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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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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'. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The frequency spectra of the Trivelpiece–Gould modes of a waveguide partially filled with non-neutral plasma are determined numerically by solving the dispersion equation. The modes having azimuthal number $m = 1$ are considered. The results are presented for the entire acceptable range of electron densities, magnetic field strengths, for different values of the charge neutralization coefficient. The Cherenkov resonance condition of an ion with a diocotron mode having a finite value of the longitudinal wave vector was studied. The characteristics of resonant low-frequency electron–ion instability caused by relative azimuth motion of electrons and ions in crossed fields and by the anisotropy of the distribution function of ions are discussed. Ions are created by ionization of residual gas in the plasma volume. Due to the anisotropy, instability occurs not only in the vicinity of the resonance, but also outside it. For typical values of plasma parameters in experiments, estimations of the frequency growth rate are given. A conclusion is drawn that this instability can be the cause of the low-frequency oscillations observed in linear devices with non-neutral plasma produced in an electron beam channel. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The multi-cell Penning–Malmberg trap concept has been proposed as a way to accumulate and confine unprecedented numbers of antiparticles, an attractive but challenging goal. We report on the commissioning and first results (using electron plasmas) of the World's second prototype of such a trap, which builds and improves on the findings of its predecessor. Reliable alignment of both 'master' and 'storage' cells with the axial magnetic field has enabled confinement of plasmas, without use of the 'rotating wall' (RW) compression technique, for over an hour in the master cell and tens of seconds in the storage cells. In the master cell, attachment to background neutrals is found to be the main source of charge loss, with an overall charge-confinement time of 8.6 h. Transfer to on-axis and off-axis storage cells has been demonstrated, with an off-axis transfer rate of $50\,\%$ of the initial particles, and confinement times in the storage cells in the tens of seconds (again, without RW compression). This, in turn, has enabled the first simultaneous plasma confinement in two off-axis cells, a milestone for the multi-cell trap concept. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This paper discusses thermal equilibrium states of single-species plasmas, such as pure electron plasmas and pure positron plasmas, that are confined in a dipole trap. Thermal equilibrium states for such plasmas are routinely realized in the homogeneous magnetic field of Penning–Malmberg traps. We generalize the theory of these states to include inhomogeneous magnetic dipole fields. The approach to thermal equilibrium takes place in two stages with well separated time scales. On the collision time scale, thermal equilibrium is established along each magnetic field line. On the much longer transport time scale, heat conduction and viscosity bring the plasmas on different flux contours into thermal equilibrium, we call this a state of global thermal equilibrium. We present numerical results for local and global thermal equilibria. These results agree with the analytic predictions for charge collections that are large compared with the Debye length. There is, in principle, no limit to the confinement time of a single-species plasma in a global thermal equilibrium state. Experiments with hot electron–ion plasmas performed in the LDX and RT1 devices give us confidence that, in contrast to a Penning–Malmberg trap, a magnetic dipole field can also confine cold quasi-neutral electron–positron pair plasmas on the time scale of the phenomena of interest. Such pair plasmas are assumed to form in the magnetosphere of neutron stars but have so far not been realized in a laboratory. The creation of an electron–positron pair plasma is the main goal of the APEX collaboration. [ABSTRACT FROM AUTHOR]

A new perturbation and continuation method is presented for computing and analysing stellarator equilibria. The method is formally derived from a series expansion about the equilibrium condition $\boldsymbol {F} \equiv \boldsymbol {J}\times \boldsymbol {B} - \boldsymbol {\nabla } p = 0$ , and an efficient algorithm for computing solutions to second- and third-order perturbations is developed. The method has been implemented in the DESC stellarator equilibrium code, using automatic differentiation to compute the required derivatives. Examples are shown demonstrating its use for computing complicated equilibria, perturbing a tokamak into a stellarator and performing parameter scans in pressure, rotational transform and boundary shape in a fraction of the time required for a full solution. [ABSTRACT FROM AUTHOR]

A two-fluid model is developed to study the stability of weakly magnetized rotating plasma columns. Previous works have shown that rotating plasma columns are prone to centrifugal flute modes. Most of these models are based on the low-frequency assumption which is valid when the instability frequency and the plasma azimuthal frequency are small compared with the ion cyclotron frequency. This assumption is challenged in many laboratory plasma devices, including weakly magnetized plasma columns. A radially global dispersion relation relaxing the low-frequency approximation and applicable in these devices is derived. The validity domain of the low-frequency approximation is discussed. In addition, the impact of the radial boundary on the linear stability is investigated and comparison with results obtained in the radially local approximation are performed. [ABSTRACT FROM AUTHOR]

The paper presents experimental results from the SMOLA device on the testing of the helical mirror confinement hypothesis. Helical mirror confinement is the technique of an active control of axial plasma losses from a confinement zone by multiple magnetic mirrors that move along the axis in the reference frame of the plasma that experiences $\boldsymbol{E} \times \boldsymbol{B}$ rotation due to an applied radial electric field. Theory predicts that a helical mirror will provide an axial force that modifies the plasma flow and, simultaneously, density pinching to the axis. The force direction depends on the plasma rotation direction. Experimental data on the axial plasma losses at different direction of the magnetic mirror movement are presented. If the trapped ions move in the direction opposite to the direction of the axial losses, then the particle flux reduces in the broad range of the plasma density. The confinement improves with the increase of the fraction of the trapped particles (effective mirror ratio was up to $R_{{\rm eff}}=5.8\pm 1.4$). If the trapped ions move in the same direction as the axial losses, then the flux depends on density. At intermediate densities, the integral flux through the transport section rises compared to the plasma flowing through the straight magnetic field. The effective mirror ratio is lower and does not significantly depend on the fraction of the trapped particles (effective mirror ratio at intermediate density was $R_{{\rm eff}}=3.3\pm 0.8$). [ABSTRACT FROM AUTHOR]

A fluid dispersion theory in partially magnetised plasmas is analysed to examine the conditions under which large-wavelength modes develop in Penning-type configurations, that is, where an electric field is imposed perpendicular to a homogeneous magnetic field. The fluid dispersion relation assuming a slab geometry shows that two types of low-frequency, gradient drift instabilities occur in the direction of the $\boldsymbol {E} \times \boldsymbol {B}$ and diamagnetic drifts. One type of instability, observed when the equilibrium electric field and plasma density gradient are in the same direction, is similar to the classic modified Simon–Hoh instability. A second instability is found for conditions in which (i) the diamagnetic drift is in the direction opposite to the $\boldsymbol {E} \times \boldsymbol {B}$ drift and (ii) the magnitude of the diamagnetic drift is sufficiently larger than the electron thermal speed. The present fluid dispersion theory suggests that the rotating spokes driven by such fluid instabilities propagate in the same direction as the diamagnetic drift, which can be in the same direction as or opposite to the $\boldsymbol {E} \times \boldsymbol {B}$ drift, depending on the plasma conditions. This finding may account for the observation, in some plasma devices, of the rotation of large-scale structures in both the $\boldsymbol {E} \times \boldsymbol {B}$ and $-\boldsymbol {E} \times \boldsymbol {B}$ directions. [ABSTRACT FROM AUTHOR]

In this study, we experimentally evaluate the ion transportation through a cone guide target, which accelerates ions up to MeV energies via target normal sheath acceleration, and transports them onto the position of imploding fuel in the fast ignition scenario of nuclear fusion. We measured the electric and magnetic fields (EM-fields) induced by return current streaming along the cone wall by proton radiography, and we report that the EM-fields are predominantly induced within a temporal window up to 30 ps after the laser injection. The magnitude of the electric field is maximized around 13 ps, reaching $4.0\times 10^{10} \mathrm {V}\ \mathrm {m}^{-1}$ , when the magnetic field is below 200 T. The present scheme provides insights on the EM-fields evaluation in the time region that is difficult to treat with simulations due to the computing resources. [ABSTRACT FROM AUTHOR]

In this paper we present an experimental study of edge turbulence in the Large Plasma Device at UCLA. We utilize a scan of discharge power and prefill pressure (neutral density) to show experimentally that turbulent density fluctuations decrease with decreasing density gradient, as predicted for resistive drift-wave turbulence (RDWT). As expected for RDWT, we observe that the cross-phase between the density and potential fluctuations is close to 0. Moreover, the addition of an electron temperature gradient leads to a reduction in the amplitude of the density fluctuations, as expected for RDWT. However, counter to theoretical expectations, we find that the potential fluctuations do not follow the same trends as the density fluctuations for changes either in density gradients or the addition of a temperature gradient. The disconnect between the density and potential fluctuations is connected to changes in the parallel flows as a result of differences in the prefill pressure, i.e. neutral density. Further analysis of the density and potential fluctuation spectra show that the electron temperature gradient reduces the low frequency fluctuations up to $10 \,{\rm kHz}$ and the introduction of a temperature gradient leads to an unexpected ${\sim }{\rm \pi}$ shift of the density–potential cross-phase at ${\sim }10\,{\rm kHz}$ , while maintaining the typical resistive drift-wave cross-phase at lower frequencies. These experiments partly confirm existing knowledge on resistive drift-wave turbulence, but also introduce new observations that indicate a need for dedicated nonlinear three-dimensional turbulence simulations that include neutrals. [ABSTRACT FROM AUTHOR]

An optimized compact stellarator with four simple coils is obtained from direct optimization via a coil shape. The new stellarator consists of two interlocking coils and two vertical field coils similar to those of the Columbia Non-neutral Torus (CNT) (Pedersen et al., Phys. Rev. Lett., vol. 88, 2002, pp. 205002). The optimized configuration has a global magnetic well and a low helical ripple level comparable to that of Wendelstein 7-X (W7-X) (Wolf et al., Nucl. Fusion, vol. 57, 2017, pp. 102020). The two interlocking coils have a smooth three-dimensional shape much simpler than those of advanced stellarators such as W7-X. This result opens up possibilities of future stellarator reactors with simplified coils. [ABSTRACT FROM AUTHOR]

A spacecraft during mission typically switches from chemical propulsion to electric propulsion once it lifts out of the Earth's gravity as the thrust requirement to drive it reduces substantially. Consequently, electric propulsion technology is commonly used for deep space mission, satellite orbit keeping and orbit correction. In the last few decades, the amount of man-made space junk (space debris) has increased enormously and has become a potential danger for space stations, space shuttles and other live satellites. A bi-directional plasma thruster, mounted on a satellite, can be used to remove space debris during satellite operation (Takahashi et al., Sci. Rep., vol. 8, 2018, p. 14417). A directed ion beam ejected from a plasma thruster imparts a net force on space debris to decelerate and facilitates manoeuvring and re-entry of space debris into the Earth's atmosphere where it can burn out. We present a detailed 1D3V PIC-MCC (particle in cell-Monte Carlo collision) simulation of a bi- directional plasma thruster. To this end, a PIC-MCC solver which resolves thruster axial direction and all three velocity dimensions is used to study a magnetic nozzle plasma thruster with both ends open (bi-directional plasma thruster). We show that such a bi-directional plasma thruster can be used to accelerate–decelerate a live satellite and also to remove space debris by altering the magnetic field spatial profile in the plasma expansion region. A detailed study is presented. [ABSTRACT FROM AUTHOR]

Quasisymmetric stellarators are an attractive class of optimised magnetic confinement configurations. The property of quasisymmetry (QS) is in practice limited to be approximate, and thus the construction requires measures that quantify the deviation from the exact property. In this paper we study three measure candidates used in the literature, placing the focus on their origin and a comparison of their forms. The analysis shows clearly the lack of universality in these measures. As these metrics do not directly correspond to any physical property (except when exactly quasisymmetric), optimisation should employ additional physical metrics for guidance. It is suggested that close to QS minima, one should treat QS metrics through inequality constraints so that additional physics metrics dominate optimisation. The impact of different quasisymmetric measures on optimisation is presented through an example, for which the standard metric that weights the asymmetric Fourier modes of the field magnitude appears to perform best. [ABSTRACT FROM AUTHOR]

Given the large anisotropy of transport processes in magnetized plasmas, the magnetic field structure can strongly impact heat diffusion: magnetic surfaces and cantori form barriers to transport while chaotic layers and island structures can degrade confinement. When a small but non-zero amount of perpendicular diffusion is included, the structure of the magnetic field becomes less important, allowing pressure gradients to be supported across chaotic regions and island chains. We introduce a metric for the effective volume over which the local parallel diffusion dominates based on the solution to the anisotropic heat diffusion equation. To validate this metric, we consider model fields with a single island chain and a strongly chaotic layer for which analytic predictions of the relative parallel and perpendicular transport can be made. We also analyse critically chaotic fields produced from different sets of perturbations, highlighting the impact of the mode number spectrum on the heat transport. Our results indicate that this metric coincides with the effective volume of non-integrability in the limit $\kappa _{\perp } \rightarrow 0$ , where $\kappa_{\perp}$ is the perpendicular diffusion coefficient. We propose that this metric be used to assess the impact of non-integrability on the heat transport in stellarator equilibria. [ABSTRACT FROM AUTHOR]

Adjoint methods can speed up stellarator optimisation by providing gradient information more efficiently compared with finite-difference evaluations. Adjoint methods are herein applied to vacuum magnetic fields, with objective functions targeting quasi-symmetry and a rotational transform value on a surface. To measure quasi-symmetry, a novel way of evaluating approximate flux coordinates on a single flux surface without the assumption of a neighbourhood of flux surfaces is proposed. The shape gradients obtained from the adjoint formalism are evaluated numerically and verified against finite-difference evaluations. [ABSTRACT FROM AUTHOR]

Particle acceleration via magnetic reconnection is a fundamental process in astrophysical plasmas. Experimental architectures are able to confirm a wide variety of particle dynamics following the two-dimensional Sweet–Parker model, but are limited in their reproduction of the fan-spine magnetic field topology about three-dimensional (3-D) null points. Specifically, there is not yet an experiment featuring driven 3-D torsional magnetic reconnection. To move in this direction, this paper expands on recent work toward the design of an experimental infrastructure for inducing 3-D torsional fan reconnection by predicting feasible particle acceleration profiles. Solutions to the steady-state, kinematic, resistive magnetohydrodynamic equations are used to numerically calculate particle trajectories from a localized resistivity profile using well-understood laboratory plasma parameters. We confine a thin, 10 eV helium sheath following the snowplough model into the region of this localized resistivity and find that it is accelerated to energies of ${\approx }2$ keV. This sheath is rapidly accelerated and focused along the spine axis propagating a few centimetres from the reconnection region. These dynamics suggest a novel architecture that may hold promise for future experiments studying solar coronal particle acceleration and for technology applications such as spacecraft propulsion. [ABSTRACT FROM AUTHOR]

The variation of pressure-gradient-driven turbulence with plasma $\beta$ (up to $\beta \approx 15\,\%$) is investigated in linear, magnetized plasma. The magnitude of magnetic fluctuations is observed to increase substantially with increasing $\beta$. More importantly, parallel magnetic fluctuations are observed to dominate at higher $\beta$ values, with $\delta B_\parallel / \delta B_\perp \approx 2$ and $\delta B / B_0 \approx 1\,\%$. Parallel magnetic fluctuations are strongly correlated with density fluctuations and the two are observed to be out of phase. The relative magnitude of and cross-phase between density and parallel magnetic field fluctuations are consistent with the dynamic pressure balance ($P+{B_{0}^2}/{2\mu _0} = \textrm {constant}$). A local slab model theory for electromagnetic, modified drift Alfvén waves, including parallel magnetic fluctuations, shows partial agreement with experimental observations. [ABSTRACT FROM AUTHOR]

We describe here efforts to create and study magnetized electron–positron pair plasmas, the existence of which in astrophysical environments is well-established. Laboratory incarnations of such systems are becoming ever more possible due to novel approaches and techniques in plasma, beam and laser physics. Traditional magnetized plasmas studied to date, both in nature and in the laboratory, exhibit a host of different wave types, many of which are generically unstable and evolve into turbulence or violent instabilities. This complexity and the instability of these waves stem to a large degree from the difference in mass between the positively and the negatively charged species: the ions and the electrons. The mass symmetry of pair plasmas, on the other hand, results in unique behaviour, a topic that has been intensively studied theoretically and numerically for decades, but experimental studies are still in the early stages of development. A levitated dipole device is now under construction to study magnetized low-energy, short-Debye-length electron–positron plasmas; this experiment, as well as a stellarator device that is in the planning stage, will be fuelled by a reactor-based positron source and make use of state-of-the-art positron cooling and storage techniques. Relativistic pair plasmas with very different parameters will be created using pair production resulting from intense laser–matter interactions and will be confined in a high-field mirror configuration. We highlight the differences between and similarities among these approaches, and discuss the unique physics insights that can be gained by these studies. [ABSTRACT FROM AUTHOR]

A new concept for the generation of thrust for space propulsion is introduced. Energetic thrust is generated in the form of plasmoids (confined plasma in closed magnetic loops) when magnetic helicity (linked magnetic field lines) is injected into an annular channel. Using a novel configuration of static electric and magnetic fields, the concept utilizes a current-sheet instability to spontaneously and continuously create plasmoids via magnetic reconnection. The generated low-temperature plasma is simulated in a global annular geometry using the extended magnetohydrodynamic model. Because the system-size plasmoid is an Alfvenic outflow from the reconnection site, its thrust is proportional to the square of the magnetic field strength and does not ideally depend on the mass of the ion species of the plasma. Exhaust velocities in the range of 20 to $500\ \textrm {km}\ \textrm {s}^{-1}$ , controllable by the coil currents, are observed in the simulations. [ABSTRACT FROM AUTHOR]

This paper presents the results of studies of plasma flow parameters on the PF-1000U facility. A distinctive feature of this facility is the ability to create profiled initial gas distributions using gas puffs. In the experiments described, a combined system for filling the vacuum chamber with a working gas was used, in which an additional injection of various gases (deuterium, helium, neon and their mixtures) into the axial region of the chamber prefilled with deuterium was performed using a pulse valve. Thus, both the pinching processes and, accordingly, the generation of axial plasma flows and the conditions of their propagation in the background gas of the facility chamber were affected. Regimes with the generation of compact stable plasma formations propagating over long distances were found. The results obtained can be used in laboratory modelling of astrophysical jets from young stellar objects. [ABSTRACT FROM AUTHOR]

The paper analyses the penetration of a magnetic field into the plasma bridge of nanosecond and microsecond opening switches. For switches with a conduction time of ~100 ns, simple formulae are derived to estimate the magnetic field velocity in collisionless and collisional plasmas. It is shown that in both cases this velocity is determined by the magnetic field rise rate to plasma density ratio raised to the power of 1/2. As the conduction time is increased to ~1 ${\rm \mu}$ s, the field velocity starts to depend on the plasma aggregation by a magnetic piston. At the same time, irrespective of the conduction time, the electron flow velocity is limited by the radial drift velocity in crossed magnetic and polarization electric fields. Such a limitation suppresses the current channel conductivity with respect to the Spitzer value by a factor equal to the electron magnetization parameter raised to one or another power. On completion of the conduction phase, the rate of rise of the switch resistance is proportional to the electron drift velocity. The peak switch voltage obtained in calculations is compared with its values recorded in experiments on mega-ampere current switching. A procedure is also presented for calculating the switch parameters to obtain the maximum possible voltage in the phase of current cutoff. [ABSTRACT FROM AUTHOR]

In this paper, we propose an efficient diagnostic technique for determining spatially resolved measurements of the ion density ratio in a magnetized two-ion species plasma. Shear Alfvén waves were injected into a mixed helium–neon plasma using a magnetic loop antenna, for frequencies spanning the ion cyclotron regime. Two distinct propagation bands are observed, bounded by $\omega and $\omega _{ii} , where $\omega _{ii}$ is the ion–ion hybrid cutoff frequency and $\varOmega _\textrm {He}$ and $\varOmega _\textrm {Ne}$ are the helium and neon cyclotron frequencies, respectively. A theoretical analysis of the cutoff frequency was performed and shows it to be largely unaffected by kinetic electron effects and collisionality, although it can deviate significantly from $\omega _{{ii}}$ in the presence of warm ions due to ion finite Larmor radius effects. A new diagnostic technique and accompanying algorithm was developed in which the measured parallel wavenumber $k_\parallel$ is numerically fit to the predicted inertial Alfvén wave dispersion in order to resolve the local ion density ratio. A major advantage of this algorithm is that it only requires a measurement of $k_\parallel$ and the background magnetic field in order to be employed. This diagnostic was tested on the Large Plasma Device at UCLA and was successful in yielding radially localized measurements of the ion density ratio. [ABSTRACT FROM AUTHOR]

It is demonstrated that finite-pressure, approximately quasi-axisymmetric stellarator equilibria can be directly constructed (without numerical optimization) via perturbations of given axisymmetric equilibria. The size of such perturbations is measured in two ways, via the fractional external rotation and, alternatively, via the relative magnetic field strength, i.e. the average size of the perturbed magnetic field, divided by the unperturbed field strength. It is found that significant fractional external rotational transform can be generated by quasi-axisymmetric perturbations, with a similar value of the relative field strength, despite the fact that the former scales more weakly with the perturbation size. High mode number perturbations are identified as a candidate for generating such transform with local current distributions. Implications for the development of a general non-perturbative solver for optimal stellarator equilibria are discussed. [ABSTRACT FROM AUTHOR]

Finding coil sets with desirable physics and engineering properties is a crucial step in the design of modern stellarator devices. Existing stellarator coil optimization codes ultimately produce zero-thickness filament coils. However, stellarator coils have finite depth and thickness, which can make the single-filament model a poor approximation, particularly when coil build dimensions are relatively large compared to the coil–plasma distance. In this paper, we present a new method for designing coils with finite builds and present a mechanism to optimize the orientation of the winding pack. We approximate finite-build coils with a multi-filament model. A numerical implementation has been developed, and applications to the Helically Symmetric eXperiment stellarator and a new UW-Madison quasihelically symmetric configuration are shown. [ABSTRACT FROM AUTHOR]

A magnetic field configuration of an island divertor for a quasi-axisymmetric stellarator (CFQS) is proposed. The configuration incorporates large islands surrounding the core confinement region. The interface between the core region and the peripheral region of the island divertor is a clear magnetic separatrix similar to a tokamak divertor. The structure of divertor magnetic field lines is very regular without stochasticity and the connection length is sufficiently long for good divertor performance. Such a divertor configuration is produced in the magnetic field configuration for the CFQS device, which is now under construction in China. [ABSTRACT FROM AUTHOR]

We present the elements required to construct two devices used in an undergraduate plasma physics laboratory. The materials and construction costs of the sources, the vacuum systems and probe drives and electrical circuits are presented in detail in the text and the first appendix. We also provide the software for probe motion and data acquisition as well as the electrical schematics for key components. Experiments which have been performed are listed and two (resonance cones and whistler waves) are described in greater detail. The machines are flexible and original research is possible. [ABSTRACT FROM AUTHOR]

The possibility of performing electron density and temperature measurements in a high power helicon plasma is a crucial issue in the framework of the AWAKE (Advanced WAKefield Experiment) project, which demonstrates acceleration of particles using $\text{GeV}~\text{m}^{-1}$ electric fields in plasmas. For AWAKE, a helicon is currently envisaged as a candidate plasma source due to its capability for low electron and ion temperature, high electron density and production of an elongated plasma column. A plasma diagnostic to accurately determine the electron density in AWAKE regimes would be a valuable supporting tool. A demonstration Thomson scattering (TS) diagnostic was installed and successfully tested on the resonant antenna ion device (RAID) at the Swiss Plasma Center of Ecole Polytechnique Fédérale de Lausanne. RAID produces a helicon plasma column with characteristics similar to those of the AWAKE helicon source, and is therefore an optimal testbed for application to the AWAKE device. The spectrometer employed in RAID is based on polychromators which collect the light scattered by plasma electrons in spectrally filtered wavelength regions. Results from TS on RAID demonstrate conditions of electron density and temperature respectively of $n_{e}=1.10\,(\pm 0.19)\times 10^{19}~\text{m}^{-3}$ and $T_{e}=2.3\,(\pm 0.6)~\text{eV}$ in a steady-state discharge in an Ar plasma with 5 kW of RF power. If the same polychromator system is used for AWAKE, where the electron density attained is $2\times 10^{20}~\text{m}^{-3}$ , the contribution to measurement error due to coherent scattering is ${\sim}2.5\,\%$. Presented here are details of the TS diagnostic and the first tests in RAID, and the expectations for the system when employed on the AWAKE device. [ABSTRACT FROM AUTHOR]

Plasma terminating disruptions in tokamaks may result in relativistic runaway electron beams with potentially serious consequences for future devices with large plasma currents. In this paper, we investigate the effect of plasma elongation on the coupled dynamics of runaway generation and resistive diffusion of the electric field. We find that elongated plasmas are less likely to produce large runaway currents, partly due to the lower induced electric fields associated with larger plasmas, and partly due to direct shaping effects, which mainly lead to a reduction in the runaway avalanche gain. [ABSTRACT FROM AUTHOR]

The effect of the magnetic field gradient in the discharge channel of a Hall thruster on the ionization of the neutral gas and power deposition on the wall is studied through adopting the 2D-3V particle-in-cell (PIC) and Monte Carlo collisions (MCC) model. The research shows that by gradually increasing the magnetic field gradient while keeping the maximum magnetic intensity at the channel exit and the anode position unchanged, the ionization region moves towards the channel exit and then a second ionization region appears near the anode region. Meanwhile, power deposition on the walls decreases initially and then increases. To avoid power deposition on the walls produced by electrons and ions which are ionized in the second ionization region, the anode position is moved towards the channel exit as the magnetic field gradient is increased; when the anode position remains at the zero magnetic field position, power deposition on the walls decreases, which can effectively reduce the temperature and thermal load of the discharge channel. [ABSTRACT FROM AUTHOR]

The effect of discharge voltage on bi-Maxwellian electrons in the diffusion region of a double plasma device has been studied. The increase in discharge voltage enhances the flux of ionizing electrons to the diffusion region separated by a mesh grid. This energetic electron flux in turn affects other important parameters such as density, electron temperature, plasma potential and floating potential in the diffusion region. Furthermore, the dependence of density and temperature of both ionizing and plasma electrons on discharge voltage is investigated. The electron energy probability function obtained from probe data also indicates the bi-Maxwellian nature of electrons. [ABSTRACT FROM AUTHOR]

The distribution of temperature in an expanded thermal plasma jet is investigated by modified Langmuir probes. The validation of classical probe theory in the entire experimental chamber pressure range of 10-100 mbar is thoroughly established before the measurements. The average temperature of the plasma jet at the nozzle exit was also measured by calorimetric estimation of total heat loss from the plasma upstream of that point. A correlation is made using simple analytical expression in between the average temperature measured from the heat loss data and the centerline temperature at the nozzle exit measured by Langmuir probe. The profile parameter n for the radial distribution of temperature in a plasma jet is calculated for different operating current and gas flow rates. [ABSTRACT FROM AUTHOR]

AbstractThe analytic and numerical approaches to the investigation of the two-dimensional steady-state plasma flows are analyzed and compared with reference to a plasma accelerator channel in the presence of a longitudinal magnetic field. The present study continues a cycle of research into the plasma flows in the coaxial channels with the traditional azimuthal magnetic field. The additional longitudinal field opens new possibilities for controlling the dynamic processes and achieving the transonic flows. The research is based on the magnetohydrodynamic equations. [ABSTRACT FROM AUTHOR]