In this study, we conducted an electrical analysis of the effects of cold plasma on the properties of distilled water, using a corona discharge in a tip–plane configuration. The discharge was initiated by applying a voltage of 7.17 kV with a 2 mm gap between the tip and the water surface. We investigated the impact of plasma treatment on the total dissolved solids (TDS) and conductivity of 20 mL of distilled water, with exposure times ranging from 2 to 12 min. The results show that plasma treatment leads to a significant increase in conductivity and TDS, with a proportional increase relative to the exposure time. In addition to these measurements, we performed a detailed electrical analysis to evaluate the energy efficiency of the plasma treatment. This analysis involved calculating the useful power and energy efficiency using an equivalent electrical model of the corona discharge reactor, as direct measurement of these parameters is challenging in this context. The model allowed us to calculate energy consumption and analyse the electrical behaviour of the system throughout the treatment process. This study also enables us to monitor, control and optimize the energy during plasma treatment, providing insights into the energy dynamics involved. The findings have potential applications in improving energy efficiency in industrial and environmental processes.

Electron-only reconnection (E-REC) is a process recently observed in the Earth’s magnetosheath, where magnetic reconnection occurs at electron kinetic scales, and ions do not couple to the reconnection process. Electron-only reconnection is likely to have a significant impact on the energy conversion and dissipation of turbulence cascades at kinetic scales in some settings. This paper investigates E-REC under different intensities of strong guide fields (the ratio between the guide field and the in-plane asymptotic field strength is 5, 10 and 20, respectively) via two-dimensional fully kinetic particle-in-cell simulations, focusing on electron heating. The simulations are initialized with a force-free current sheet equilibrium under various intensities of strong guide fields. Similarly to previous experimental studies, electron temperature anisotropy along separatrices is observed, which is found to be mainly caused by the variations of parallel temperature. Both regions of anisotropy and parallel temperature increase/decrease along separatrices become thinner with increasing guide fields. Besides, we find a transition from a quadrupolar to a hexapolar (six-polar) to an octopolar (eight-polar) structure in temperature anisotropy and parallel temperature as the guide field intensifies. Non-Maxwellian electron velocity distribution functions (EVDFs) at different locations in the three simulations are observed. Our results show that parallel electron velocity varies notably with different guide field intensities and finite parallel electron heat flux density is observed. The three simulations exhibit features of the Chew–Goldberger–Low theory, with the level of consistency increasing as the guide field strength increases. This explains the electron parallel temperature variations and the shape of the EVDFs observed along the separatrices. This work may provide insights into the understanding of electron heating and parallel heat flux density in E-REC observed in the turbulent magnetosheath.

Using two counter-propagating ultra-intense laser interactions with a solid target, we conducted a study on the generation of electron-positron pairs via the multi-photon Breit–Wheeler (BW) process and trident process. These processes were simulated using the particle-in-cell (PIC) code EPOCH. Our proposed scheme involves irradiating two targets with two counter-propagating lasers. High-energy photons are produced when hot electrons collide with the reflected laser pulse at the target's front, leading to electron and positron pair production. In the single-target scenario, electron bunches are extracted from the target by the p-polarized laser electromagnetic field and accelerated by the laser ponderomotive force before colliding with the counter-propagating laser. However, using two targets enhances pair creation compared with the single-target set-up. We observed that in two-target configurations, the increased number of high-energy gamma-rays contributes to higher-energy electron–positron generation. Additionally, the generation of hot electrons is also more pronounced in this scheme. Consequently, the laser demonstrates higher efficiency in generating gamma photons and positrons in the dual-target set-up, which is beneficial for investigating high-energy pair production and gamma-ray emission. The generated positrons exhibit a density of the order of $10^{27}\,\text {m}^{-3}$ and can be accelerated to energies of 1.5 GeV. The involvement of hot electrons in the target is crucial for generating high-energy photons and positrons. The maximum pair yield reaches $8 \times 10^9$ for the BW process and $10^8$ for the trident process. Notably, the total laser energy conversion efficiencies to electrons, $\gamma$-rays and positrons show improvement in the dual-target configuration. Specifically, the laser energy absorbed by positrons increases from 11.62 % in Case A to 13.12 % in Case B. These enhancements in conversion efficiency and electron/positron density have significant practical implications in experimental set-ups. In both the BW and trident processes, the two-target set-up dominates, highlighting its effectiveness. We also compared the strengths of both approaches, suggesting that these simple models of implementing two targets can be used in experiments as well.

The kinetic stability of collisionless, sloshing beam-ion ($45^\circ$ pitch angle) plasma is studied in a three-dimensional (3-D) simple magnetic mirror, mimicking the Wisconsin high-temperature superconductor axisymmetric mirror experiment. The collisional Fokker–Planck code CQL3D-m provides a slowing-down beam-ion distribution to initialize the kinetic-ion/fluid-electron code Hybrid-VPIC, which then simulates free plasma decay without external heating or fuelling. Over $1$–$10\;\mathrm{\unicode{x03BC} s}$, drift-cyclotron loss-cone (DCLC) modes grow and saturate in amplitude. The DCLC scatters ions to a marginally stable distribution with gas-dynamic rather than classical-mirror confinement. Sloshing ions can trap cool (low-energy) ions in an electrostatic potential well to stabilize DCLC, but DCLC itself does not scatter sloshing beam-ions into the said well. Instead, cool ions must come from external sources such as charge-exchange collisions with a low-density neutral population. Manually adding cool $\mathord {\sim } 1\;\mathrm{keV}$ ions improves beam-ion confinement several-fold in Hybrid-VPIC simulations, which qualitatively corroborates prior measurements from real mirror devices with sloshing ions.

We develop a phenomenological model of strong imbalanced magnetohydrodynamic (MHD) turbulence that accounts for intermittency and the reflection of Alfvén waves by spatial variations in the Alfvén speed. Our model predicts the slopes of the inertial-range Elsasser power spectra, the scaling exponents of the higher-order Elsasser structure functions and the way in which the parallel (to the magnetic field) length scale of the fluctuations varies with the perpendicular length scale. These predictions agree reasonably well with measurements of solar-wind turbulence from the Parker Solar Probe (PSP). In contrast to previous models of intermittency in balanced MHD turbulence, we find that intermittency in reflection-driven MHD turbulence increases the parallel wavenumbers of the energetically dominant fluctuations at small perpendicular length scales. This, like the PSP measurements with which our model agrees, suggests that turbulence in the solar wind and solar corona may lead to more ion cyclotron heating than previously realized.

Starting from the assumption that saturation of plasma turbulence driven by temperature-gradient instabilities in fusion plasmas is achieved by a local energy cascade between a long-wavelength outer scale, where energy is injected into the fluctuations, and a small-wavelength dissipation scale, where fluctuation energy is thermalised by particle collisions, we formulate a detailed phenomenological theory for the influence of perpendicular flow shear on magnetised-plasma turbulence. Our theory introduces two distinct regimes, called the weak-shear and strong-shear regimes, each with its own set of scaling laws for the scale and amplitude of the fluctuations and for the level of turbulent heat transport. We discover that the ratio of the typical radial and poloidal wavenumbers of the fluctuations (i.e. their aspect ratio) at the outer scale plays a central role in determining the dependence of the turbulent transport on the imposed flow shear. Our theoretical predictions are found to be in excellent agreement with numerical simulations of two paradigmatic models of fusion-relevant plasma turbulence: (i) an electrostatic fluid model of slab electron-scale turbulence, and (ii) Cyclone-base-case gyrokinetic ion-scale turbulence. Additionally, our theory envisions a potential mechanism for the suppression of electron-scale turbulence by perpendicular ion-scale flows based on the role of the aforementioned aspect ratio of the electron-scale fluctuations.

Collisionless shocks are frequently analysed using the magnetohydrodynamic (MHD) formalism, even though the required collisionality hypothesis is not fulfilled. In a previous work (Bret & Narayan, 2018 J. Plasma Phys. vol. 84, p. 905840604), we presented a model of collisionless shock displaying an important departure from the expected MHD behaviour, in the case of a strong flow aligned magnetic field. This model was non-relativistic. Here, it is extended to the relativistic regime, considering zero upstream pressure and upstream Lorentz factor $\gg 1$. The result agrees satisfactorily with Particle-in-Cell simulations and shows a similar, and important, departure from the MHD prediction. In the strong field regime, the density jump $r$, seen in the downstream frame, behaves like $r \sim 2 + 1/\gamma _{\mathrm{up}}$, while MHD predicts 4 ($\gamma _{\mathrm{up}}$ is the Lorentz factor of the upstream measured in the downstream frame). Only pair plasmas are considered.

The selection, design and optimization of a suitable blanket configuration for an advanced high-field stellarator concept is seen as a key feasibility issue and has been incorporated as a vital and necessary part of the Infinity Two fusion pilot plant physics basis. The focus of this work was to identify a baseline blanket which can be rapidly deployed for Infinity Two while also maintaining flexibility and opportunities for higher performing concepts later in development. Results from this analysis indicate that gas-cooled solid breeder designs such as the helium-cooled pebble bed (HCPB) are the most promising concepts, primarily motivated by the neutronics performance at applicable blanket build depths, and the relatively mature technology basis. The lithium lead (PbLi) family of concepts, particularly the dual-cooled lithium lead, offer a compelling alternative to solid blanket concepts as they have synergistic developmental pathways while simultaneously mitigating much of the technical risk of those designs. Homogenized three-dimensional neutronics analysis of the Infinity Two configuration indicates that the HCPB achieves an adequate tritium breeding ratio (TBR) (1.30 which enables sufficient margin at low engineering fidelity), and near appropriate shielding of the magnets (average fast fluence of 1.3 ${\times}$ 10$^{18}$ n cm$^{-2}$ per full-power year). The thermal analysis indicates that reasonably high thermal efficiencies (greater than 30 %) are readily achievable with the HCPB paired with a simple Rankine cycle using reheat. Finally, the tritium fuel cycle analysis for Infinity Two shows viability, with anticipated operational inventories of less than one kilogram (approximately 675 g) and a required TBR (TBR$_{\textrm {req}}$) of less than 1.05 to maintain fuel self-sufficiency (approximately 1.023 for a driver blanket with no inventory doubling). Although further optimization and engineering design are still required, at the physics basis stage all initial targets have been met for the Infinity Two configuration.

We present the first experimental observations of the dust acoustic wave where the wave was observed to propagate in the directions of gravity and magnetic field when these directions were not aligned. The experiments were conducted in the Magnetized Dusty Plasma eXperiment facility using a novel electrode system that allows for the angle between gravity and the magnetic field to be varied in a controlled way. This letter reports on measurements in an rf glow discharge argon plasma environment where the angle between direction of gravity and the magnetic field is 45$^{\circ }$. When there was no applied magnetic field, the wave was observed to propagate in the direction of gravity. However, as the magnetic field increased and the ions transitioned from flowing in the direction of gravity to the direction of the magnetic field, a second wave emerged and two distinct waves were observed to simultaneously propagate, one in the direction of gravity and one in the direction of the magnetic field. As the magnetic field was further increased, the wave that propagated in the direction of gravity was suppressed and the wave was only observed to propagate in the direction of the applied magnetic field. We also observe that the speed and the kinetic temperature of the dust for the mode that propagated in the direction of gravity decreased with increasing magnetic field while the speed and the kinetic temperature of the dust for the mode that propagated in the direction of the magnetic field increased with increasing magnetic field. These measurements suggest that an ion-dust streaming instability is at least partially responsible for the high temperatures that have previously been observed in dusty plasmas when the dust acoustic wave is present.

We have investigated the modified Jeans instability and gravitational collapse in uniformly rotating, anisotropic quantum plasmas, including the effects of intrinsic magnetisation, viscosity tensor and Ohmic diffusivity. The closure of the Chew, Goldberger and Low and quantum magnetohydrodynamic fluid models describes the dynamical properties and modified dispersion characteristics of the system. The modified Jeans instability criteria and Jeans wavenumbers for the onset conditions of gravitational collapse are obtained, which are significantly modified due to spin magnetisation, quantum corrections and rotation of the system. Strong magnetisation and electrical resistivity are found to enhance the growth rate of Jeans instability, making the system more gravitationally unstable. The magnetic field shows both stabilising (in weak magnetisation limit) and destabilising (in strong magnetisation limit) influence on the growth rate by affecting the gravitational collapse mechanism of dense stars. The growth rate of pressure-anisotropy-driven firehose instability is destabilised due to pressure anisotropy, rotation and spin magnetisation effects. The results are discussed in order to understand the Jeans instability and gravitational collapse of low-mass strongly magnetised white dwarfs.

Presented here is a transcription of the lecture notes from Professor Allan N. Kaufman’s graduate statistical mechanics course Physics 212A and 212B at the University of California Berkeley from the 1972–1973 academic year. 212A addressed equilibrium statistical mechanics with topics: fundamentals (micro-canonical and sub-canonical ensembles, adiabatic law and action conservation, fluctuations, pressure, and virial theorem), classical fluids and other systems (equation of state, deviations from ideality, virial coefficients and van der Waals potential, canonical ensemble and partition function, quasistatic evolution, grand-canonical ensemble and partition function, chemical potential, simple model of a phase transition, quantum virial expansion, numerical simulation of equations of state, and phase transition), chemical equilibrium (systems with multiple species and chemical reactions, law of mass action, Saha equation, chemical equilibrium including ionization and excited states), and long-range interactions (including Coulomb, dipole, and gravitational interactions, Debye–Hückel theory, and shielding). 212B addressed nonequilibrium statistical mechanics with topics: fundamentals (definitions: realizations, moments, characteristic function, and discrete variables), Brownian motion (Langevin equation, fluctuation–dissipation theorem, spatial diffusion, Boltzmann’s H-theorem), Liouville and Klimontovich equations, Landau equation (derivation, elaboration, and H-theorem, and irreversibility), Markov processes and Fokker–Planck equation (derivations of the Fokker–Planck equation and a master equation), linear response and transport theory (linear Boltzmann equation, linear response theory of Kubo and Mori, relation of entropy production to electrical conductivity, transport relations and coefficients, normal mode solutions of the transport equations, sketch of a generalized Langevin equation method for transport theory), and an introduction to nonequilibrium quantum statistical mechanics.

A quasi-linear reduced transport model is developed from a database of high-$\beta$ electromagnetic nonlinear gyrokinetic simulations performed with spherical tokamak for energy production (STEP) relevant parameters. The quasi-linear model is fully electromagnetic and accounts for the effect of equilibrium flow shear using a novel approach. Its flux predictions are shown to agree quantitatively with predictions from local nonlinear gyrokinetic simulations across a broad range of STEP-relevant local equilibria. This reduced transport model is implemented in the T3D transport solver that is used to perform the first flux-driven simulations for STEP to account for transport from hybrid kinetic ballooning mode turbulence, which dominates over a wide region of the core plasma. Nonlinear gyrokinetic simulations of the final transport steady state from T3D return turbulent fluxes that are consistent with the reduced model, indicating that the quasi-linear model may also be appropriate for describing the transport steady state. Within the assumption considered here, our simulations support the existence of a transport steady state in STEP with a fusion power comparable to that in the burning flat top of the conceptual design, but do not demonstrate how this state can be accessed.

The near-axis description of optimised stellarators, at second order in the expansion, provides important information about the field, both of physical and practical importance for stellarator optimisation. It, however, remains relatively underdeveloped for an important class of such stellarators, called quasi-isodynamic (QI). In this paper we develop the theoretical and numerical framework, applying the second-order omnigeneity conditions derived in Rodríguez & Plunk (2023), to make explicit construction of equilibrium solutions. We find that the case of QI stellarators calls for the careful treatment of continuity, smoothness and periodicity of the various functions involved, especially for so-called half-helicity fields, which feature prominently in existing QI designs. The numerical implementation of necessary elements is described, and several examples are constructed and quantitatively verified in detail. This work establishes a basis for further systematic exploration of the space of QI stellarators, and the development of both theoretical and practical tools to facilitate effective optimisation of QI stellarators.

Isolated, undamped geodesic-acoustic-mode (GAM) packets have been demonstrated to obey a (focusing) nonlinear Schrödinger equation (NLSE) (E. Poli, Phys. Plasmas, 2021). This equation predicts susceptibility of GAM packets to the modulational instability (MI). The necessary conditions for this instability are analysed analytically and numerically using the NLSE model. The predictions of the NLSE are compared with gyrokinetic simulations performed with the global particle-in-cell code ORB5, where GAM packets are created from initial perturbations of the axisymmetric radial electric field $E_r$. An instability of the GAM packets with respect to modulations is observed both in cases in which an initial perturbation is imposed and when the instability develops spontaneously. However, significant differences in the dynamics of the small scales are discerned between the NLSE and gyrokinetic simulations. These discrepancies are mainly due to the radial dependence of the strength of the nonlinear term, which we do not retain in the solution of the NLSE, and to the damping of higher radial spectral components $k_r$. The damping of the high-$k_r$ components, which develop as a consequence of the nonlinearity, can be understood in terms of Landau damping. The influence of the ion Larmor radius $\rho _i$ as well as the perturbation wavevector $k_\text {pert}$ on this effect is studied. For the parameters considered here the aforementioned damping mechanism hinders the MI process significantly from developing to its full extent and is strong enough to stabilize some of the (according to the undamped NLSE model) unstable wavevectors.

The magnetohydrodynamic (MHD) equilibrium and stability properties of the Infinity Two fusion pilot plant baseline plasma physics design are presented. The configuration is a four-field period, aspect ratio $A = 10$ quasi-isodynamic stellarator optimised for excellent confinement at elevated density and high magnetic field $B = 9\,T$. Magnetic surfaces exist in the plasma core in vacuum and retain good equilibrium surface integrity from vacuum to an operational $\beta = 1.6 \,\%$, the ratio of the volume average of the plasma and magnetic pressures, corresponding to $800\ \textrm{MW}$ deuterium–tritium fusion operation. Neoclassical calculations show that a self-consistent bootstrap current of the order of ${\sim} 1\ \textrm{kA}$ slightly increases the rotational transform profile by less than 0.001. The configuration has a magnetic well across its entire radius. From vacuum to the operating point, the configuration exhibits good ballooning stability characteristics, exhibits good Mercier stability across most of its minor radius and it is stable against global low-n MHD instabilities up to $\beta = 3.2\,\%$.

The phenomenon of focusing of microwave beams in a plasma near a turning-point caustic is discussed by exploiting the analytical solution to the Gaussian beam-tracing equations in the two-dimensional (2-D) linear-layer problem. The location of maximum beam focusing and the beam width at that location are studied in terms of the beam initial conditions. This focusing must be taken into account to interpret Doppler backscattering (DBS) measurements. We find that the filter function that characterises the scattering intensity contribution along the beam path through the plasma is inversely proportional to the beam width, predicting enhanced scattering from the beam focusing region. We show that the DBS signal enhancement for decreasing incident angles between the beam path and the density gradient is due to beam focusing and not due to forward scattering, as was originally proposed by (Gusakov et al., (Plasma Phys. Contr. Fusion, vol. 56, 2014, p. 0250092014, 2017); Plasma Phys. Rep. vol. 43(6), 2017, pp. 605–613). The analytic beam model is used to predict the measurement of the $k_y$ density-fluctuation wavenumber power spectrum via DBS, showing that, in an NSTX-inspired example, the spectral exponent of the turbulent, intermediate-to-high $k_y$ density-fluctuation spectrum might be quantitatively measurable via DBS, but not the spectral peak corresponding to the driving scale of the turbulent cascade.

A theoretical investigation on the space–time evolution of low-frequency dust acoustic waves (DAWs) in opposite polarity dusty plasmas reveals that they undergo phase mixing for arbitrary initial amplitudes, causing them to suffer a gradual loss in coherency. Both positively and negatively charged dynamical dust grains have been considered to coexist in the plasma, in addition to Maxwell–Boltzmann distributed hot electrons and ions. A perturbative analysis of the governing fluid-Maxwell equations leads us to conclude that the competing dynamics of the opposite polarity dust grains is what causes the DAWs to phase mix. An estimate for the phase-mixing time has also been obtained, which has been found to be profoundly influenced by the values of the various plasma parameters, such as the equilibrium densities of the plasma species, the masses of the opposite polarity dust grains and the electron and ion temperatures. The investigation has also been extended to include phase mixing of DAWs in electron-depleted dusty plasmas. The findings of this study are expected to have relevance in various astrophysical and laboratory plasma environments.

A theoretical framework has been established to investigate the modulational instability of electromagnetic waves in magnetized electron–positron plasmas. The framework is capable of analyzing electromagnetic waves of any intensity and plasmas at any temperature. A fully relativistic hydrodynamic model, incorporating relativistic velocities and thermal effects, is used to describe the relativistic dynamics of particles in plasmas. Under the weakly magnetized approximation, a modified nonlinear Schrödinger equation, governing the dynamics of the envelope of electromagnetic waves in plasmas, is obtained. The growth rate of the modulational instability is then given both theoretically and numerically. By analyzing the dependence of the growth rate on some key physical parameters, the coupled interplay of relativistic effects, ponderomotive forces, thermal effects and magnetic fields on electromagnetic waves can be clarified. The findings demonstrate that specific combinations of physical parameters can significantly enhance modulational instability, providing a theoretical basis for controlling the propagation of electromagnetic waves in plasmas. This framework has broad applicability to most current laser–plasma experiments and high-energy radiation phenomena from stellar surfaces.

The heating effect of electromagnetic waves in ion cyclotron range of frequencies (ICRFs) in magnetic confinement fusion device is different in different plasma conditions. In order to evaluate the ICRF heating effect in different plasma conditions, we conducted a series of experiments and corresponding TRANSP simulations on the EAST tokamak. Both simulation and experimental results show that the effect of ICRF heating is poor at low core electron density. The decrease in electron density changes the left-handed electric field near the resonant layer, resulting in a significant decrease in the power absorbed by the hydrogen fundamental resonance. However, quite a few experiments must be performed in plasma conditions with low electron density. It is necessary to study how to make ICRF heating best in low electron density plasma. Through a series of simulation scans of the parallel refractive index (n//) of the ICRF antenna, it is concluded that the change of the ICRF antenna n// will lead to the change of the left-handed electric field, which will change the fundamental absorption of ICRF power by the hydrogen minority ions. Fully considering the coupling of ion cyclotron wave at the tokamak boundary and the absorption in the plasma core, optimizing the ICRF antenna structure and selecting appropriate parameters such as parallel refractive index, minority ion concentration, resonance layer position, plasma current and core electron temperature can ensure better heating effect in the ICRF heating experiments in the future EAST upgrade. These results have important implications for the enhancement of the auxiliary heating effect of EAST and other tokamaks.

We present a study on the solitons in strongly coupled Yukawa fluids using a simple fluid model (SFE), supplemented by an appropriate equation of state for the medium. The formulation covers a broad range of coupling ($\Gamma$) and screening ($\kappa$) parameters, showing an agreement with the nonlinear quasilocalized charged approximation and generalized hydrodynamic models in the weak screening regime of the solitons in Yukawa media. The results also show a quantitative agreement with the experimentally measured values of the width and Mach number with the normalized amplitude. It has also been observed that the amplitude and width of the soliton in the weak screening limit increase with $\Gamma$ up to $\Gamma \sim 10$, beyond which they remain independent of $\Gamma$ values. Molecular dynamics simulations also confirm that the localization begins to emerge beyond $\Gamma \sim 10$, showing no significant effects on the characteristics of the solitons in Yukawa media. Therefore, the SFE model is capable of predicting the impact of the onset of the localization on the solitons in Yukawa media. Additionally, the amplitude of the soliton increases while its width decreases with $\kappa$ values. The SFE model also explores the possibility of forming refractive soliton structures, whose intensity increases with $\kappa$ values and decreases with $\Gamma$ values.