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This theme issue collects together papers summarising the conceptual design of the Spherical Tokamak for Energy Production (STEP). In 2019, the UK government funded the first design stages of a prototype fusion powerplant based on a compact toroidal geometry, called STEP. The primary technical aims of STEP are to produce net energy, to be self-sufficient in tritium fuel and to demonstrate a maintenance regime that would extrapolate to appropriate availability for commercial powerplants. After 5 years and over 1000 person-years of detailed scientific and engineering conceptual design, this theme issue acts as a compendium of the current design basis for STEP, noting that this is a snapshot in time and that the design will continue to evolve. This article is part of the theme issue 'Delivering Fusion Energy - The Spherical Tokamak for Energy Production (STEP)'.

It is shown that the magnetic-field coils of a stellarator can, at least in principle, be substantially simplified by the use of permanent magnets. Such magnets cannot create toroidal magnetic flux, but they can be used to shape the plasma and thus to create poloidal flux and rotational transform, thereby easing the requirements on the magnetic-field coils. As an example, a quasiaxisymmetric stellarator configuration is constructed with only 8 circular coils (all identical) and permanent magnets.

The theory of tokamak stability to nonlinear "ballooning" displacements of elliptical magnetic flux tubes is presented. Above a critical pressure profile the energy stored in the plasma may be lowered by finite (but not infinitesimal) displacements of such tubes (metastability). Above a higher pressure profile, the linear stability boundary, such tubes are linearly and nonlinearly unstable. The predicted saturated flux tube displacement can be of the order of the pressure gradient scale length. Plasma transport from these displaced flux tubes may explain the rapid loss of confinement in some experiments.

The eruption of multiple flux tubes in a magnetized plasma is proposed as a mechanism for explosive release of energy in plasmas. A significant fraction of the linearly stable isolated flux tubes are shown to be metastable in a box model magnetized atmosphere in which ends of the field lines are embedded in conducting walls. The energy released by destabilizing such field lines can be a large proportion of the gravitational energy stored in the system. This energy can be released in a fast dynamical time.

This paper presents a complete theoretical framework for studying turbulence and transport in rapidly rotating tokamak plasmas. The fundamental scale separations present in plasma turbulence are codified as an asymptotic expansion in the ratio ε = ρi/α of the gyroradius to the equilibrium scale length. Proceeding order by order in this expansion, a set of coupled multiscale equations is developed. They describe an instantaneous equilibrium, the fluctuations driven by gradients in the equilibrium quantities, and the transport-timescale evolution of mean profiles of these quantities driven by the interplay between the equilibrium and the fluctuations. The equilibrium distribution functions are local Maxwellians with each flux surface rotating toroidally as a rigid body. The magnetic equilibrium is obtained from the generalized Grad-Shafranov equation for a rotating plasma, determining the magnetic flux function from the mean pressure and velocity profiles of the plasma. The slow (resistive-timescale) evolution of the magnetic field is given by an evolution equation for the safety factor q. Large-scale deviations of the distribution function from a Maxwellian are given by neoclassical theory. The fluctuations are determined by the 'high-flow' gyrokinetic equation, from which we derive the governing principle for gyrokinetic turbulence in tokamaks: the conservation and local (in space) cascade of the free energy of the fluctuations (i.e. there is no turbulence spreading). Transport equations for the evolution of the mean density, temperature and flow velocity profiles are derived. These transport equations show how the neoclassical and fluctuating corrections to the equilibrium Maxwellian act back upon the mean profiles through fluxes and heating. The energy and entropy conservation laws for the mean profiles are derived from the transport equations. Total energy, thermal, kinetic and magnetic, is conserved and there is no net turbulent heating. Entropy is produced by the action of fluxes flattening gradients, Ohmic heating and the equilibration of interspecies temperature differences. This equilibration is found to include both turbulent and collisional contributions. Finally, this framework is condensed, in the low-Mach-number limit, to a more concise set of equations suitable for numerical implementation.

Beam emission spectroscopy (BES) measurements of ion-scale density fluctuations in the MAST tokamak are used to show that the turbulence correlation time, the drift time associated with ion temperature or density gradients, the particle (ion) streaming time along the magnetic field, and the magnetic drift time are consistently comparable, suggesting a "critically balanced" turbulence determined by the local equilibrium. The resulting scalings of the poloidal and radial correlation lengths are derived and tested. The nonlinear time inferred from the density fluctuations is longer than the other times; its ratio to the correlation time scales as ν(*i)(-0.8 ± 0.1), where ν(*i) = ion  collision rate/streaming rate. This is consistent with turbulent decorrelation being controlled by a zonal component, invisible to the BES, with an amplitude exceeding those of the drift waves by ∼ ν(*i)(-0.8).

Sheared toroidal flows can cause bifurcations to zero-turbulent-transport states in tokamak plasmas. The maximum temperature gradients that can be reached are limited by subcritical turbulence driven by the parallel velocity gradient. Here it is shown that q/ϵ (magnetic field pitch/inverse aspect ratio) is a critical control parameter for sheared tokamak turbulence. By reducing q/ϵ, far higher temperature gradients can be achieved without triggering turbulence, in some instances comparable to those found experimentally in transport barriers. The zero-turbulence manifold is mapped out, in the zero-magnetic-shear limit, over the parameter space (γ(E), q/ϵ, R/L(T)), where γ(E) is the perpendicular flow shear and R/L(T) is the normalized inverse temperature gradient scale. The extent to which it can be constructed from linear theory is discussed.

Nonlinear gyrokinetic simulations are conducted to investigate turbulent transport in tokamak plasmas with rotational shear. At sufficiently large flow shears, linear instabilities are suppressed, but transiently growing modes drive subcritical turbulence whose amplitude increases with flow shear. This leads to a local minimum in the heat flux, indicating an optimal E×B shear value for plasma confinement. Local maxima in the momentum fluxes are observed, implying the possibility of bifurcations in the E×B shear. The critical temperature gradient for the onset of turbulence increases with flow shear at low flow shears; at higher flow shears, the dependence of heat flux on temperature gradient becomes less stiff. The turbulent Prandtl number is found to be largely independent of temperature and flow gradients, with a value close to unity.

The effect of momentum injection on the temperature gradient in tokamak plasmas is studied. A plausible scenario for transitions to reduced transport regimes is proposed. The transition happens when there is sufficient momentum input so that the velocity shear can suppress or reduce the turbulence. However, it is possible to drive too much velocity shear and rekindle the turbulent transport. The optimal level of momentum injection is determined. The reduction in transport is maximized in the regions of low or zero magnetic shear.

The effect of flow shear on turbulent transport in tokamaks is studied numerically in the experimentally relevant limit of zero magnetic shear. It is found that the plasma is linearly stable for all nonzero flow shear values, but that subcritical turbulence can be sustained nonlinearly at a wide range of temperature gradients. Flow shear increases the nonlinear temperature gradient threshold for turbulence but also increases the sensitivity of the heat flux to changes in the temperature gradient, except over a small range near the threshold where the sensitivity is decreased. A bifurcation in the equilibrium gradients is found: for a given input of heat, it is possible, by varying the applied torque, to trigger a transition to significantly higher temperature and flow gradients.

A detailed numerical study of magnetic reconnection in resistive MHD for very large, previously inaccessible, Lundquist numbers (10(4) 10(4).

Electrostatic turbulence in weakly collisional, magnetized plasma can be interpreted as a cascade of entropy in phase space, which is proposed as a universal mechanism for dissipation of energy in magnetized plasma turbulence. When the nonlinear decorrelation time at the scale of the thermal Larmor radius is shorter than the collision time, a broad spectrum of fluctuations at sub-Larmor scales is numerically found in velocity and position space, with theoretically predicted scalings. The results are important because they identify what is probably a universal Kolmogorov-like regime for kinetic turbulence; and because any physical process that produces fluctuations of the gyrophase-independent part of the distribution function may, via the entropy cascade, result in turbulent heating at a rate that increases with the fluctuation amplitude, but is independent of the collision frequency.

The feasibility of a mean-field dynamo in nonhelical turbulence with a superimposed linear shear is studied numerically in elongated shearing boxes. Exponential growth of the magnetic field at scales much larger than the outer scale of the turbulence is found. The characteristic scale of the field is lB proportional S(-1/2) and the growth rate is gamma proportional S, where S is the shearing rate. This newly discovered shear dynamo effect potentially represents a very generic mechanism for generating large-scale magnetic fields in a broad class of astrophysical systems with spatially coherent mean flows.

In turbulent high-beta astrophysical plasmas (exemplified by the galaxy cluster plasmas), pressure-anisotropy-driven firehose and mirror fluctuations grow nonlinearly to large amplitudes, deltaB/B approximately 1, on a time scale comparable to the turnover time of the turbulent motions. The principle of their nonlinear evolution is to generate secularly growing small-scale magnetic fluctuations that on average cancel the temporal change in the large-scale magnetic field responsible for the pressure anisotropies. The presence of small-scale magnetic fluctuations may dramatically affect the transport properties and, thereby, the large-scale dynamics of the high-beta astrophysical plasmas.

This Letter presents the first ab initio, fully electromagnetic, kinetic simulations of magnetized turbulence in a homogeneous, weakly collisional plasma at the scale of the ion Larmor radius (ion gyroscale). Magnetic- and electric-field energy spectra show a break at the ion gyroscale; the spectral slopes are consistent with scaling predictions for critically balanced turbulence of Alfvén waves above the ion gyroscale (spectral index -5/3) and of kinetic Alfvén waves below the ion gyroscale (spectral indices of -7/3 for magnetic and -1/3 for electric fluctuations). This behavior is also qualitatively consistent with in situ measurements of turbulence in the solar wind. Our findings support the hypothesis that the frequencies of turbulent fluctuations in the solar wind remain well below the ion cyclotron frequency both above and below the ion gyroscale.

Direct numerical simulations of incompressible nonhelical randomly forced MHD turbulence are used to demonstrate for the first time that the fluctuation dynamo exists in the limit of large magnetic Reynolds number Rm>>1 and small magnetic Prandtl number Pm<<1. The dependence of the critical Rmc for dynamo on the hydrodynamic Reynolds number Re is obtained for 1 less than or similar Re less than or similar 6700. In the limit Pm<<1, Rmc is about 3 times larger than for the previously well-established dynamo at large and moderate Prandtl numbers: Rmc less than or similar 200 for Re greater than or similar 6000 compared to Rmc approximately 60 for Pm>or=1. It is not yet possible to determine numerically whether the growth rate of the magnetic energy is proportional, Rm1/2 in the limit Rm-->infinity, as it should be if the dynamo is driven by the inertial-range motions at the resistive scale.

High beta poloidal tokamaks can confine plasma pressures an order of magnitude higher than their low beta poloidal counterparts. The theoretical stability of these high beta poloidal magnetohydrodynamics equilibria was left unresolved for many years. Using modern computational tools, such configurations are now found stable to Mercier, resistive and high-n (ideal and resistive) ballooning criteria as well as fixed and free-boundary modes for a wide range of current density profiles in the framework of a low field large-aspect-ratio machine.

We study the nonlinear evolution of the resistive tearing mode in slab geometry in two dimensions. We show that, in the strongly driven regime (large delta'), a collapse of the X point occurs once the island width exceeds a certain critical value approximately 1/delta'. A current sheet is formed and the reconnection is exponential in time with a growth rate proportional eta(1/2), where eta is the resistivity. If the aspect ratio of the current sheet is sufficiently large, the sheet can itself become tearing-mode unstable, giving rise to secondary islands, which then coalesce with the original island. The saturated state depends on the value of delta'. For small delta', the saturation amplitude is proportional delta' and quantitatively agrees with the theoretical prediction. If delta' is large enough for the X-point collapse to have occurred, the saturation amplitude increases noticeably and becomes independent of delta'.

This Letter provides information on the spatial and temporal structure of periodic eruptions observed in magnetically confined laboratory fusion plasmas, called edge-localized modes (ELMs), and highlights similarities with solar eruptions. Taken together, the observations presented in this Letter provide strong evidence for ELMs being associated with a filamentlike structure. These filaments are extended along a field line, are generated on a 100 micros time scale, erupt from the outboard side, and connect back into the plasma. Such structures are predicted by a theoretical model based on the "ballooning" instability, developed for both solar and tokamak applications.

Flux tubes confined in tokamaks are observed to erupt explosively in some plasma disruptions and edge localized modes. Similar eruptions occur in astrophysical plasmas, for example, in solar flares and magnetospheric substorms. A single unifying nonlinear evolution equation describing such behavior in both astrophysical and tokamak plasmas is derived. This theory predicts that flux tubes rise explosively, narrow, and twist to pass through overlying magnetic field lines without reconnection.

We consider the problem of incompressible, forced, nonhelical, homogeneous, and isotropic MHD turbulence with no mean magnetic field and large magnetic Prandtl number. This type of MHD turbulence is the end state of the turbulent dynamo, which generates folded fields with small-scale direction reversals. We propose a model in which saturation is achieved as a result of the velocity statistics becoming anisotropic with respect to the local direction of the magnetic folds. The model combines the effects of weakened stretching and quasi-two-dimensional mixing and produces magnetic-energy spectra in remarkable agreement with numerical results at least in the case of a one-scale flow. We conjecture that the statistics seen in numerical simulations could be explained as a superposition of these folded fields and Alfvén-like waves that propagate along the folds.

Two green fluorescent protein (Gfp) fusion vectors were constructed for use in Mycobacterium spp. The first plasmid facilitates quantification of mycobacterial promoter activity. The second vector permits construction of translational fusions of mycobacterial proteins to Gfp in order to study subcellular localization including protein secretion. Using this translational fusion construct, we verify that a Gfp fusion to the putative secreted M. tuberculosis protein ChoD is translocated to the extracellular milieu when cloned and expressed in Mycobacterium smegmatis.

In order to identify genes involved in LPS biosynthesis we isolated random mutants generated by transposon insertion in Francisella novicida. The resulting mutant bank yielded mutants with three distinct LPS phenotypes, and three representative mutants were chosen for further study. One mutant that had short O-antigen chains was sensitive to serum; this mutant and one other were more sensitive to killing by deoxycholate than control strains. The third mutant was resistant to deoxycholate killing but slightly sensitive to serum. The three mutants varied in their ability to grow in macrophages. The DNA sequences interrupted by the transposon in two of the three mutants showed similarity to known LPS biosynthetic genes at the deduced amino acid level.

The valAB locus of Francisella novicida has previously been found to be highly similar at the deduced amino acid level to msbA lpxK of Escherichia coli. Both ValA and MsbA are members of the superfamily of ABC transporters, and they appear to have similar functions. In this study we describe the isolation of a temperature-sensitive valAB locus. DNA sequence analysis indicates that the only changes to the ValAB deduced amino acid sequence are changes of S453 to an F and T458 to an I in ValA. E. coli strains defective in msbA and expressing temperature-sensitive ValA rapidly ceased growth when shifted from a permissive temperature to a restrictive temperature. After 1 h at the restrictive temperature, cells were much more sensitive to deoxycholate treatment. To test the hypothesis that ValA is responsible for the transport or assembly of lipopolysaccharide, we introduced gseA, a Kdo (3-deoxy-D-manno-octulosonic acid) transferase from Chlamydia trachomatis, into a strain with a temperature-sensitive valA allele and a nonfunctional msbA locus. These recombinants were defective in cell surface expression of the chlamydial genus-specific epitope within 15 min of a shift to the nonpermissive temperature. Also, there was enhanced association of the epitope with the inner membrane after a shift to the nonpermissive temperature. Thus, we propose that ValA is involved in the transport of lipopolysaccharide to the outer membrane.

We have previously shown that when cultured in vitro, peritoneal rat macrophages infected with Francisella novicida spontaneously release nitric oxide in sufficient quantities to inhibit bacterial growth. However, it is not known whether F. novicida can have a similar antimicrobial effect in vivo. Here we show that a co-infection of F. novicida with Francisella tularensis can suppress the number of F. tularensis cells in rat spleens by as much as 100-fold.

Many microbial pathogens, such as Mycobacterium spp. and Salmonella spp., use macrophage intracellular growth or antigenic variation as mechanisms for avoiding the host immune system. In this work we present evidence to show that the intracellular pathogen Francisella tularensis uses phase variation to alter antigenicity and the host macrophage nitric oxide response simultaneously, thereby modulating its intracellular growth. The lipopolysaccharide (LPS) and lipid A of F. tularensis fails to stimulate production of significant levels of nitric oxide (NO) by rat macrophages. However, spontaneous variants of F. tularensis expressing an antigenically distinct LPS induce rat macrophages to produce increased levels of NO, thereby suppressing microbial intramacrophage growth. Similarly, lipid A isolated from these variants stimulates increased levels of NO production. A reverse phase shift can occur, which returns the LPS to the original antigenic form, reduces NO production, and restores intramacrophage growth. These findings represent the first demonstration of a phase-variation phenomenon which modulates intracellular growth and an innate immune response. Furthermore, these results suggest that a microbial pathogen can exploit macrophage NO production for its own benefit, perhaps by prolonging the host-pathogen association during the acute phase of disease or during the process of establishing a carrier state.

We constructed mutant strains of Francisella tularensis biotype novicida by insertional mutagenesis with a kanamycin resistance (KmR) cassette. One mutant, KEM7, was defective for survival in macrophages in comparison with the wild-type (WT) strain and a random insertion strain, KEM21. While all three strains exhibited intracellular growth, the number of viable KEM7 present after 24-48 h of infection was approximately 10 times less than that of WT or KEM21. This observation was apparently due to a reduced number of viable KEM7 associated with the macrophages one hour after phagocytosis. KEM7 was approximately 3 times more susceptible than WT or KEM21 to killing by the products of the xanthine-xanthine oxidase reaction or by hydrogen peroxide. KEM7 was also found to be susceptible to killing by serum, whereas WT and KEM21 were resistant. Upon intravenous inoculation of C57BL/6 mice, the number of KEM7 in the livers and spleens 48 h post-infection was found to be 1,000- to 10,000-times less than that of either KEM21 or WT. DNA sequence analysis at the KmR insertion site suggested that the F. tularensis homologue of minD had been interrupted. Western immunoblot analysis confirmed the presence of a MinD homologue in F. tularensis WT and KEM21, and demonstrated its absence in KEM7.

We describe methods for transposon mutagenesis and allelic replacement in the facultative intracellular pathogen Francisella. Recombinant clones were constructed by insertion of partially cut F. tularensis or F. novicida DNA into pUC19 and then mutagenized with a mini-Tn10-Km transposon. F. novicida could be transformed with these plasmids either by a chemical transformation method or by electroporation, whereas F. tularensis could be transformed only by electroporation. Transformation of F. tularensis by electroporation was enhanced in the absence of the capsule. Southern blot analysis showed that the KmR marker was rescued either by integration of the plasmid into the Francisella chromosome or by allelic replacement. Allelic replacement was found to be the mechanism underlying a site-specific mutation affecting FopA, an outer-membrane protein of Francisella. F. novicida could also be transformed with chromosomal DNA carrying the KmR marker and the transformation frequency obtained using chromosomal DNA was generally greater than that obtained using plasmid DNA. F. novicida was also transformed by an IncQ plasmid containing an F. novicida DNA insert, which replicated autonomously in this host.