The application scopes of two different reductive perturbation methods to derive the Korteweg–de Vries (KdV) equation and coupled KdV (CKdV) equation in two-temperature-ion dusty plasma are given by using the particle-in-cell (PIC) numerical method in the present paper. It suggests that the reductive perturbation method (RPM) is valid if the amplitude of the CKdV solitary wave is small enough. However, for the KdV solitary wave, RPM is valid not only if the amplitude of the KdV solitary wave is small enough, but also if the nonlinear coefficient of the KdV equation is not tending to zero.

The relaxation of relativistic hot electron–positron plasma is investigated by incorporating the effect of non-zero photon mass, and a quadruple Beltrami (QB) relaxed state for the magnetic vector potential is derived. The QB state is a linear superposition of four single force-free fields and is characterized by four self-organized structures of different length scales. The analysis of QB states shows that for certain values of generalized helicities at lower relativistic temperatures, plasma shows diamagnetic behaviour. It is also noteworthy that the inclusion of non-zero photon mass naturally provides the possibility of multiscale structure formation in the relaxed state. In this scenario, one of the field structures is significantly larger than the Compton wavelength of photons, while the other three structures are on the scale of the electron skin depth. The potential implications of this QB state for astrophysical environments are also discussed.

Alpha particle confinement is one of the most demanding issues for stellarators. It now seems clear that it is possible to design optimized stellarators that confine the background plasma at near tokamak radial transport levels. Moreover, adequate collisionless alpha particle confinement is possible in the core of a highly optimized stellarator. Here, the collisional confinement of barely trapped alphas in an optimized stellarator is considered by accounting for the resonance due to the reversal in direction of the drift within a flux surface and investigating the sensitive role of magnetic shear in keeping this resonance close to the passing boundary in some nearly quasisymmetric stellarator configurations. The treatment relies on a narrow collisional boundary layer formulation that combines the responses of both these resonant pitch angle alphas and the remaining barely trapped alphas. A novel merged regime treatment leads to explicit expressions for the energy diffusivity for both superbanana plateau (or resonant plateau) and $\sqrt \nu$ transport in the large aspect ratio limit for a slowing down tail alpha distribution function, where $\nu$ is the effective pitch angle scattering collision frequency of the trapped alphas off the background ions. Depending on the details of the optimization scheme and the sign of the magnetic shear, modest magnetic shear can be used to reduce superbanana (or resonant) plateau transport to below the $\sqrt \nu$ transport level. In addition, a quasilinear equation retaining spatial diffusion is derived for a general alpha distribution function that allows the radial alpha transport to modify the distribution so it is no longer isotropic in velocity space.

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.

A collisionless plasma possesses a certain amount of ‘available energy’, which is that part of the thermal energy that can be converted into kinetic energy of plasma motion and electromagnetic fluctuations. In this paper we present a calculation of the available energy carried by trapped electrons in a slender non-omnigenous flux tube of plasma. This quantity is compared with gyrokinetic simulations of the nonlinear saturated radial energy flux resulting from turbulence driven by collisionless trapped-electron modes in various stellarators and a tokamak. The numerical calculation of available energy is fast and shows a strong correlation with the turbulent energy fluxes found in the gyrokinetic simulations. Indeed, the energy flux is found to be proportional to the available energy to the power of approximately $3/2$, which is what one would expect from a simple argument. We furthermore investigate how available energy is distributed across different bounce wells, and it is found that deeply trapped electrons typically contribute most to the available energy. Finally, we investigate the dependence of available energy on gradient strength, and we find important differences between weakly and strongly driven regimes for stellarators and tokamaks.

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.

How much does the cross-section of a toroidal magnetic field configuration tell us about its magnetohydrodynamic (MHD) stability? It is generally believed that positive triangularity (typically leading to bean-shaped cross-sections with their indentation on the inboard side in stellarators) contributes positively to MHD stability. In this paper, we explore the basis of this statement within a near-axis description for axisymmetric and quasisymmetric magnetic configurations. In agreement with the existing literature, we show that positive triangularity stabilises vertically elongated tokamaks. In quasisymmetric stellarators, the toroidal asymmetry of flux surfaces modifies this relation. The behaviour of stellarator-symmetric, quasisymmetric stellarators can still be described in terms of the shape of one of their up–down symmetric cross-sections. However, we show that for a sample of quasisymmetric configurations, the positive-bean-shaped cross-sections do not contribute positively to stability. Unlike in the axisymmetric case, we also learn that finite $\beta$ can improve stability even without magnetic shear.

Plasma turbulence plays a critical role in the transport of energy from large-scale magnetic fields and plasma flows to small scales, where the dissipated turbulent energy ultimately leads to heating of the plasma species. A major goal of the broader heliophysics community is to identify the physical mechanisms responsible for the dissipation of the turbulence and to quantify the consequent rate of plasma heating. One of the mechanisms proposed to damp turbulent fluctuations in weakly collisional space and astrophysical plasmas is electron Landau damping. The velocity-space signature of electron energization by Landau damping can be identified using the recently developed field–particle correlation technique. Here, we perform a suite of gyrokinetic turbulence simulations with ion plasma beta values $\beta _i = 0.01, 0.1, 1$ and $10$ and use the field–particle correlation technique to characterize the features of the velocity-space signatures of electron Landau damping in turbulent plasma conditions consistent with those observed in the solar wind and planetary magnetospheres. We identify the key features of the velocity-space signatures of electron Landau damping as a function of varying plasma $\beta _i$ to provide a critical framework for interpreting the results of field–particle correlation analysis of in situ spacecraft observations of plasma turbulence.

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.

The theory of terahertz (THz) wave emission at the oblique incidence of a focused s-polarized laser pulse on the boundary of a rarefied plasma is developed. The angular, spectral and energy characteristics of the THz signal as a function of the focal spot size and the incidence angle of laser radiation, as well as the plasma density, are investigated. It is shown that the THz radiation energy increases with a decrease in the laser pulse focal spot and has the maximum value when the tightly focused laser pulse is incident at the angle of total reflection on the plasma boundary.

Simulating plasmas in the Hall-magnetohydrodynamics (Hall-MHD) regime represents a valuable approach for the investigation of complex nonlinear dynamics developing in astrophysical frameworks and fusion machines. The Hall electric field is computationally very challenging as it involves the integration of an additional term, proportional to $\boldsymbol {\nabla } \times ((\boldsymbol {\nabla }\times \boldsymbol {B})\times \boldsymbol {B})$, in Faraday's induction law. The latter feeds back on the magnetic field $B$ at small scales (between the ion and electron inertial scales), requiring very high resolutions in both space and time to properly describe its dynamics. The computational advantage provided by the kinetic lattice Boltzmann (LB) approach is exploited here to develop a new code, the fast lattice-Boltzmann algorithm for MHD experiments (flame). The flame code integrates the plasma dynamics in lattice units coupling two kinetic schemes, one for the fluid protons (including the Lorentz force), the other to solve the induction equation describing the evolution of the magnetic field. Here, the newly developed algorithm is tested against an analytical wave-solution of the dissipative Hall-MHD equations, pointing out its stability and second-order convergence, over a wide range of the control parameters. Spectral properties of the simulated plasma are finally compared with those obtained from numerical solutions from the well-established pseudo-spectral code ghost. Furthermore, the LB simulations we present, varying the Hall parameter, highlight the transition from the MHD to the Hall-MHD regime, in excellent agreement with the magnetic field spectra measured in the solar wind.

We present a convergence study of the gyromoment (GM) approach, which is based on projecting the gyrokinetic distribution function onto a Hermite–Laguerre polynomial basis, focused on the cyclone base case (CBC) (Lin et al., Phys. Rev. Lett., vol. 83, no. 18, 1999, pp. 3645–3648) and Dimits shift (Dimits et al., Phys. Plasmas, vol. 7, no. 3, 2000, pp. 969–983) as benchmarks. We report that the GM approach converges more rapidly in capturing the nonlinear dynamics of the CBC than the continuum GENE code (Jenko et al., Phys. Plasmas, vol. 7, no. 5, 2000, pp. 1904–1910) when comparing the number of points representing the velocity space. Increasing the velocity dissipation improves the convergence properties of the GM approach, albeit yielding a slightly larger saturated heat flux. By varying the temperature equilibrium gradient, we show that the GM approach successfully reproduces the Dimits shift (Dimits et al., Phys. Plasmas, vol. 7, no. 3, 2000, pp. 969–983) and effectively captures its width, which is in contrast to the gyrofluid framework. In the collisional regime, the convergence properties of the GM approach improve and a good agreement with previous global particle-in-cell results on transport is obtained (Lin et al., Phys. Rev. Lett., vol. 83, no. 18, 1999, pp. 3645–3648). Finally, we report that the choice of collision model has a minimal impact both on the ion temperature gradient growth rate and on the nonlinear saturated heat flux, at tokamak-relevant collisionality.

It has long been known that the equilibrium of an electron plasma in a stellarator possesses unique properties when compared with other geometries. Previous analyses, both numerical and analytical, as well as experimental results, have indicated that these equilibria are minimum-energy states. Here, it is definitively shown that the equilibrium of an electron plasma on magnetic surfaces with finite rotational transform minimises a constrained physical energy, which has a thermal and an electrostatic contribution. As such, these equilibria are established to be macroscopically stable to all perturbations that do not change the flux-surface average of the density and do not decrease the entropy of the plasma, under the definition of ‘formal stability’ established by Holm et al. (Phys. Rep., vol. 123, no. 1, 1985, 1–116).

Fishbone bursts have been observed to strongly correlate to internal transport barrier (ITB) formation in a number of tokamak devices. A simple model incorporating the fishbone dynamics and ion pressure gradient evolution is proposed in order to investigate the key physics parameters assisting the triggering of ITB. The time evolution of fishbone is described by the well-known predator–prey model. For each burst cycle, the energetic particles (EPs) resonantly interact with fishbone and are radially expelled from inner region leading to a radial current. A compensating bulk plasma return current and, hence, poloidal flow can be induced if the fishbone cycle frequency is greater than the poloidal flow damping rate. When the shear of the poloidal flow exceeds a critical value, the turbulent fluctuations are suppressed and the bulk ion pressure gradient transits to the high-confinement state. It is shown that this process is only sensitive to the deposition rate of the trapped EPs within the $q=1$ surface, but not sensitive to other parameters. A quantitative formula for the shearing rate of poloidal flow induced by fishbone bursts is derived and verified numerically.

All-optical Compton sources combine laser-wakefield accelerators and intense scattering pulses to generate ultrashort bursts of backscattered radiation. The scattering pulse plays the role of a small-period undulator (${\sim }1\,\mathrm {\mu }{\rm m}$) in which relativistic electrons oscillate and emit X-ray radiation. To date, most of the working laser-plasma accelerators operate preferably at energies of a few hundreds of megaelectronvolts and the Compton sources developed so far produce radiation in the range from hundreds of kiloelectronvolts to a few megaelectronvolts. However, for such applications as medical imaging and tomography the relevant energy range is 10–100 keV. In this article, we discuss different scattering geometries for the generation of X-rays in this range. Through numerical simulations, we study the influence of electron beam parameters on the backscattered photons. We find that the spectral bandwidth remains constant for beams of the same emittance regardless of the scattering geometry. A shallow interaction angle of $30^{\circ }$ or less seems particularly promising for imaging applications given parameters of existing laser-plasma accelerators. Finally, we discuss the influence of the radiation properties for potential applications in medical imaging and non-destructive testing.

Buffer-gas traps (BGTs) use inelastic interactions with nitrogen molecules to capture positrons from a continuous beam. These devices are invaluable for high-resolution studies of matter–antimatter interactions, antihydrogen research and positronium laser spectroscopy. We present a new project with the goal of producing a non-neutral plasma containing ${\sim }10^8$ low-energy positrons by installing a BGT on the NEPOMUC (NEutron induced POsitron source MUniCh) high-intensity positron beam. Details of the BGT are outlined and results are presented from experiments in which an electron beam, with a similar intensity and energy spread to the remoderated NEPOMUC beam, was used to create pulses of non-neutral electron plasma. The device is a vital component of the APEX (A Positron Electron eXperiment) project, which aims to create a low-temperature electron–positron pair plasma.

In this work, we revisit the linear gyro-kinetic theory of geodesic acoustic modes (GAMs) and derive a general dispersion relation for an arbitrary equilibrium distribution function of ions. A bi-Maxwellian distribution of ions is then used to study the effects of ion temperature anisotropy on GAM frequency and growth rate. We find that ion temperature anisotropy yields sensible modifications to both the GAM frequency and growth rate as both tend to increase with anisotropy and these results are strongly affected by the electron to ion temperature ratio.

This work reports on the development and numerical implementation of the linear electromagnetic gyrokinetic (GK) model in a tokamak flux-tube geometry using a moment approach based on the expansion of the perturbed distribution function on a velocity-space Hermite–Laguerre polynomials basis. A hierarchy of equations of the expansion coefficients, referred to as the gyro-moments (GMs), is derived. We verify the numerical implementation of the GM hierarchy in the collisionless limit by performing a comparison with the continuum GK code GENE, recovering the linear properties of the ion temperature gradient, trapped electron, kinetic ballooning and microtearing modes, as well as the collisionless damping of zonal flows. An analysis of the distribution functions and ballooning eigenmode structures is performed. The present investigation reveals the ability of the GM approach to describe fine velocity-space-scale structures appearing near the trapped and passing boundary and kinetic effects associated with parallel and perpendicular particle drifts. In addition, the effects of collisions are studied using advanced collision operators, including the GK Coulomb collision operator. The main findings are that the number of GMs necessary for convergence decreases with plasma collisionality and is lower for pressure gradient-driven modes, such as in H-mode pedestal regions, compared with instabilities driven by trapped particles and magnetic gradient drifts often found in the core. The accuracy of approximations often used to model collisions (relative to the GK Coulomb operator) is studied in the case of trapped electron modes, showing differences between collision operator models that increase with collisionality and electron temperature gradient, consistent with the results of Pan et al. (Phys. Rev. E, vol. 103, 2021, L051202). Such differences are not observed in other edge microinstabilities, such as microtearing modes. The importance of a proper collision operator model is also confirmed by analysing the collisional damping of geodesic acoustic modes and zonal flows.

Starting from the equations of collisionless linear gyrokinetics for magnetised plasmas with an imposed inhomogeneous magnetic field, we present the first known analytical, closed-form solution for the resulting velocity-space integrals in the presence of resonances due to both parallel streaming and constant magnetic drifts. These integrals are written in terms of the well-known plasma dispersion function (Faddeeva & Terent'ev, Tables of Values of the Function $w(z)=\exp (-z^2)(1+2i/\sqrt {\pi }\int _0^z \exp (t^2) \,\mathrm {d} t)$ for Complex Argument, 1954. Gostekhizdat. English translation: Pergamon Press, 1961; Fried & Conte, The Plasma Dispersion Function, 1961. Academic Press), rendering the subsequent expressions simpler to treat analytically and more efficient to compute numerically. We demonstrate that our results converge to the well-known ones in the straight-magnetic-field and two-dimensional limits, and show good agreement with the numerical solver by Gürcan (J. Comput. Phys., vol. 269, 2014, p. 156). By way of example, we calculate the exact dispersion relation for a simple electrostatic, ion-temperature-gradient-driven instability, and compare it with approximate kinetic and fluid models.