC self-bias voltage is modulated by the applied EAE is mediated by the orientation and magnitude of the applied magnetic field. The EAE induced DC self-bias modulations exhibit non-linear behaviour in response to a superimposed MAE, such that the resulting DC self-bias differs from an additive combination of the two effects alone Simultaneous application of the electrical and MAEs offers the possibility of further decoupling ion and electron dynamics in RF plasma sources, and represents an improvement over each approach in isolation.
Abstract. A high yield and beam stable neutron tube can be applied in many fields. It is of great significance to the optimal external magnetic field intensity of cold cathode Penning ion source (PIS) and precisely control the movement of deuterium (D), tritium (T) ions and electrons in the source of the neutron tubes. A cold cathode PIS is designed based on the solenoidal magnetic field to obtain better uniformity of the magnetic field and higher yield of the neutron tube. The degree of magnetic field uniformity among the magnetic block, double magnetic rings, and solenoidal ion sources is compared by finite element simulation (FES) methods. By using drift diffusion approximation (DDA) and magnetic field coupling method, the plasma distribution of hydrogen and the relationship between plasma density and magnetic field intensity at 0.06 Pa pressure and solenoid magnetic field are obtained. The results show that the solenoidal ion source has the most uniform magnetic field distribution. The optimum magnetic field strength of about 0.1 T is obtained in the ion source at an excitation voltage of 1 V. The maximum average number density of monatomic hydrogen ions (H+) is 1×108 /m3 and an ion beam current of about 14.51 μA is formed under the -5000 V extraction field. The study of the solenoidal magnetic field contributes to the understanding of the particle dynamics within the PIS and provides a reference for the further improvement of the source performance for the neutron tube in the future. Keywords: Plasma; PIS; DDA; Magnetic field intensityity
Multi-field singular value decompositions (SVDs) is applied to turbulence obtained in a cylindrical magnetized plasma, PANTA. This method enables us to obtain the spatial mode structures with common temporal evolution of di ff erent physical quantities, such as the fluctuations of density and flows. Turbulence driven particle transport is evaluated by the method. It is shown that only the coupling of the same mode drives the transport, which stems from the orthogonality of the SVD. Thanks to this characteristics, the number of degrees of freedom which plays roles for the transport dynamics could be significantly reduced.
D. A. Kaltsas, A. Kuiroukidis, P. J. Morrison
et al.
We derive axisymmetric equilibrium equations in the context of the hybrid Vlasov model with kinetic ions and massless fluid electrons, assuming isothermal electrons and deformed Maxwellian distribution functions for the kinetic ions. The equilibrium system comprises a Grad-Shafranov partial differential equation and an integral equation. These equations can be utilized to calculate the equilibrium magnetic field and ion distribution function, respectively, for given particle density or given ion and electron toroidal current density profiles. The resulting solutions describe states characterized by toroidal plasma rotation and toroidal electric current density. Additionally, due to the presence of fluid electrons, these equilibria also exhibit a poloidal current density component. This is in contrast to the fully kinetic Vlasov model, where axisymmetric Jeans equilibria can only accommodate toroidal currents and flows, given the absence of a third integral of the microscopic motion.
Abstract The physical principles of natural occurrences are frequently examined using nonlinear evolution equations (NLEEs). Nonlinear equations are intensively investigated in mathematical physics, ocean physics, scientific applications, and marine engineering. This paper investigates the Boiti-Leon-Manna-Pempinelli (BLMP) equation in (3+1)-dimensions, which describes fluid propagation and can be considered as a nonlinear complex physical model for incompressible fluids in plasma physics. This four-dimensional BLMP equation is certainly a dynamical nonlinear evolution equation in real-world applications. Here, we implement the generalized exponential rational function (GERF) method and the generalized Kudryashov method to obtain the exact closed-form solutions of the considered BLMP equation and construct novel solitary wave solutions, including hyperbolic and trigonometric functions, and exponential rational functions with arbitrary constant parameters. These two efficient methods are applied to extracting solitary wave solutions, dark-bright solitons, singular solitons, combo singular solitons, periodic wave solutions, singular bell-shaped solitons, kink-shaped solitons, and rational form solutions. Some three-dimensional graphics of obtained exact analytic solutions are presented by considering the suitable choice of involved free parameters. Eventually, the established results verify the capability, efficiency, and trustworthiness of the implemented methods. The techniques are effective, authentic, and straightforward mathematical tools for obtaining closed-form solutions to nonlinear partial differential equations (NLPDEs) arising in nonlinear sciences, plasma physics, and fluid dynamics.
Hydrogen peroxide (H2O2) detection with high sensitivity plays an important role in biomedical research and food engineering. By combining colorimetry and surface enhanced Raman spectroscopy (SERS), we synthetize a novel H2O2 dual-sensor constructed via TMB-Fe3O4@AuNPs. In the presence of H2O2, the peroxide model enzyme might catalyze the oxidation of 3,3',5,5'- tetramethylbenzidine (TMB) as blue charge transfer complex (CTC) for colorimetry, and then facilitate the sensitivity improvement of SERS detection. The achieved results show that in colorimetry, the linear range is from 40 μM to 5.5 mM with the detection limit of 11.1 μM; in SERS detection, the linear range is from 2 nM to 1 μM with the detection limit of 0.275 nM. Clearly, this mutual reference strategy improves both the detection limit of colorimetry and the sensitivity of SERS detection. Moreover, this colorimetry/SERS dual-sensor constructed via TMB-Fe3O4@AuNPs is successfully applied to the H2O2 detection in plasma and milk, indicating the excellent performance and flexibility.
Abstract Nonlinear evolution equations (NLEEs) are primarily relevant to nonlinear complex physical systems in a wide range of fields, including ocean physics, plasma physics, chemical physics, optical fibers, fluid dynamics, biology physics, solid-state physics, and marine engineering. This paper investigates the Lie symmetry analysis of a generalized (3+1)-dimensional breaking soliton equation depending on five nonzero real parameters. We derive the Lie infinitesimal generators, one-dimensional optimal system, and geometric vector fields via the Lie symmetry technique. First, using the three stages of symmetry reductions, we converted the generalized breaking soliton (GBS) equation into various nonlinear ordinary differential equations (NLODEs), which have the advantage of yielding a large number of exact closed-form solutions. All established closed-form wave solutions include special functional parameter solutions, as well as hyperbolic trigonometric function solutions, trigonometric function solutions, dark-bright solitons, bell-shaped profiles, periodic oscillating wave profiles, combo solitons, singular solitons, wave-wave interaction profiles, and various dynamical wave structures, which we present for the first time in this research. Eventually, the dynamical analysis of some established solutions is revealed through three-dimensional sketches via numerical simulations. Some of the new solutions are often useful and helpful for studying the nonlinear wave propagation and wave-wave interactions of shallow water waves in many new high-dimensional nonlinear evolution equations.