A systematic theory of the asymptotic expansion of the magnetohydrostatics (MHS) equilibrium in the distance from the magnetic axis is developed to include arbitrary smooth currents near the magnetic axis. Compared with the vacuum and the force-free system, an additional magnetic differential equation must be solved to obtain the pressure-driven currents. It is shown that there exist variables in which the rest of the MHS system closely mimics the vacuum system. Thus, a unified treatment of MHS fields is possible. The mathematical structure of the near-axis expansions to arbitrary order is examined carefully to show that the double-periodicity of physical quantities in a toroidal domain can be satisfied order by order. The essential role played by the leading-order Birkhoff–Gustavson normal form in solving the magnetic differential equations is highlighted. Several explicit examples of vacuum, force-free and MHS equilibrium in different geometries are presented.

New plasma applications in advanced fields, such as fundamental nuclear fusion research, require high-density, large-diameter plasma with a strong and non-uniform magnetic field. A helicon plasma (HP) source using a flat-type antenna is expected to be one of the promising methods for such applications. In this study, we developed an HP source with a two-turn flat-loop antenna connected to a 30 kW radio frequency power supply in the Compact Test Plasma device. In the argon plasma generation experiment with various magnetic fields, HP generation was observed for the first time in this device. The electron density was calculated from the dispersion relation with the magnetic field strength at 45 cm from the antenna surface, assuming a fundamental radial mode and an azimuthal mode of $m=0$. The electron density expected from the experimental result was approximately in the same range as the calculation result by a factor of 2.3 to 3.5. In addition, the magnetic field strength and shape around the antenna are important factors in the plasma properties. This plasma source has been installed in the pilot GAMMA PDX-SC, which is under development for nuclear plasma research, and it contributes to the study of the HP generation process.

The paper presents experimental results from the SMOLA device, which was built in the Budker Institute of Nuclear Physics for the verification of the helical mirror confinement idea. This concept involves active control of axial losses from the confinement zone in an open magnetic trap through the use of multiple mirrors that move in the plasma frame of reference. The discussed experiments focused on determining the cumulative effect of a helical mirror system in combination with a short segment of a stronger magnetic field. Combination of these two methods of axial flow suppression results in higher efficiency compared with each method individually. Different combinations of the mirrors were tested. The most effective flow suppression was observed if the short mirror was placed between the confinement region and the helical mirror. In this configuration, an effective mirror ratio of $R_{{\rm eff}} = 32.6\pm 7.8$ was achieved, along with a more than three-fold increase in plasma density within the confinement region. The possibility of a cumulative effect of different types of magnetic mirrors offers a way to improve the confinement performance of the reactor-grade mirror confinement devices.

A unique field-reversed configuration (FRC) experiment is presently being assembled at the Plasma Technology Research Institute, KFE. It is a compact small-scale FRC device, which uses a set of radio frequency (RF) antennas to produce an internal E × B that drives the electrons for current-drive, in which E is the electric field and B is the magnetic field. This is very similar to the rotating magnetic field (RMF) current-drive, where the horizontal and vertical antennas are driven 90° out of phase. For this device, the RF antennas are arranged differently than the RMF. The RF antennas, being two separate sets, are positioned inside the vacuum chamber. Each set consists of 8 coils, for a total of 16 coils, where 80~100 kHz sine and cosine waveform currents are applied. One set of coils generates a radial B-field, while the other set provides an E-field in the z-direction. As the phase changes, the E and B fields are switched by these two sets. Nevertheless, E × B propagates in the same θ-direction so that this allows the electrons to rotate around the circumference of the device. The FRC device will test wave heating by launching 2.45 GHz microwaves. Also, passive stabilizers are positioned at each end to provide extra stability while preventing tilt instability. The experiment is expected to produce its first plasma in 2025.

Many stellarator coil design problems are plagued by multiple minima, where the locally optimal coil sets can sometimes vary substantially in performance. As a result, solving a coil design problem a single time with a local optimization algorithm is usually insufficient and better optima likely do exist. To address this problem, we propose a global optimization algorithm for the design of stellarator coils and outline how to apply box constraints to the physical positions of the coils. The algorithm has a global exploration phase that searches for interesting regions of design space and is followed by three local optimization algorithms that search in these interesting regions (a ‘global-to-local’ approach). The first local algorithm (phase I), following the globalization phase, is based on near-axis expansions and finds stellarator coils that optimize for quasisymmetry in the neighbourhood of a magnetic axis. The second local algorithm (phase II) takes these coil sets and optimizes them for nested flux surfaces and quasisymmetry on a toroidal volume. The final local algorithm (phase III) polishes these configurations for an accurate approximation of quasisymmetry. Using our global algorithm, we study the trade-off between coil length, aspect ratio, rotational transform and quality of quasi-axisymmetry. The database of stellarators, which comprises approximately 200 000 coil sets, is available online and is called QUASR, for ‘quasi-symmetric stellarator repository’.

In a recent publication (Toler et al., J. Plasma Phys., vol. 89, issue 2, 2023, p. 905890210), we demonstrated that for axisymmetric geometries, the Kapur–Rokhlin quadrature rule provided an efficient and high-order accurate method for computing the normal component, on the plasma surface, of the magnetic field due to the toroidal current flowing in the plasma, via the virtual-casing principle. The calculation was indirect, as it required the prior computation of the magnetic vector potential from the virtual-casing principle, followed by the computation of its tangential derivative by Fourier differentiation, to obtain the normal component of the magnetic field. Our approach did not provide the other components of the virtual-casing magnetic field. In this letter, we show that a more direct and more general approach is available for the computation of the virtual-casing magnetic field. The Kapur–Rokhlin quadrature rule accurately calculates the principal value integrals in the expression for all the components of the magnetic field on the plasma boundary, and the numerical error converges at a rate nearly as high as the indirect method we presented previously.

This paper is based on a report at the 2nd International Fusion Plasma Conference & 13th International Conference on Open Magnetic Systems for Plasma Confinement (iFPC & OS 2023), August 21–25, 2023, Busan, Korea and provides a brief overview of the status of work at the Budker Institute on the study of hot plasma confinement in open-type magnetic traps with a linear axisymmetric configuration. The main attention is paid to key problems: magnetohydrodynamics (MHD) stability in regimes with extremely high relative pressure, longitudinal electronic thermal conductivity, stability with respect to the development of kinetic modes and transverse transport. This paper provides an overview of the methods we are developing to address these problems, the experimental and theoretical results achieved and plans for future development. The last section of the article provides brief information about the preliminary design of the gas-dynamic multiple-mirror trap device, the development of which has been completed.

A new magnetic mirror machine named KAIMIR (KAIST mirror) has been designed and constructed at the Korea Advanced Institute of Science and Technology (KAIST) to study mirror plasma physics and simulate the boundary regions of magnetic fusion plasmas such as in a tokamak. The purpose of this paper is to introduce the characteristics and initial experimental results of KAIMIR. The cylindrical vacuum chamber has a length of 2.48 m and a diameter of 0.5 m and consists of three sub-chambers, namely the source, centre and expander chambers. A magnetic mirror configuration is achieved by electromagnetic coils with a maximum magnetic field strength of 0.4 T at the mirror nozzles and 0.1 T at the centre. The source plasma is generated by a plasma washer gun installed in the source chamber with a pulse forming network system. The typical discharge time is ~12 ms with a ~6 ms (1–7 ms) steady period. Initial results show that the on-axis electron density at the centre is 1019–20 m−3 and the electron temperature is 4–7 eV. Two parameters were varied in this initial phase, the source power and the mirror ratio, which is the ratio of highest to lowest magnetic field strength in the mirror-confined region. We observed that the increase of the electron density was mitigated for a source power above 0.2 MW. It was also found that the electron density increases almost linearly with the mirror ratio. Accordingly, the stored electron energy was also linearly proportional to the mirror ratio, similar to the scaling of the gas dynamic trap.

Influence of the local-ionization-induced neutral depletion on the thrust imparted by the magnetic nozzle plasma thruster is discussed by simply considering reduction of the neutral density due to the ionization in the thruster model combining the global source model and the one-dimensional magnetic nozzle model. When increasing the rf power, it is shown that the increase rate of the plasma density is reduced, while the electron temperature continues to increase due to a decrease in the neutral density. Since the major components of the thrust are originated from the electron pressures in the source and in the magnetic nozzle, the increase in the electron temperature contributes to the increase in the thrust in addition to the gradual density increase by the rf power. The model qualitatively predicts the reduction of the thruster efficiency by the neutral depletion for the high-power condition, compared with the constant neutral density model.

We investigate the effects of different guard geometries on the currents to needle-type Langmuir probes. The results are based on particle-in-cell numerical simulations. We show that if the guard length is less than 6–8 Debye lengths there can be a significant effect on the currents to the probe. A guard radius should not be larger than the Debye length, otherwise it can also significantly affect the currents. However, since guard radii are often close to the probe radius, the second condition is usually satisfied.

Radio frequency quadrupole coolers (RFQCs) are very suitable to cool ion beams with moderate energy spread, typically ions of exotic nuclear species (like $^{132}$Sn$^{1+}$) as in the Selective Production of Exotic Species project at the Laboratori Nazionali di Legnaro, whose ion source supplies 40 keV ions. Beam dynamics includes ion–gas collisions (with a balance of cooling and diffusion effects), acceleration and deceleration and radiofrequency confinement, which can be supplemented by static magnetic field effects. Insertion of a prototype RFQC in the solenoid of the Eltrap machine is also discussed here, with innovations in beam extraction and in modelling, now also based on stochastic equations. Practical consideration on gas pumping and voltage distribution are also included. Typical limits of RFQC are discussed, with special attention to the extracted beam root mean square emittance, which is shown to strongly depend not only on cooler parameters, but also on extraction optics.

In this paper, the modelling and manufacturing of a two-stage supersonic gas jet nozzle enabling the formation of adaptive plasma concentration profiles for injection and acceleration of electrons using few-cycle laser beams are presented. The stages are modelled using the rhoSimpleFoam algorithm of the OpenFOAM computational fluid dynamics software. The first 200–300 ${\rm \mu}$m diameter nozzle stage is dedicated to 1 % N2 + He gas jet formation and electron injection. By varying the pressure between the first and second stages of the injectors, the electron injection location could be adjusted, and the maximum acceleration distance could be ensured. By changing the concentration of the nitrogen in the gas mixture, the charge of the accelerated electrons could be controlled. The second nozzle stage is designed for acceleration in fully ionised He or hydrogen gas and forms the optimal plasma concentration for bubble formation depending on the laser pulse energy, duration and focused beam diameter. In order to reduce the diameter of the plasma profile formed by the first nozzle and the concentration drop gap between the two nozzles, a one-side straight section was introduced in the first nozzle. The shock wave reflected from the straight section of the wall propagates parallel to the shock wave of the intersecting supersonic jets and ensures a minimal gap between the jets. The second-stage longitudinal plasma concentration profile could have an increasing gas density gradient to compensate for dephasing between the electron bunch and the plasma wave due to wave shortening with increasing plasma concentration.

This paper explores the feasibility of a break-even-class mirror referred to as BEAM (break-even axisymmetric mirror): a neutral-beam-heated simple mirror capable of thermonuclear-grade parameters and $Q\sim 1$ conditions. Compared with earlier mirror experiments in the 1980s, BEAM would have: higher-energy neutral beams, a larger and denser plasma at higher magnetic field, both an edge and a core and capabilities to address both magnetohydrodynamic and kinetic stability of the simple mirror in higher-temperature plasmas. Axisymmetry and high-field magnets make this possible at a modest scale enabling a short development time and lower capital cost. Such a $Q\sim 1$ configuration will be useful as a fusion technology development platform, in which tritium handling, materials and blankets can be tested in a real fusion environment, and as a base for development of higher-$Q$ mirrors.

Our earth is immersed in the near-earth space plasma environment, which plays a vital role in protecting our planet against the solar-wind impact and influencing space activities. It is significant to investigate the physical processes dominating the environment, for deepening our scientific understanding of it and improving the ability to forecast the space weather. As a crucial part of the National Major Scientific and Technological Infrastructure–Space Environment Simulation Research Infrastructure (SESRI) in Harbin, the Space Plasma Environment Research Facility (SPERF) builds a system to replicate the near-earth space plasma environment in the laboratory. The system aims to simulate the three-dimensional (3-D) structure and processes of the terrestrial magnetosphere for the first time in the world, providing a unique platform to reveal the physics of the 3-D asymmetric magnetic reconnection relevant to the earth's magnetopause, wave–particle interaction in the earth's radiation belt, particles’ dynamics during the geomagnetic storm, etc. The paper will present the engineering design and construction of the near-earth space plasma simulation system of the SPERF, with a focus on the critical technologies that have been resolved to achieve the scientific goals. Meanwhile, the possible physical issues that can be studied based on the apparatus are sketched briefly. The earth-based system is of great value in understanding the space plasma environment and supporting space exploration.

Astrophysical flows may be studied by reproducing similar conditions using a coaxial plasma accelerator operating in the deflagration regime (or plasma deflagration accelerator). This allows for the recreation and investigation of dynamics present in complex highly coupled plasma systems at the laboratory scale. We report on measurements of the plasma density, temperature, plasma potential and velocity found using a quadruple Langmuir probe (QLP) on such a deflagration accelerator in the form of the Stanford Coaxial High ENerGy (CHENG) device operating with multiple gases – specifically argon, nitrogen and hydrogen. Experiments show a general decrease in bulk plasma velocity with gas atomic mass from upwards of $120\ {\rm km}\ {\rm s}^{-1}$ with hydrogen to less than $30\ {\rm km}\ {\rm s}^{-1}$ with argon. There was an accompanying increase in peak plasma density with increasing atomic mass from ${\sim }3\times 10^{20}\ {\rm m}^{-3}$ with hydrogen to ${\sim }1.5 \times 10^{21}\ {\rm m}^{-3}$ with argon. It was found that the momentum flux and internal energy density also generally increase with atomic mass while the particle flux is constant between shots. Further investigation is needed to understand these correlations and the underlying physics. Lastly, comparisons with scaling laws show that while the CHENG device may be operated in such a way as to simulate the effects of bulk solar wind movement, it may not properly capture the thermal effects.

The ASACUSA (atomic spectroscopy and collisions using slow antiprotons) Cusp experiment requires the production of dense positron plasmas with a high repetition rate to produce a beam of antihydrogen. In this work, details of the positron production apparatus used for the first observation of the antihydrogen beam, and subsequent measurements, are described in detail. This apparatus replaced the previous compact trap design resulting in an improvement in the positron accumulation rate by a factor of $52\pm 3$.

In this study, we explore the influence of the helicity of the magnetic axis – defined as the self-linking number of the curve – on the quality of quasi-isodynamic stellarator-symmetric configurations constructed using the near-axis expansion method (Plunk et al., J. Plasma Phys., vol. 85, 2019, 905850602; Camacho Mata et al., J. Plasma Phys., vol. 88, 2022, 905880503). A class of magnetic axes previously unexplored within this formalism is identified when analysing the axis shape of the QIPC configuration (Subbotin et al., Nucl. Fusion, vol. 46, 2006, p. 921): the case of half-helicity (per field period). We show that these shapes are compatible with the near-axis formalism and how they can be used to construct near-axis stellarators with up to five field periods, $\def\iotaslash{{\require{HTML} \style{display: inline-block; transform: rotate(-13deg)}{\iota}}\kern-7pt{\require{HTML} \style{display: inline-block; transform: rotate(-25deg)}{-}}}{\epsilon _{\mathrm {eff}}} \approx 1.3\,\%$, and similar rotational transform to existing conventionally optimized designs, without the need of a plasma boundary optimization.

This paper documents the design and construction of MUSE, the world's first permanent magnet (PM) stellarator and the first quasi-axisymmetric experiment. The purpose of MUSE is to develop and assess a new way of building optimised stellarators that uses simple planar coils PMs. Our PM optimisation algorithm consists of initialising a geometry to pack dipoles densely, running the FAMUS code to minimise surface field error subject to PM constraints and applying discrete jumps to reach a physically realisable solution. FAMUS treats the PM system as a set of ideal point dipoles. From there we construct finite-volume magnet towers to be housed in 3D-printed PM holders. We describe the design of the PM holders, which were validated by laser metrology. We analyse the effects of finite permeability, sensitivity to perturbations and magnetostatic forces. An exact analytic formula for the magnetic field from a finite-volume PM tower is presented to compute PM–PM forces and stress on the PM holder. Stellarator construction is complete and experiments are underway.

The Wisconsin high-temperature superconductor axisymmetric mirror experiment (WHAM) will be a high-field platform for prototyping technologies, validating interchange stabilization techniques and benchmarking numerical code performance, enabling the next step up to reactor parameters. A detailed overview of the experimental apparatus and its various subsystems is presented. WHAM will use electron cyclotron heating to ionize and build a dense target plasma for neutral beam injection of fast ions, stabilized by edge-biased sheared flow. At 25 keV injection energies, charge exchange dominates over impact ionization and limits the effectiveness of neutral beam injection fuelling. This paper outlines an iterative technique for self-consistently predicting the neutral beam driven anisotropic ion distribution and its role in the finite beta equilibrium. Beginning with recent work by Egedal et al. (Nucl. Fusion, vol. 62, no. 12, 2022, p. 126053) on the WHAM geometry, we detail how the FIDASIM code is used to model the charge exchange sources and sinks in the distribution function, and both are combined with an anisotropic magnetohydrodynamic equilibrium solver method to self-consistently reach an equilibrium. We compare this with recent results using the CQL3D code adapted for the mirror geometry, which includes the high-harmonic fast wave heating of fast ions.

In designing stellarators, any design decision ultimately comes with a trade-off. Improvements in particle confinement, for instance, may increase the burden on engineers to build more complex coils, and the tightening of financial constraints may simplify the design and worsen some aspects of transport. Understanding trade-offs in stellarator designs is critical in designing high performance devices that satisfy the multitude of physical, engineering and financial criteria. In this study, we show how multi-objective optimization (MOO) can be used to investigate trade-offs and develop insight into the role of design parameters. We discuss the basics of MOO, as well as practical solution methods for solving MOO problems. We apply these methods to bring insight into the selection of two common design parameters: the aspect ratio of an ideal magnetohydrodynamic equilibrium and the total length of the electromagnetic coils.