Plasma Equilibrium Research Articles

Free-Boundary Plasma Equilibrium Computation in Spherical Globus-M2 Tokamak by Means of the pyGSS Code

The pyGSS code constructed for computation of free-boundary plasma equilibrium in sphericalGlobus-M2 tokamak is described. Currents in the coils of the electromagnetic system, their coordinates,plasma current, positions of the limiter and current-conducting wall, etc., are used as the input parameters.Free parameters determining spatial distribution of equilibrium pressure and current density are selected inthe course of code execution in such a way that the results of reconstruction would agree with the experimentalmeasurements of the poloidal magnetic flux by means of toroidally closed loops. The results of computationof equilibrium are compared with those obtained by means of other codes and experimentally measuredthermal plasma energy, position of the separatrix outer leg, the diamagnetic-loop signal, etc.

Interplay of plasma resistivity and rotation on β limits in free boundary diverted tokamaks

A plasma resistivity-β driving mechanism aimed at explaining the appearance of long wavelength global instabilities in free boundary high-β tokamak plasmas with a divertor is presented. These perturbations resemble very closely the resistive wall mode phenomenon. Performing a proper toroidal analysis, we show that the magnetohydrodynamic stability is worsened by the interplay of plasma β and resistivity. By modelling the effect of a magnetic separatrix through a careful positioning of the resonant surfaces, we find that in an ideal plasma wall effects are effectively screened, so that the ideal β limit becomes independent of the wall position/physics. A lower wall dependent critical β is found if plasma resistivity is allowed. We find that global stability can be improved with a toroidal flow, small enough not to induce equilibrium modification. The rotation stabilisation effectiveness depends upon the proximity of the plasma equilibrium parameters to the resistive marginal boundary.

Maximum likelihood bolometry for ASDEX upgrade experiments

Bolometry is an essential diagnostic for calculating the power balances and for the understanding of different physical aspects of tokamak experiments. The reconstruction method based on the Maximum Likelihood (ML) principle, developed initially for JET, has been implemented for ASDEX Upgrade. Due to the availability of a limited number of views, the reconstruction problem is mathematically ill-posed. A regularizing procedure, based on the assumption of smoothness along the magnetic surfaces, given by plasma equilibrium, must also be implemented. A new anisotropic smoothing technique, which acts along locally oriented kernels, has been implemented. The performances of the method have been evaluated, in terms of shapes, resolution and of the derived radiated power, and compared with the bolometry method used routinely on ASDEX Upgrade. The specific advantage of the ML reconstruction algorithm consists of the possibility to assess the uncertainties of the reconstruction and to derive confidence intervals in the emitted radiation levels. The importance of this capability is illustrated.

Equilibria as boundary value problems under Lie transformations

The use of transformations recently gained attention in obtaining invariant solutions to the equilibrium problem of plasma physics. In all of the cases considered, the new solutions were related to a (Generalized) Grad–Shafranov equation. In the same context, the present study focuses on the issue of an axisymmetric, toroidal plasma equilibrium as a boundary value problem associated with new solutions obtained by means of Lie group transformations. It appears that in all the cases examined, only a single infinitesimal generator of the symmetry group permits closed boundary that remains invariant under the transformation. The respective equilibrium, in addition to a peculiar axisymmetric magnetically confined plasma with current hole reaching the axis of symmetry, describes a planet's magnetosphere for low heights.

Phase Mixing of Propagating Alfvén Waves in a Single-fluid Partially Ionized Solar Plasma

The phase mixing of Alfvén waves is one of the most promising mechanisms for the heating of the solar atmosphere. The damping of waves in this case requires small transversal scales, relative to the magnetic field direction; this requirement is achieved by considering a transversal inhomogeneity in the equilibrium plasma density profile. Using a single-fluid approximation of a partially ionized chromospheric plasma, we study the effectiveness of the damping of phase-mixed shear Alfvén waves and investigate the effect of varying the ionization degree on the dissipation of waves. Our results show that the dissipation length of shear Alfvén waves strongly depends on the ionization degree of the plasma, but more importantly, in a partially ionized plasma, the damping length of shear Alfvén waves is several orders of magnitude shorter than in the case of a fully ionized plasma, providing evidence that phase mixing could be a large contributor to heating the solar chromosphere. The effectiveness of phase mixing is investigated for various ionization degrees, ranging from very weakly to very strongly ionized plasmas. Our results show that phase-mixed propagating Alfvén waves in a partially ionized plasma with ionization degrees in the range μ = 0.518–0.657, corresponding to heights of 1916–2150 km above the solar surface, can provide sufficient heating to balance chromospheric radiative losses in the quiet Sun.

Exploration of non-resonant divertor features on the Compact Toroidal Hybrid

Non-resonant divertors (NRDs) separate the confined plasma from the surrounding plasma facing components (PFCs). The resulting striking field line intersection pattern on these PFCs is insensitive to plasma equilibrium effects. However, a complex scrape-off layer (SOL), created by chaotic magnetic topology in the plasma edge, connects the core plasma to the PFCs through varying magnetic flux tubes. The Compact Toroidal Hybrid (CTH) serves as a test-bed to study this by scanning across its inductive current. Simulations observe a significant change of the chaotic edge structure and an effective distance between the confined plasma and the instrumented wall targets. The intersection pattern is observed to be a narrow helical band, which we claim is a resilient strike line pattern. However, signatures of finger-like structures, defined as heteroclinic tangles in chaotic domains, within the plasma edge connect the island chains to this resilient pattern. The dominant connection length field lines intersecting the targets are observed via heat flux modeling with EMC3-EIRENE. At low inductive current levels, the excursion of the field lines resembles a limited plasma wall scenario. At high currents, a private flux region is created in the area where the helical strike line pattern splits into two bands. These bands are divertor legs with distinct SOL parallel particle flow channels. The results demonstrate the NRD strike line pattern resiliency within CTH, but also show the underlying chaotic edge structure determining if the configuration is diverted or limited. This work supports future design efforts for a mechanical structure for the NRD.

Visualization of phase-space orbit topological boundary using imaging neutral particle analyzer

A newly-developed Imaging Neutral Particle Analyzer (INPA) in the DIII-D tokamak interrogates phase space occupied by fast ions on multiple different orbit topologies, including passing, stagnation, trapped and potato orbits. Depending on plasma parameters and beam injection geometries, this new INPA system is capable of visualizing distributions of fast ions on the selected orbit topology and its associated orbit topological boundaries. More importantly, the system is able to directly visualize the effective pitch angle scattering ν eff in phase space by measuring fast ions that are scattered across the trapped-passing orbit topological boundaries and from counter-passing orbits to co-passing orbits. It also enables visualization of fast ion confined-loss boundaries and resolves the change of the boundary in phase space, as plasma equilibrium evolves. The key goal of this new INPA system is to directly measure ν eff across phase space induced by drift waves and its interaction with Alfvén eigenmodes, i.e. a key issue towards a future fusion power plant.

Numerical study of alpha particle loss with toroidal field ripple based on CFETR steady-state scenario

Abstract Effects of plasma equilibrium parameters on the alpha particle loss with the toroidal field ripple based on the CFETR steady-state scenario have been numerically investigated by the orbit-following code GYCAVA. It is found that alpha particle losses decrease and loss regions become narrower with the plasma current increasing or with the magnetic field decreasing. It is because the ripple stochastic transport and the ripple well loss of alpha particle are reduced with the safety factor decreasing. Decrease of the plasma density and temperature can reduce alpha particle losses due to enhancement of the slowing-down effect. The direction of the toroidal magnetic field can significantly affect heat loads induced by lost alpha particle. The vertical asymmetry of heat loads induced by the clockwise and counter-clockwise toroidal magnetic fields are due to the fact that the ripple distribution is asymmetric about the mid-plane, which can be explained by the typical orbits of alpha particle. The maximal heat load of alpha particle for the clockwise toroidal magnetic field is much smaller than that for the counter-clockwise one.

Nitrogen thermometry in an inductively coupled plasma torch using broadband nanosecond coherent anti-Stokes Raman scattering.

The development of atmospheric hypersonic flight and re-entry capabilities requires the characterization of the thermo-chemical state of representative test environments. This study demonstrates the usage of multiplex nanosecond N 2 coherent anti-Stokes Raman scattering (CARS) to measure temperatures in an atmospheric, high-temperature (>6000K), air plasma plume, generated by an inductively coupled plasma torch. These are some of the highest temperatures ever accessed via gas-phase CARS, to our knowledge. Temperatures of N 2 in the equilibrium plasma plume are determined via theoretical fits to measured CARS spectra. We discuss the practical implementation of CARS at very high temperatures, including the scaling of the N 2 CARS signal strength from 300 to 6700K, where the expected peak signal from the high-temperature plasma torch gases is two orders of magnitude less than commonly encountered in combustion environments. An intensified CCD camera enables single-laser-shot detection at temperatures as high as 6200K, by increasing sensitivity and providing a time gate against intense background luminosity. We also discuss the impacts of unwanted two-beam CARS contributions from outside the nominal three-beam measurement volume. We present mean axial and radial temperature profiles, as well as time-series data derived from both single-laser-shot and accumulated CARS spectra. The single-laser-shot precision is 1.7%-2.6% at temperatures of 3500 to 6200K. The presented results pave the way for the use of CARS at very high temperatures and the measurement of spatially resolved interface processes in high-enthalpy flows.

Magnetic pickup coil systems on the HL-3 tokamak

HL-3 is a new medium-sized copper conducting tokamak, which is dedicated to the plasma shaping control for plasma high performance and flexible operation, especially the advanced divertor configurations. According to the physics needs of the project, three types of magnetic pickup coils are designed and developed on HL-3 for magnetic field measurements. The coils emphasize different geometry sizes and array layouts. The coils are installed carefully by using high-precision positioning equipment to ensure the measurement accuracy of the system. After calibration, the magnetic field measurements are supplied for real-time equilibrium reconstruction and plasma control, e.g., with snowflake-shaped divertor configuration reconstruction. Mirnov coils satisfy the requirements for physical analysis, including determining the mode number from raw signals and detecting the magnetohydrodynamic instabilities.

Partial ponderomotive forces of Alfvén waves in near-Earth plasma

In the study of the ponderomotive action of Alfvén waves on near-Earth plasma, the general formula for ponderomotive forces, known in classical electrodynamics of continuous media, was previously used. The formula does not explicitly take into account the multi-ion composition of the plasma. Under the action of the waves, significant changes were found in macroscopic parameters — plasma density and velocity. Plasma in Earth’s magnetosphere contains ions with different charge-to-mass ratios. Besides hydrogen and helium ions, the plasma has an admixture of oxygen ions of ionospheric origin, as well as an admixture of other heavy ions. In this connection, a wide range of problems arise on the ponderomotive separation of ions of various types. To solve these problems, it is proposed to use partial ponderomotive forces and to describe the plasma not by hydrodynamic, but by quasi-hydrodynamic equations. In this paper, we discuss the derivation of partial forces for a traveling monochromatic Alfvén wave, and also suggest a method for deriving more general formulas by expanding the classical formula, known in macroscopic electrodynamic, into the sum of partial forces. The ponderomotive separation of ions is illustrated by the example of the problem for diffusion equilibrium of magnetospheric plasma. We propose a hypothesis that Alfvén waves redistribute plasma along geomagnetic field lines in such a way that the plasma at the magnetic field minima is characterized by an increased content of heavy ions. We suggest that a small admixture of heavy ions exists in the polar wind jet stream. The article is dedicated to the 80th anniversary of the discovery of Alfvén waves.

Парциальные пондеромоторные силы волн Альфвена в околоземной плазме

In the study of the ponderomotive action of Alfvén waves on near-Earth plasma, the general formula for ponderomotive forces, known in classical electrodynamics of continuous media, was previously used. The formula does not explicitly take into account the multi-ion composition of the plasma. Under the action of the waves, significant changes were found in macroscopic parameters — plasma density and velocity. Plasma in Earth’s magnetosphere contains ions with different charge-to-mass ratios. Besides hydrogen and helium ions, the plasma has an admixture of oxygen ions of ionospheric origin, as well as an admixture of other heavy ions. In this connection, a wide range of problems arise on the ponderomotive separation of ions of various types. To solve these problems, it is proposed to use partial ponderomotive forces and to describe the plasma not by hydrodynamic, but by quasi-hydrodynamic equations. In this paper, we discuss the derivation of partial forces for a traveling monochromatic Alfvén wave, and also suggest a method for deriving more general formulas by expanding the classical formula, known in macroscopic electrodynamic, into the sum of partial forces. The ponderomotive separation of ions is illustrated by the example of the problem for diffusion equilibrium of magnetospheric plasma. We propose a hypothesis that Alfvén waves redistribute plasma along geomagnetic field lines in such a way that the plasma at the magnetic field minima is characterized by an increased content of heavy ions. We suggest that a small admixture of heavy ions exists in the polar wind jet stream. The article is dedicated to the 80th anniversary of the discovery of Alfvén waves.

Development of prototype power supply for ohmic transformer system of SSST

The conceptual design of Small Scale Spherical Tokamak (SSST) has been completed at Institute for Plasma Research (IPR). It consists of poloidal field (or Equilibrium) field coils, Toroidal field coils and Ohmic Transformer (OT) system. The poloidal magnets are used for the plasma shaping and equilibrium. The plasma current ramp up and sustenance up to 20 ms is achieved by OT system. The OT system comprises of Central Solenoid (CS) and compensating coils TR1, TR2 & TR3. The Preliminary design for power supply for OT system has been finalized and a prototype OT power supply has been developed at IPR. The conceptual design of prototype Ohmic Transformer Power Supply (OTPS), its philosophy of operation, simulation results and experimental results are presented in this paper.

Optimization of the equilibrium magnetic sensor set for the SPARC tokamak

Accurate reconstruction of the plasma equilibrium is imperative for successful operation of the SPARC tokamak. In order to assess the expected reconstruction accuracy throughout the duration of design-point discharges, the EFIT equilibrium reconstruction code was deployed for SPARC. Reconstructions from SPARC baseline scenarios were compared with free-boundary equilibria generated by FreeGS, Toksys, and the Tokamak Simulation Code. The key geometric areas of interest, where design constraints are imposed, included: the inner and outer midplane gaps, the X-point locations, as well as the strike point locations. Successful reconstructions of various reference discharges, using deviations in these key geometric quantities as metrics, were calculated from synthetic signals considering an optimized equilibrium magnetic sensor set. The optimization process for this sensor set combined a scan of randomized sensor placement with a linear perturbation analysis to determine critical sensor locations, while simultaneously conforming to design constraints on the sensor placement. This optimized set was also successful in performing equilibrium reconstructions with the addition of error to synthetic measurements of magnetic flux and magnetic field, as well as contributions from eddy currents in conducting structures. These methods represent a workflow of optimization and validation that balances the engineering constraints of sensor placement with achieving sufficient reconstruction fidelity for science and operations missions for SPARC.

GS-DeepNet: mastering tokamak plasma equilibria with deep neural networks and the Grad–Shafranov equation

The force-balanced state of magnetically confined plasmas heated up to 100 million degrees Celsius must be sustained long enough to achieve a burning-plasma state, such as in the case of ITER, a fusion reactor that promises a net energy gain. This force balance between the Lorentz force and the pressure gradient force, known as a plasma equilibrium, can be theoretically portrayed together with Maxwell’s equations as plasmas are collections of charged particles. Nevertheless, identifying the plasma equilibrium in real time is challenging owing to its free-boundary and ill-posed conditions, which conventionally involves iterative numerical approach with a certain degree of subjective human decisions such as including or excluding certain magnetic measurements to achieve numerical convergence on the solution as well as to avoid unphysical solutions. Here, we introduce GS-DeepNet, which learns plasma equilibria through solely unsupervised learning, without using traditional numerical algorithms. GS-DeepNet includes two neural networks and teaches itself. One neural network generates a possible candidate of an equilibrium following Maxwell’s equations and is taught by the other network satisfying the force balance under the equilibrium. Measurements constrain both networks. Our GS-DeepNet achieves reliable equilibria with uncertainties in contrast with existing methods, leading to possible better control of fusion-grade plasmas.

Plasma Properties of Electric Arc Discharge Burning Between Cu-W Composites Electrodes

Plasma of electric arc discharge burning between different types of composite Cu-W electrodes was investigated. Electrodes manufactured of Cu-W composite materials (30/70% by mass) by shock sintering technology at temperatures of 750, 850, 950, and 1050°C were used. Optical emission spectroscopy techniques were applied to determine the main plasma parameters. Specifically, the side-on spectra of plasma emission were registered using a space-resolved spectrograph with a CMOS camera as a sensor device. The plasma thermodynamics properties were calculated based on the equilibrium plasma composition, which was determined using experimentally obtained radial distributions of temperatures and atom concentrations of the metals.

Influence of Thermionic Emission on He Ionization and Plasma Enhancement in Thermionic Energy Conversion

In this paper, the influence of thermionic emission on He ionization and plasma enhancement in thermionic energy conversion (TEC) are studied by experiment and numerical simulation. A 1D unsteady plasma TEC model, which includes a He ionization model, plasma conservation equations, and a thermionic emission formula for the wall, is developed. A He plasma thermionic energy conversion device composed of a barium–tungsten cathode and a tungsten anode is established. The volt–ampere curves of the He plasma TEC device are measured at 1050 K, 1150 K, 1250 K, 1300 K, and 1350 K temperatures. Both important cathode parameters, work function and emission area, are estimated. Based on the modelling simulation and the experiment, the He ionization mechanism in plasma TEC is discovered. The effects of cathode temperature on several distributions of plasma reaction rates, particle number density, and potential in He plasma TEC are described. Some important parameters, including electron mobility, resistivity, and plasma equilibrium are analyzed. The relationship of thermionic emission on plasma enhancement to the output power of plasma TEC is presented. The output powers of plasma TEC and vacuum TEC are compared at various cathode temperatures. A dimensionless analyzing method concerning thermionic emission intensity and plasma enhancement power is proposed. A brief dimensionless relationship is deduced regarding thermionic emission intensity and the plasma enhancement contribution of TEC. The principles and methods for quantitative calculations concerning the output power of plasma TEC under the action of thermionic emission are established. It is possible to do quantitative research on the effects of thermionic emission on plasma-enhanced TEC.

The role of electron current in high-β plasma equilibria

This paper is aimed at investigating the role of electrons in creation of currents in plasma equilibria with high plasma pressure (β≈1). Despite the long history of studies of these equilibria, there is still no consensus on what kind of particle species is responsible for the creation of the diamagnetic current and what characteristic size the current layer should have. For example, simulations of isothermal plasma injection into a multi-cusp magnetic trap [J. Park et al., Front. Astron. Space Sci. 6, 74 (2019)] demonstrate the formation of a transition layer with a thickness comparable to the electron Larmor radius, where the equilibrium current is carried by electrons. At the same time, studies of a diamagnetic bubble created by a hot-ion plasma in a mirror trap [I. Kotelnikov, Plasma Phys. Control Fusion 62, 075002 (2020)] assume ion dominance and completely ignore electron currents. In this paper, we show that the equilibrium initially governed by the ion diamagnetic current is unstable against perturbations at the ion-cyclotron frequency harmonics, and this instability forces the plasma to come to a new equilibrium state in which the current is mainly created by the E×B-drift of electrons. The same type of equilibrium is also found to form in a more realistic problem setup when plasma is continuously injected into the uniform vacuum magnetic field.

Investigation of thermodynamic properties in picosecond laser-produced plasmas on silicon

The validity of local thermodynamic equilibrium (LTE) in plasma is a long-term concern for laser-induced breakdown spectroscopy applications. In this paper, the spatial and temporal dependence of LTE deviation in picosecond laser-induced plasmas has been proved. A picosecond (∼20 ps) laser operated at 532 nm was used to ablate a silicon target to produce plasma at a pressure of 10−5 mbar. A general electron energy distribution function was used to provide access to the insight into population ratios of different energy levels for the spatially and temporally resolved optical emission intensity of laser-induced plasma. A precise temporal and spatial LTE boundary of plasma generated in picosecond laser ablation was obtained, and the results showed that only at delay times of 180–300 ns, the plasma away from the surface (>4 mm) is in LTE.

Tokamak plasma equilibrium with relativistic runaway electrons

We consider axisymmetric equilibrium of a tokamak plasma that includes current carried by relativistic runaway electrons (REs). Using a guiding center approach, a qualitative picture of the equilibrium of a pure RE beam is elucidated. In a hot thermal plasma, none of the classical drifts of charged particles contribute to the net field-perpendicular current density, which is purely due to magnetization current. In the case of a runaway beam, however, the curvature drift of REs provides the Lorentz force needed to maintain the centripetal acceleration associated with the relativistic toroidal motion. Two different equilibrium formulations are derived for the general case consisting of a mix of thermal and RE current. At higher RE energies, the shift between flux-surfaces and surfaces of constant generalized angular momentum of REs in such equilibria can exceed the radial extent of a typical magnetohydrodynamic mode such that its stability properties could be altered. Simplified one-dimensional governing equations are derived for the absolute and relative orbit shifts in the case of a circular tokamak, enabling quick estimates of parameter dependencies.