Landau damping is one of the cornerstones of plasma physics. Based on the initial-value approach adopted by Landau in his original derivation of Landau damping, we examine the solutions of the linear Vlasov–Poisson system for different equilibrium distribution functions $f_0(v)$, going beyond the traditional focus on the root with largest imaginary part and investigating the full set of roots that the dispersion relation of the system generally admits. Specifically, we provide analytical insights into the number and the structure of the roots for entire and meromorphic functions $f_0(v)$, such as Maxwellian and $\kappa$ distributions, we discuss the potential issues related to the redefinition of $\partial{f}_0/\partial{v}$ as a complex variable function and we show how different sigmoids affect the root structure associated with non-meromorphic cut-off distribution functions. Finally, based on the comparison of the several root structures considered, we wonder if the multiple roots might hint at a deeper understanding of the Landau damping phenomenon.

The available energy of a plasma is defined as the maximum amount by which the plasma energy can be lowered by volume-preserving rearrangements in phase space, so-called Gardner restacking. A general expression is derived for the available energy of a nearly homogeneous plasma and is shown to be closely related to the Helmholtz free energy, which it can never exceed. A number of explicit examples are given.

It is known that a nonlinear Schrödinger equation describes the self-modulation of a large amplitude circularly polarized wave in relativistic electron–positron plasmas in the weakly and strongly magnetized limits. Here, we show that such an equation can be written as a modified second Painlevé equation, producing accelerated propagating wave solutions for those nonlinear plasmas. This solution even allows the plasma wave to reverse its direction of propagation. The acceleration parameter depends on the plasma magnetization. This accelerating solution is different to the usual soliton solution propagating at constant speed.

The heating rate of plasma electrons induced by external fields or other processes can be used as an experimental tool to measure fundamental plasma properties such as electrical conductivity or electron–ion collision rates. We have developed a technique that can measure electron heating rates in ultracold neutral plasmas (UNPs) with $\sim 10\,\%$ precision while simultaneously referencing the measurement to a calibrated amount of heating. This technique uses a sequence of applied electric fields in four sections: to control the ratio of electrons to ions in the UNP; to provide a time for the application of fields that cause electron heating and subsequent thermalization of the electrons after the application of those fields; to extract electrons from the UNP using a method sensitive to electron temperature that allows the measurement of electron heating; and to extract the remaining electrons to measure the total electron (and therefore ion) number. The primary signal used to measure the heating rate is the measurement of the number of electrons that escape in the third section of the experiment as a larger number of escaping electrons indicates a larger amount of heating. We illustrate the use of this technique by measuring electron heating caused by high-frequency radiofrequency (RF) fields. In addition to the main technique, several subtechniques to calibrate the electron temperature, electron density, amount of heating and applied RF field amplitude were developed as well.

A conducting cylinder with a uniform magnetic field along its axis and radial temperature gradient is considered at the stationary state. At large temperature gradients the azimuthal Hall electrical current creates an axial magnetic field whose strength may be comparable with the original one. It is shown that the magnetic field, generated by the azimuthal Hall current, leads to the decrease of a magnetic field originated by external sources, and this suppression increases with an increase of the electromotive force, connected with thermodiffusion. Obtained results can help to investigate the influence of the Hall current on the coupled magnetothermal evolution of magnetic and electric fields in neutron stars, white dwarfs and, possibly, in laboratory facilities.

Methods for reducing the radius, temperature and space charge of a non-neutral plasma are usually reported for conditions which approximate an ideal Penning Malmberg trap. Here, we show that (i) similar methods are still effective under surprisingly adverse circumstances: we perform strong drive regime (SDR) compression and SDREVC in a strong magnetic mirror field using only 3 out of 4 rotating wall petals. In addition, we demonstrate (ii) an alternative to SDREVC, using e-kick instead of evaporative cooling (EVC) and (iii) an upper limit for how much plasma can be cooled to $T<20\ \mathrm {K}$ using EVC. This limit depends on the space charge, not on the number of particles or the plasma density.

Tokamak start-up is strongly dependent on the state of the initial plasma formed during plasma breakdown. To acquire a better understanding of the process and to estimate the influence of the impurity of beryllium on the ohmic heating tokamak start-up process, one-dimensional particle-in-cell coupled with a Monte Carlo collision method has been developed. The main aim is to investigate the plasma performance under various amounts of beryllium with different discharge parameters. Tokamak breakdown with the impurity of beryllium in the ohmic heating strategy has been simulated. The simulation results show that with the impurity of beryllium, the increase of plasma density is suppressed compared with the case without beryllium. The breakdown time is delayed by the impurity. Moreover, the successful breakdown has a much higher requirement on discharge parameters with a low electric field operational scenario, since in the low electric field discharge the influence of beryllium impurity is greater. As the plasma density increases, the effect of beryllium impurity on plasma becomes more critical. It indicates that impurities cannot be neglected in the high plasma density.

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.

We present a novel method for numerically finding quasi-isodynamic stellarator magnetic fields with excellent fast-particle confinement and extremely small neoclassical transport. The method works particularly well in configurations with only one field period. We examine the properties of these newfound quasi-isodynamic configurations, including their transport coefficients, particle confinement and available energy for trapped-electron-instability-driven turbulence, as well as the degree to which they change when a finite pressure profile is added. We finally discuss the differences between the magnetic axes of the optimized solutions and their respective initial conditions, and conclude with the prospects for future quasi-isodynamic optimization.

In the classical treatment the screening phenomenon of electric fields in a plasma is solely caused by charged particles, i.e. electrons and ions. In contrast, the present consideration focuses on the role of neutrals in a situation when the correlations between the charged and neutral components of the plasma medium turn rather significant. The consideration is entirely based on the renormalization procedure for interparticle interactions, which takes into account collective events in the generalized Poisson–Boltzmann equation relating the true microscopic potentials with their effective macroscopic counterparts. A meaningful approach is proposed to analytically derive the screening length from an appropriate assumption on the asymptotic behaviour of the macroscopic potential at large interparticle separations. It is clearly demonstrated that the neutral component really affects the screening length when the plasma reaches states corresponding to warm dense matter conditions. It is also shown that, at certain critical values of the plasma parameters, the character of the screening changes from exponential to oscillatory decay.

We present a theoretical study of two- and three-dimensional massless Dirac one-component plasmas embedded in a constant uniform magnetic field. We determine the wavefunctions and Landau energy levels of a massless Dirac fermion in a constant magnetic field. On this basis we consider magnetism of Fermi fluids of massless charged particles. We show that such a three-dimensional Dirac plasma consisting of fermions with the same helicity has its own magnetic moment. We also consider the limit of strong magnetic fields and investigate the De Haas–van Alphen effect. We derive the Kubo formula for the electrical conductivity tensor of massless Dirac plasmas and consider the Shubnikov–de Haas effect. In addition, we propose a model of the static conductivity tensor and employ the matrix version of the classical method of moments to derive a Drude-like formula for the dynamic conductivity tensor for massless Dirac plasmas. We find that the electrical conductivity tensor for Dirac fermions with the right helicity is not isotropic in the plane perpendicular to the magnetic field.

Simulations of high-energy density physics often need non-local thermodynamic equilibrium opacity data. These data, however, are expensive to produce at relatively low fidelity. It is even more so at high fidelity such that the opacity calculations can contribute 95 % of the total computation time. This proportion can even reach large proportions. Neural networks can be used to replace the standard calculations of low-fidelity data, and the neural networks can be trained to reproduce artificial, high-fidelity opacity spectra. In this work, it is demonstrated that a novel neural network architecture trained to reproduce high-fidelity krypton spectra through transfer learning can be used in simulations. Further, it is demonstrated that this can be done while achieving a relative per cent error of the peak radiative temperature of the hohlraum of approximately 1 % to 4 % while achieving a 19.4$\times$ speed up.

Weakly collisional plasmas are subject to nonlinear relaxation processes, which can operate at rates much faster than the particle collision frequencies. This causes the plasma to respond like a magnetised fluid despite having long particle mean free paths. In this Letter the effective collisional mechanisms are modelled in the plasma kinetic equation to produce density, pressure and magnetic-field responses to compare with spacecraft measurements of the solar wind compressive fluctuations at 1 AU. This enables a measurement of the effective mean free path of the solar wind protons, found to be ${\approx }4 \times 10^{5}$ km, which is approximately $10^{3}$ times shorter than the collisional mean free path. These measurements are shown to support the effective fluid behaviour of the solar wind at scales above the proton gyroradius and demonstrate that effective collision processes alter the thermodynamics and transport of weakly collisional plasmas.

In this paper, effects of discharge parameters and modulation frequency on the signal of laser-induced fluorescence measurements of ion velocity distribution functions are investigated in the LIF Test Source. A maximum modulation frequency is found for each given set of parameters, beyond which the signal gradually declines. Meanwhile, this maximum modulation frequency occurred consistently at ~1/10 of the theoretical frequency limit and photon counts received by a photomultiplier tube, which indicates that as modulation frequency and the associated per-pulse-excitation-event count decrease, the transition from the macroscopic statistical signal to the microscopic probabilistic signal is a gradual process.

In the presence of a stationary gravitomagnetic field, a weakly rotating self-gravitating fluid relaxes into equilibrium flow configurations which admit both large- and small-scale structures. Unlike the traditional Beltrami equilibria in fluid, the equilibrium states in a rotating self-gravitating fluid in a gravitomagnetic field have structure similar to that of double curl Beltrami equilibria in plasma where the generalized vortical lines are aligned with the flow field. Different equilibrium flow configurations in the rotating fluid can be distinguished by the ratio between total energy and helicity. However, these fluid equilibria do not exhibit diamagnetic behaviours as observed in multi-species plasma equilibria.

We show that non-relativistic scaling of the collisionless Vlasov–Maxwell system implies the existence of a formal invariant slow manifold in the infinite-dimensional Vlasov–Maxwell phase space. Vlasov–Maxwell dynamics restricted to the slow manifold recovers the Vlasov–Poisson and Vlasov–Darwin models as low-order approximations, and provides higher-order corrections to the Vlasov–Darwin model more generally. The slow manifold may be interpreted to all orders in perturbation theory as a collection of formal Vlasov–Maxwell solutions that do not excite light waves, and are therefore ‘dark’. We provide a heuristic lower bound for the time interval over which Vlasov–Maxwell solutions initialized optimally near the slow manifold remain dark. We also show how the dynamics on the slow manifold naturally inherits a Hamiltonian structure from the underlying system. After expressing this structure in a simple form, we use it to identify a manifestly Hamiltonian correction to the Vlasov–Darwin model. The derivation of higher-order terms is reduced to computing the corrections of the system Hamiltonian restricted to the slow manifold.

The prominence of nulls in reconnection theory is due to the expected singular current density and the indeterminacy of field lines at a magnetic null. Electron inertia changes the implications of both features. Magnetic field lines are distinguishable only when their distance of closest approach exceeds a distance $\varDelta _d$. Electron inertia ensures $\varDelta _d\gtrsim c/\omega _{pe}$. The lines that lie within a magnetic flux tube of radius $\varDelta _d$ at the place where the field strength $B$ is strongest are fundamentally indistinguishable. If the tube, somewhere along its length, encloses a point where $B=0$ vanishes, then distinguishable lines come no closer to the null than $\approx (a^2c/\omega _{pe})^{1/3}$, where $a$ is a characteristic spatial scale of the magnetic field. The behaviour of the magnetic field lines in the presence of nulls is studied for a dipole embedded in a spatially constant magnetic field. In addition to the implications of distinguishability, a constraint on the current density at a null is obtained, and the time required for thin current sheets to arise is derived.

A plasma gun for forming a plasma stream in the open magnetic mirror trap with additional helicoidal field SMOLA is described. The plasma gun is an axisymmetric system with a planar circular hot cathode based on lanthanum hexaboride and a hollow copper anode. The two planar coils are located around the plasma source and create a magnetic field of up to 200 mT. The magnetic field forms the magnetron configuration of the discharge and provides a radial electric insulation. The source typically operates with a discharge current of up to 350 A in hydrogen. Plasma parameters in the SMOLA device are Ti ~ 5 eV, Te ~ 5–40 eV and ni ~ (0.1–1)  × 1019 m−3. Helium plasma can also be created. The plasma properties depend on the whole group of initial technical parameters: the cathode temperature, the feeding gas flow, the anode-cathode supply voltage and the magnitude of the cathode magnetic insulation.

We present experimental data providing evidence for the formation of transient (${\sim }20\ \mathrm {\mu }\textrm {s}$) plasmas that are simultaneously weakly magnetized (i.e. Hall magnetization parameter $\omega \tau > 1$) and dominated by thermal pressure (i.e. ratio of thermal-to-magnetic pressure $\beta > 1$). Particle collisional mean free paths are an appreciable fraction of the overall system size. These plasmas are formed via the head-on merging of two plasmas launched by magnetized coaxial guns. The ratio $\lambda _{\textrm {gun}}=\mu _0 I_{\textrm {gun}}/\psi _{\textrm {gun}}$ of gun current $I_{\textrm {gun}}$ to applied magnetic flux $\psi _{\textrm {gun}}$ is an experimental knob for exploring the parameter space of $\beta$ and $\omega \tau$. These experiments were conducted on the Big Red Ball at the Wisconsin Plasma Physics Laboratory. The transient formation of such plasmas can potentially open up new regimes for the laboratory study of weakly collisional, magnetized, high-$\beta$ plasma physics; processes relevant to astrophysical objects and phenomena; and novel magnetized plasma targets for magneto-inertial fusion.