Abstract Three-dimensional particle-in-cell simulations are employed to investigate electron-transport characteristics in Hall thrusters, with particular focus on how magnetic-field configuration affects the electron transport due to electron drift instabilities. Comparing analytic and realistic magnetic-field models reveals significant differences in electron-transport patterns, indicating that spatial variations in magnetic-field strength and topology can strongly reshape turbulent electron transport. In the realistic-field cases considered here, enhanced transport is observed near the upper radial region, where weaker local magnetic fields are associated with reduced electron magnetisation and stronger azimuthal fluctuation amplitudes. The derived correlation-based turbulent electron mobility shows agreement with direct simulation diagnoses, and the obtained two-dimensional transport profiles provide a foundation for developing more accurate reduced-dimensional models.
MIDAS-1D2V is a plasma simulation code for axially symmetric open traps. It solves the non-stationary kinetic equation for the ion distribution function, accounting for Coulomb collisions. This paper presents two key modifications to the model. The first modification enables the calculation of fusion reactions in the plasma, with charged reaction products treated as an additional source term in the kinetic equation. The second modification incorporates beam capture dynamics, including ionisation and charge-exchange processes. Both modifications have been implemented for hydrogen isotopes.
Axisymmetric cylindrical configurations of the magnetic field are used to confine and guide plasmas in fusion and electric propulsion devices, where plasma equilibria are established as a balance between plasma pressure, magnetic stress (pressure) and inertial forces due to azimuthal plasma rotation and axial flow rotation. Most generally, in an axially inhomogeneous case, plasma rotation and azimuthal magnetic field are related via Alfv & eacute;n wave type coupling. We show that, for a special case of a current-free nozzle and, therefore, absence of the azimuthal plasma rotation, the plasma flow along the magnetic surface can be analysed independently of the exact shape of the magnetic surface. The velocity of the transonic plasma flow is determined by the magnitude of the magnetic field on the magnetic surface, while the actual shape of the magnetic surface is determined by the solution of the generalised Grad-Shafranov equation that includes the inertial forces. These analytical results are confirmed with numerical simulations that highlight the contribution of the inertial forces to plasma acceleration and equilibrium. Implications for the flows in the magnetic nozzle for the electric propulsion and open mirrors for fusion are discussed.
In this study, a radiative divertor simulator was developed using the linear magnetic mirror device KAIMIR, considering the center chamber as the upstream scrape-off layer and the expander chamber as the downstream region. To achieve divertor-relevant conditions, the gas feed system of the KAIMIR device was upgraded to increase the particle flux at the downstream region. In addition, a differential pumping system using a skimmer structure was implemented to enable independent control of the neutral pressure between the upstream and downstream regions by reducing the vacuum conductance between the chambers. With this system, a neutral pressure up to 70 mTorr was achieved in the expander chamber while maintaining plasma characteristics in the center chamber. Simulations were then conducted, where non-monotonic behaviour of the ion saturation current and line-integrated density was observed with increasing neutral pressure in the expander chamber, suggesting a transition from attached to detached plasma regimes. Visible emission profiles from fast camera measurements revealed enhanced recombination emission and the formation of localised low-temperature plasma near the downstream region. These results demonstrate that the upgraded KAIMIR device provides a controllable linear divertor simulator suitable for the investigation of radiative and detached divertor plasma physics in a linear configuration.
The above question may be answered as follows. A typical longitudinal plasma wave for which the collision frequency, nu ν $\nu$ , is low relative to the angular wave frequency, omega ω $\omega$ , only interacts with the degree of freedom, upper D D $D$ , related to motion parallel to the wave vector. This gives an adiabatic coefficient corresponding to upper D equals 1 D = 1 $D = 1$ , i.e. 3. At high nu divided by omega ν / ω $\nu /\omega$ , relevant to neutral gases, collisions cause even longitudinal sound waves to interact with all active upper D D $D$ , yielding an adiabatic coefficient of left parenthesis upper D plus 2 right parenthesis divided by upper D ( D + 2 ) / D $(D+2)/D$ . We present a minimal example illustrating the above transition based on linear analysis of a non-relativistic, isotropic, homogeneous, Maxwellian one-component system with a Bhatnagar–Gross–Krook collision operator. Macroscopic forces, mainly included in plasma physics, are essential for the transition at low nu divided by omega ν / ω $\nu /\omega$ . Additionally, the tensor nature of pressure and collision operators satisfying mass, momentum and energy conservation must be invoked to obtain the correct response. Our analysis yields a polytropic index at arbitrary omega ω $\omega$ and wavenumbers, which reduces to the adiabatic coefficient in the corresponding limit. An adiabatic wave response is found in two distinct regimes. If the wave phase velocity far exceeds the thermal particle speed, an adiabatic response occurs at any nu divided by omega ν / ω $\nu /\omega$ (plasma wave case). Alternatively, for mean free paths much shorter than the wavelength, an adiabatic response can be obtained even at phase velocities comparable with the thermal particle speed (sound wave case). The analysis finally demonstrates the occurrence of Landau damping in neutral gases with arbitrary upper D D $D$ at low nu divided by omega ν / ω $\nu /\omega$ .
One of the more interesting features of kinetic descriptions of plasmas are resonant wave particle interactions. These often appear to be collisionless as the collision frequency does not appear in key results even though collisions are actually vital whenever the Coulomb logarithm is large. This deceptive behaviour normally occurs when a resonance is resolved by causality or by inserting a small Krook collision frequency in a linearised kinetic equation to resolve a singularity. However, the actual behaviour of the resonance is more complicated as a narrow collisional boundary layer is responsible for resolving the singular behaviour. The most remarkable example is linear Landau damping, which is normally viewed as a collisionless process. However, an evaluation by Zakharov & Karpman (1963 Sov. Phys. JETP vol. 16, pp. 351-357) proved it to be a collisional process for which collisions can never be ignored for a finite wave amplitude in the collisionless limit. This realisation implies that a small tail bump on a Maxwellian will have a growth or damping rate sensitive to collisions for a finite amplitude monochromatic plasma wave in the very weak collisionality limit. This behaviour is verified here by retaining collisions in both the island dominated limit, as well as the linear, collisional boundary layer dominated regime.
Oscillations and instabilities in $E\!\times\!B$ plasma discharges play a major role in driving turbulence and anomalous transport. The presence of gradients and applied fields that result in a relative drift between the charged species causes the onset of drift-gradient instabilities. This work puts forward a kinetic approach to the low-frequency stability of $E\!\times\!B$ , two-species, partially magnetised plasmas. It presents a local linear analysis of electrostatic modes in the long-wavelength limit, assuming wave propagation perpendicular to the magnetic field. Magnetised electrons are described by a drift-kinetic equation, while unmagnetised ions are described as a cold fluid. This allows for a consistent treatment of electron temperature perturbations in an inhomogeneous plasma that takes into account kinetic resonance effects, changing the threshold conditions for drift instabilities previously found in fluid descriptions. The well-known fluid dispersion relation for the collisionless Simon–Hoh instability is recovered by considering the weak magnetic inhomogeneity limit of our kinetic model and, in addition, a perturbative extension of the instability criterion that includes the gradients of the magnetic field and the electron temperature is obtained.
An overview of new experimental results obtained at the GOL-NB multiple-mirror trap over the past two years is presented. The main scientific objectives of GOL-NB are the direct demonstration of the multiple-mirror confinement efficiency with hydrogen plasma. The device has a configuration that simulates, at reduced plasma parameters, the configuration of a reactor-class facility with a central gas dynamic trap and sections with a strong magnetic field attached to it, which can be turned on both as long solenoids or as multiple mirrors. Plasma is heated by 1 MW neutral beam injection. The following elements are discussed in the paper: magnetohydrodynamic (MHD) stability, plasma parameters in the central trap, neutral beam trapping and fast ion spectrum, comparison of the multiple-mirror and solenoidal configurations at high collisionality, and measures for the reduction in neutral density. The main goals of the experiments were plasma properties characterisation in the central trap and studies of plasma flow in the strong-field sections. We also introduce two new systems for additional plasma heating, a low-energy electron beam mounted at the exit plasma receiver and a 13.56 MHz ICRH system, which is under tests at several kilowatts of input power.
By a detailed comparison of leaky magnetohydrodynamic waves in coronal magnetic flux tubes with leaky electromagnetic waves in dielectric media, it is shown that the latter kind may be called quasi-normal modes, since they can be regularised by a normalisation which systematically cuts off the contribution of the external homogeneous region, whereas such a possibility is forbidden for the former kind by the conservation of magnetic flux. Consequently, leaky magnetohydrodynamic waves cannot be systematically applied to coronal seismology, i.e. to the inverse spectral problem of determining the different equilibrium distributions of the fields by comparing the spectra they produce with the observed ones.
In toroidal confinement systems, the scrape-off layer (SOL) magnetic field exhibits characteristics analogous to those of a magnetic mirror configuration, particularly in the edge plasma region. Therefore, linear plasma devices have advanced divertor simulation studies. To further promote divertor simulation studies, a new divertor simulator, ‘Pilot GAMMA PDX-SC (PGX-SC)’ has been developed, incorporating a pair of superconducting coils that generate a simple magnetic mirror configuration. An electrode-biasing system was installed on the PGX-SC to regulate the plasma potential. The system comprises three concentric basing plates installed at the east end of the main chamber of PGX-SC, in conjunction with a DC-stabilised power supplies for each basing plate. This system can also measure the floating potentials and electrode currents by connecting a resistor to each plate in the absence of an external power supply. Preliminary experiments were conducted to investigate the effect of plasma by applying a bias to the electrode plates. Applying a voltage to the inner electrode increased the plasma potential at the outer electrode. This result suggests the feasibility of controlling the peripheral plasma potential using concentric biasing plates. When voltage was applied to the outer electrode, the amplitude of the fluctuating current decreased. These results collectively indicate the capability of plasma control employing concentric biasing plates.
Bridging the spatiotemporal scales of magnetic seed field generation and subsequent dynamo amplification in the weakly collisional intracluster medium presents an extreme numerical challenge. We perform collisionless turbulence simulations with initially unmagnetised electrons that capture both magnetic seed generation via the electron Weibel instability and the ensuing dynamo amplification. Going beyond existing pair-plasma studies, we use an ion-to-electron mass ratio of $100$ for which we find electron and ion dynamics are sufficiently decoupled. These simulations are enabled by the 10-moment collisionless fluid solver of Gkeyll , which evolves the full pressure tensor for all species. The electron heat-flux closure regulates pressure isotropisation and effectively sets the magnetic Reynolds number. We investigate how the strength of the closure influences the transition between a regime reminiscent of previous kinetic pair-plasma simulations and a regime exhibiting dynamo behaviour qualitatively similar to magnetohydrodynamics.
Geometrical optics (GO) is widely used for reduced modelling of waves in plasmas, but it fails near reflection points, where it predicts a spurious singularity of the wave amplitude. We show how to avoid this singularity by adopting a different representation of the wave equation. Instead of the physical coordinate $x$ and the wavevector $k$ , we use the ray time $ au$ as the new canonical coordinate and the ray energy $h$ as the associated canonical momentum. To derive the envelope equation in the $ au$ -representation, we construct the Weyl symbol calculus on the $( au , h)$ space and show that the corresponding Weyl symbols are related to their $(x, k)$ counterparts by the Airy transform. This allows us to express the coefficients in the envelope equation through the known properties of the original dispersion operator. When necessary, solutions of this equation can be mapped to the $x$ -space using a generalised metaplectic transform. However, the field per se might not even be needed in practice. Instead, knowing the corresponding Wigner function usually suffices for linear and quasilinear calculations. As a Weyl symbol itself, the Wigner function can be mapped analytically, using the aforementioned Airy transform. We show that the standard Airy patterns that form in regions where conventional GO fails are successfully reproduced within metaplectic GO (MGO) simply by remapping the field from the $ au$ -space to the $x$ -space. An extension to mode-converting waves is also presented. This formulation, which we call generalised MGO, can be particularly useful, for example, for reduced modelling of the O-X conversion in inhomogeneous plasma near the critical density, an effect that is important for fusion applications and also occurs in the ionosphere. Overall, MGO can replace GO for any practical purposes, because it better handles cutoffs and is similar otherwise.
Phase-space electron holes, recognised as fundamental nonlinear electrostatic structures in space plasmas, have recently been detected near the mantle boundary of the Venusian magnetosheath by both the Parker Solar Probe (PSP) and the Pioneer Venus Orbiter (PVO). To understand their origin and characteristics, we develop a hydrodynamic model coupled with reductive perturbation theory that incorporates a small population of non-isothermal trapped electrons together with the dynamical effects of solar-wind ions and electrons. This formulation yields a generalised Schamel-Korteweg de Vries equation supporting two distinct classes of nonlinear electrostatic modes: solitary waves and double layers. Using parameter ranges constrained by in situ measurements-including relative densities, drift velocities and temperature ratios-we conduct a detailed parametric investigation of both structures. For the solitary-wave solutions, the model predicts electric field amplitudes of similar to 20 mV m(-1), temporal scales of similar to(2.5-4.5) ms and characteristic frequencies of similar to(0.31-5.6) kHz. The double-layer solutions exhibit fields of similar to 18 mV m(-1), durations of similar to 4.5 ms and frequencies of similar to(0.63-1.6) kHz. These results are in strong agreement with PSP and PVO observations, which report electrostatic fluctuations near 5.4 kHz with amplitudes of similar to 20 mV m(-1). The present analysis therefore provides a consistent physical interpretation of electron-hole structures in the Venusian magnetosheath and highlights their role in mediating kinetic processes at unmagnetised planetary boundaries.
The paper presents a fusion plant concept called VOYAGER developed by leading groups in fusion research (BINP SB RAS) and high-temperature superconductivity (SuperOx LLC). This plant has an open trap configuration with high-temperature superconducting (HTS) vortex (helical) magnets for plasma confinement. The plant is designed with deuterium-deuterium fusion in the ignited regime (without external plasma heating) providing an unlimited supply of reactor fuel, using already proven technologies, and thus maximising the plant's electrical power output and revenue. The costs for construction and operation of the power plant, as well as levelised cost of electricity (LCOE) for the plant, are calculated. The VOYAGER plant has comparable construction and operating costs with existing fusion plant projects; however, VOYAGER, due to the high electrical power output, has the lowest LCOE. The low LCOE value for the proposed plant makes it competitive with conventional electricity sources. Reduced research and development costs due to the use of proven technologies and modular nature of open trap confinement make VOYAGER an even more attractable preposition among fusion plant concepts.
A magnetohydrodynamic (MHD) shock is a discontinuity through which plasma flows, while the mass, momentum and energy are conserved, and the entropy increases. In a collisionless system, the entropy is strictly constant along the phase-space trajectory. The MHD required entropy increase is attributed to dissipative processes causing relaxation to local thermodynamic equilibrium. The search for such dissipative processes in the shock observations usually explores variations of the entropy density or entropy per particle across the shock front. We show that both quantities may increase or decrease across the shock front even when the entropy is strictly conserved. Entropy production should be assessed using the entropy flux density.
An analytical framework is presented for determining the ground states of a collisionless plasma with a given density profile, and its associated available energy, which bounds the field energy, is calculated. We show that the bound can be tightened by enforcing that the ground state is physically realisable, i.e. that the released energy is consistently stored in the fields supported by the density profile. A simple waterbag model is employed to retrieve nonlinear bounds for particularly simple conditions, further finding a phase-transition-like behaviour at the critical energy where the constraint of non-negative number densities becomes relevant. We verify the derived bounds with one-dimensional particle-in-cell simulations, where it is found that the true energy released is typically tilde 20 percent sign similar to 20 % ${\sim} 20\,\%$ of the bound derived. Next, we present an asymptotic framework for calculating ground states with given density profiles of distribution functions close to this ground state. This framework is employed to describe a magnetised plasma, where it is shown that the ground state seeks long-wavelength structures for large electron-to-ion temperature ratios, highlighting unfavourable transport properties in this regime. By using the corrected adiabatic response in toroidal geometry (with a flux-surface average subtracted), it is found that the ground state seeks long-wavelength zonal structures. Furthermore, a crude model of a toroidal, multispecies, quasineutral plasma highlights that there is non-trivial dependence on the impurity content with certain optimal mixing ratios. A similar model is constructed to capture the effects of a fast-ion population, showing a non-trivial dependence on the exact shape of the fast-ion distribution. These results provide rigorous, density-aware limits on energy release in collisionless plasmas, and similar methods may be used to account for electromagnetic effects.
Commonwealth Fusion Systems (CFS) plans to operate a tokamak power plant called ARC in the early 2030s. Tokamak plasmas have stability limits that, if crossed, lead to a rapid termination of the plasma, referred to as a disruption. Disruptions pose a melt risk to the first wall resulting from thermal and non-thermal particle heat fluxes, and an electromagnetic loading risk on all metal components within the equilibrium coils. A comprehensive set of models is used herein to provide an assessment of both mitigated and unmitigated ARC disruption loads. A preliminary massive gas injection system is baselined and a runaway electron mitigation coil option is proposed to close possible gaps in the baseline. It is predicted that all ARC disruption loads are within a factor of 2 of the disruption loads in SPARC, a tokamak presently under construction by CFS, and therefore SPARC provides an opportunity to calibrate models, test solutions and inform the design of ARC. The goal for ARC is disruption-free operation, however, the pragmatic design target is to withstand one mitigated disruption per day, and to restart the plasma following mitigation in tens of seconds without interrupting the power output. Unmitigated disruptions must be rare, and experience with unmitigated disruption impacts in SPARC will better define what rare means. The implications of this strategy for plasma disruptivity and disruption prediction are discussed, and operating the ARC scenario on SPARC is expected to refine the ARC final design and operational plan.
The ARC $<^>{ extrm {TM}}$ tokamak, a high-field ( $B_T$ = 11.4 T) fusion power plant, under development by Commonwealth Fusion Systems, is studied using a suite of integrated modelling tools to predict its fusion power generation ( $P_{fus}$ ), transport and confinement properties. Analysis is based off an ARC operational point scoped first with zero-dimensional (0-D) plasma operational contour (POPCON) modelling to produce 1.13 GW of fusion power. A suite of integrated modelling tools (TRANSP, ASTRA and TORAX) were applied to predict the performance and kinetic profiles of the ARC design point, yielding a range of predicted performance spanning from ${\sim} 900$ to 1300 MW in rough quantitative agreement with POPCON predictions. The sensitivity of these results to uncertain modelling inputs was probed using scans of pedestal boundary conditions around EPED-predicted values (total pressure and temperature ratios), tungsten concentration and seperatrix density around their nominal assumptions. Pedestal pressure and pedestal top $(T_i/T_e)$ play a large role in 1.5-dimensional performance predictions, able to modify the predicted $P_{fus}$ by a factor of 2 within reasonable assumptions. High-fidelity core nonlinear gyrokinetic profile predictions, performed using CGYRO (Candy et al. 2016 J. Comput. Phys., vol. 324, pp. 73-93) coupled with the PORTALS (Rodriguez-Fernandez et al. 2024 Nucl. Fusion, vol. 64, 076034; Phys. Plasmas, vol. 31, 2024, 062501) framework, yield substantially lower performance ( $P_{fus} = 677$ MW) compared with 0-D and medium-fidelity modelling for nominal assumptions, showing that there is non-negligible uncertainty between models and that future work on SPARC may help resolve discrepancies. Lower overall performance results from significantly reduced volume-averaged densities and temperatures, along with reduced levels of density and temperature peaking. Turbulence and transport are largely dominated by ion temperature gradient across the profile, confirmed by both linear stability and the response of the nonlinear fluxes to changes in gradients, with some impact of kinetic ballooning modes in the deep core. This work represents one of the most complete scoping of potential fusion power plant conditions performed to date. The extensive integrated modelling provides confidence in ARC performance approaching 1 GW, while nonlinear gyrokinetic modelling results in open questions into the physics of density and temperature peaking in fusion-power-plant-relevant operational space. A discussion of results and the role that the SPARC tokamak (Creely et al. 2020 J. Plasma Phys., vol. 86, 865860502) will play in informing ARC design, performance and operation is presented.
In this work, we investigate the dynamics of particles accelerated by electromagnetic wave pulses under the effects of a radiation reaction as described by the Landau-Lifshitz model. The radiation reaction breaks the invariant used to predict both the critical carrier amplitude required for efficient particle acceleration and the particle's final ejection velocity. Moreover, it alters the dynamical regimes predicted by models that neglect it. Numerical simulations of single-particle dynamics, performed using both the full dynamical equations and the canonical averaged formulation, support the analytical results.
