Fully kinetic, energy-conserving electrostatic particle-in-cell (PIC) simulations are employed to quantify how geometry and two-dimensional (2-D-$rz$) and three-dimensional (3-D) effects modify confinement, acceleration and cross-field transport by comparing our results with previous 1-D simulations in an open magnetic mirror. The bulk of the simulations are performed using an explicit scheme at a plasma density of approximately $10^{16}\,\mathrm{m}^{-3}$. In addition to being computationally accessible to explicit PIC, this regime has a relatively large Debye length and therefore emphasises charge-separation effects important in 2-D and 3-D simulations. Starting from a 2-D axisymmetric (2-D-$rz$) model and extending to three dimensions, we isolate finite-ion-Larmor-radius (FLR) effects and azimuthal instabilities. In the 2-D-$rz$ case, FLR effects partially decouple ions from magnetised electrons, producing charge separation near the plasma edge and modest radial ion leakage to the wall, while the near-axis density, potential and acceleration profiles remain close to those in the reduced 1-D model. Full 3-D simulations demonstrate azimuthal modes that induce radial currents, broaden radial density profiles and reduce the confining potential and the total axial potential drop. At low ion temperature, a coherent azimuthal mode of low frequency and low mode number $m=2$ is observed. At high ion temperature, fluctuations shift toward higher mode numbers $m\simeq 4$–$5$ and higher frequencies, with a broadband turbulent spectrum. The particle and energy (for ions and electrons) radial and axial losses are studied in detail. We show that for 3-D cases, radial ion losses account for approximately $30\,\%$ of the flux injected from the source region. The radial electric field produced by the endplate biasing introduces azimuthal shear that weakens coherent structures and reduces radial losses. Finally, additional simulations at densities of the order $10^{18}\,\mathrm{m}^{-3}$ have been performed with a semi-implicit electrostatic PIC algorithm.

The transient detachment dynamics under upstream perturbations was investigated in the GAMMA 10/PDX tandem mirror device using a combination of supersonic molecular beam injection (SMBI) and radio-frequency heating. These actuators generated intermittent high-density plasma fluxes directed toward the divertor-simulation module, enabling controlled studies of detachment stability under pulsed loading. The experiments revealed rapid transitions between detached and partially reattached plasma states, accompanied by significant increases in electron density and ion flux. Time-resolved diagnostics – including microwave interferometry, Thomson scattering and high-speed Balmer-line imaging – captured the spatio-temporal evolution of excitation and recombination processes, highlighting localised emission structures potentially related to molecular activated recombination activity and asymmetric plasma modification associated with directional SMBI fuelling. A delayed response in the divertor-simulation module indicated finite axial propagation of particle flux from the central cell. The combined observations demonstrate the sensitivity of detached plasma to upstream particle perturbations and provide insight into the possible role of molecular processes in mediating transient partial reattachment. These results provide new insight into detachment control and transient plasma behaviour in mirror-based divertor-simulation experiments.

This paper presents experimental investigations of a non-resonant photon trap featuring adiabatic radiation confinement, designed for the photoneutralisation of negative hydrogen (H−/D−) ion beams in fusion plasma injection heating systems. The trap is formed by two monolithic dielectric mirrors with high reflectivity. The study focuses on the methodology and results of measuring the confinement time and integral optical losses. The diagnostic approach is based on analysing the decay rate of radiation within the optical cavity following abrupt interruption of the pump source, utilising wire attenuators for signal reduction. The influence of the laser beam angular divergence on the accumulation efficiency is examined. The obtained data confirm the adiabatic nature of the photon confinement, demonstrate consistency between the measured losses and the specified mirror coating parameters and validate the feasibility of controlling the density of the photon ensemble within the trap. This work confirms the technical feasibility and potential of this approach for the development of high-efficiency photoneutralisation systems.

The magnetic confinement topologies potentially capable of macro-stability with core plasma pressure greatly exceeding the vacuum magnetic field pressure (or ‘$\beta \rightarrow \infty$’) are discussed. An emphasis is placed on application to magnetic fusion energy (MFE) given the perceived advantages. The particle loss rate from highly diamagnetic plasmas in open-field topologies is quantified, including a generalised model for the gas-dynamic regime. It is concluded that, regardless of the topology type, attractive fusion energy gain from such a system is impossible unless (i) the scrape-off-layer can be made much thinner than one thermal ion gyroradius through ambipolar effects, (ii) sufficient stability exists in the stochastic phase space of certain topologies so as to increase the average number of ion orbits before loss by $\sim$1000 times over the isotropic prediction or (iii) electrostatic or centrifugal effects are used to recover adiabatic confinement. Outside of MFE, high-$\beta$ topologies offer many alternative applications in plasma science. The required magnet bore to limit perpendicular particle loss in a point cusp is estimated. Additionally, the unique spherical multipole topology is reviewed and comments are made on the use of cusp topologies for ‘electromagnetic’ confinement efforts.

Collisional merging experiments on field-reversed configurations (FRCs) in the FRC amplification via translation–collisional merging (FAT-CM) device have suggested that the mirror magnetic field strength influences the final merged plasma state. Analytical models do not account for mirror magnetic fields at the ends of the confinement section. To explore their effect, experiments were conducted at FAT-CM, where the strength of mirror magnetic fields were varied. Increasing the mirror field strength was found to promote relaxation to an FRC with larger radius and shorter axial length. Based on these observations, the dependence of equilibrium states on the mirror field strength and the resulting plasma parameters were investigated using a model that reconstructs fully two-dimensional equilibria primarily constrained by wall-mounted magnetic probe measurements. Consistent with the experimental results, computed equilibria with stronger mirror fields converged to plasma states with a larger radius and shorter length. Further, these results showed a bifurcation of topologies with a closed FRC core for higher mirror field and an open-field high-$\beta$ mirror for lower field. This result agreed with internal magnetic probe data which confirm the FRC-to-high-$\beta$ mirror transition. This demonstrates the importance of employing fully two-dimensional modelling of plasma equilibria.

The Gas Dynamic Trap (GDT) facility at the Budker Institute of Nuclear Physics continues experimental studies in support of the Gas-Dynamic Multiple-Mirror Trap (GDMT) project – a prospective neutron source and thermonuclear reactor concept based on open-ended magnetic confinement. During the 2024–2025 upgrade campaign, key engineering systems and diagnostic suites were substantially modernised to address critical physics and technology challenges for the GDMT development. Three key research and development directions were pursued. First, a conductive wall stabilisation system was designed to suppress magnetohydrodynamic (MHD) instabilities at high plasma beta. Second, a new second-harmonic X-mode electron cyclotron resonance heating (ECRH) system operating at 54.5 GHz with 0.8 MW power was commissioned. Preliminary experiments demonstrated increased electron temperature compared with non-ECRH heated plasmas. Third, proof-of-principle experiments on bulk plasma fuelling using a Marshall gun injector were successfully performed, supporting further development towards a high-repetition-rate injector. These results provide essential experimental validation and technological groundwork for the GDMT project, demonstrating progress towards high-beta plasma operation, efficient heating schemes and particle balance control in open magnetic traps.

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.

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.

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.

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 Alfvén 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 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.

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.

Formation of a high-beta plasma in a mirror magnetic field is studied for the first time using three-dimensional semi-implicit particle-in-cell simulations providing a fully kinetic description of not only ions but also electrons. It is shown that, in addition to the longitudinal jump in electric potential between the centre of the trap and the wall, a radial electric field appears in the plasma. Due to this radial field, almost all of the azimuthal electric current required for equilibrium is created by electrons. It was also found that continuous model injection of plasma into the centre of the trap does not result in reaching the magnetohydrodynamic pressure limit ($\beta =1$) due to the development of the flute instability with an azimuthal number $m=1$. The instability growth rate in such a compact system is found to be comparable to the ion-cyclotron frequency. No stabilising effect is observed either from conducting ends or from the perfectly conducting sidewall. The probable reason for that is fast fluctuations of electric field localised inside the injection region that prevent electrons from being frozen into the field lines.

Plasma in axisymmetric mirror traps is unstable versus flute-like modes if no stabilising measures are taken. Instead of stability it is also possible to aim at suppressing the convective transverse transport generated by unstable modes. A ‘vortex confinement’ scheme of this type is utilised in current operation regimes of the Gas-Dynamic Trap in Novosibirsk Bagryansky et al.(2011 Fusion Sci. Technol., vol. 59, pp. 31–35). The relevant model Beklemishev et al. (2010Fusion Sci. Technol., vol. 57, pp. 351–360) describes the effect as due to nonlinear interaction of the flute modes with the background sheared rotation induced by plasma biasing via end plates and limiters. The rigid $m=1$ mode is saturated only due to current dissipation at the end plates, i.e. the partial line tying. The original model assumes flat radial profiles of plasma density and electron temperature, neglecting possible centrifugal and electron-temperature effects. These sources of instability are added to the original framework using a single scalar forming its hybrid extension. Efficiency of the biasing scheme for nonlinear suppression of flute-like convection is shown to depend primarely on spatial positions of biased facility elements, rather than on additional sources of instability.

This paper presents experimental results from the SMOLA device, constructed at the Budker Institute of Nuclear Physics, to verify the concept of helical mirror confinement. The experiments discussed focus on collision regimes and plasma rotation in the transport section, controlled primarily by the axisymmetric plasma gun. The plasma gun of the SMOLA comprises a lanthanum hexaboride cathode, a hollow copper anode and magnetic coils, forming a magnetron discharge with a high degree of ionisation and a radial electric field for ${\textbf{E}} \boldsymbol{\times} {\textbf{B}}$ drift. Ion collisionality is adjustable from collisional to collisionless via magnetic configuration and gas feed of the plasma gun. The main processes in collisions are the ion–ion binary collisions. Electric potential radial distribution, governed by discharge voltage, the anode geometry and its potential, enables ${\textbf{E}} \boldsymbol{\times} {\textbf{B}}$ plasma rotation such that the axial magnetic mirrors velocity in the rotating plasma reference frame can be comparable to the ion thermal velocity ($V_Z \geqslant V_{T_i}$), which realises conditions for effective plasma confinement.

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.

In this work, we describe the use of a 1D-2V quasi-neutral hybrid electrostatic PIC with Monte-Carlo Coulomb collisions and non-uniform magnetic field to model the parallel transport and confinement in an axisymmetric tandem mirror device. End-plugs, based on simple-mirrors, are positioned at each end of the device and fueled with neutral beams (25 and 100 keV) to produce a sloshing ion population and increase the density of the end-plugs relative to the central cell. Results show the formation of a potential difference barrier between the central cell and the end-plugs. This potential confines a large fraction of the low energy thermal ions in the central cell which would otherwise be lost in a simple mirror, demonstrating the advantage of the beam-driven tandem mirror configuration relative to simple mirrors. In addition, we explore the effect of end-plug electron temperature on the confinement time of the device and compare it with theoretical estimates. Finally, we discuss the limitations of the code in its present form and describe the next logical steps to improve its predictive capability such as a fully nonlinear Fokker–Planck collision operator, multiply nested flux surface solutions and modeling the exhaust region up to the wall.

Collisions are crucial in governing particle and energy transport in plasmas confined in a magnetic mirror trap. Modern gyrokinetic codes model transport in magnetic mirrors, but some use approximate model collision operators. This study focuses on a Pastukhov-style method of images calculation of particle and energy confinement times using a Lenard–Bernstein model collision operator. Prior work on parallel particle and energy balances used a different Fokker–Planck plasma collision operator. The method must be extended in non-trivial ways to study the Lenard–Bernstein operator. To assess the effectiveness of our approach, we compare our results with a modern finite element solver. Our findings reveal that the particle confinement time scales as $a \exp (a^2)$ using the Lenard–Bernstein operator, in contrast to the more accurate scaling that the Coulomb collision operator would yield, $a^2 \exp (a^2)$, where $a^2$ is approximately proportional to the ambipolar potential. We propose that codes solving for collisional losses in magnetic mirrors using the Lenard–Bernstein or Dougherty collision operator scale their collision frequency of any electrostatically confined species. This study illuminates the collision operator’s intricate role in the Pastukhov-style method of images calculation of collisional confinement.

Stability of the ‘rigid’ ($m = 1$) ballooning mode in a mirror axisymmetric trap is studied for the case of oblique neutral beam injection (NBI), which creates an anisotropic population of fast sloshing ions. Since small-scale modes with azimuthal numbers $m>1$ in long thin (paraxial) mirror traps are easily stabilized by finite-Larmor-radius (FLR) effects, suppression of the rigid ballooning and flute modes would mean stabilization of all magnetohydrodynamic (MHD) modes, with the exception of the mirror and firehose disturbances, which are intensively studied in geophysics, but have not yet been identified in mirror traps. Large-scale ballooning mode can, in principle, be suppressed either by the lateral perfectly conducting wall, or by the end MHD anchors such as the cusp, by biased limiters or by a combination of these two methods. The effects of the wall shape, vacuum gap width between the plasma column and the lateral wall, angle of oblique NBI, radial profile of the plasma pressure and axial profile of the vacuum magnetic field are studied. It is confirmed that the lateral conducting wall still creates the upper stability zone, where the ratio $\beta$ of the plasma pressure to the pressure of vacuum magnetic field exceeds the second critical value $\beta_{\text{cr2}}$, $\beta >\beta _{\text {cr2}}$. However, in many cases the upper zone is clamped from above by mirror instability. When the lateral wall is combined with end MHD anchors, a lower stability zone $\beta <\beta _{\text {cr}1}$ appears, where $\beta$ is below the first critical value $\beta_{\text{cr1}}$. These two zones can overlap in the case of a sufficiently smooth radial pressure profile, and/or a sufficiently low mirror ratio and/or a sufficiently narrow vacuum gap between the plasma column and the lateral wall. However, even in this case, the range of permissible values of beta is limited from above by the threshold of mirror instability $\beta_{\text{mm}}$, so that $\beta <\beta _{\text {mm}}<1$, in contrast to the case of transversal NBI, when neutral beams are injected perpendicularly to the magnetic field.

Thanks to advances in plasma science and enabling technology, mirror machines arebeing reconsidered for fusion power plants and as possible fusion volumetricneutron sources. However, cross-field transport and turbulence in mirrorsremains relatively understudied compared with toroidal devices. Turbulence andtransport in mirror configurations were studied utilizing the flexible magneticgeometry of the Large Plasma Device (LAPD). Multiple mirror ratios from $M=1$ to $M=2.68$ and three mirror-cell lengths from $L=3.51$ to $L=10.86$ m were examined. Langmuir and magneticprobes were used to measure profiles of density, temperature, potential andmagnetic field. The electric field-fluctuation-driven ${\tilde {\boldsymbol{E}}} \times {\boldsymbol{B}}$ particle flux, where $\boldsymbol{B}$ is the background field, was calculatedfrom these quantities. Two probe correlation techniques were used to inferwavenumbers and two-dimensional structure. Cross-field particle flux and densityfluctuation power decreased with increased mirror ratio. Core density andtemperatures remain similar with mirror ratio, but radial line-integrateddensity increased. The physical expansion of the plasma in the mirror cell byusing a higher field in the source region may have led to reduced densityfluctuation power through the increased gradient scale length. This increasedscale length reduced the growth rate and saturation level of rotationalinterchange and drift-like instabilities. Despite the introduction of magneticcurvature, no evidence of mirror-driven instabilities – interchange,velocity space or otherwise – were observed. For curvature-inducedinterchange, many possible stabilization mechanisms were present, suppressingthe visibility of the instability.