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One of the outstanding challenges of solar physics is understanding the mechanism for heating the solar corona, a low-β, low-resistivity plasma driven slowly by the shuffling of "footpoints" (ends of flux tubes) anchored in the photosphere. The corona's low resistivity means that enormous current densities must be present for Ohmic dissipation to be effective. Two ways that this can occur in a slowly evolving, "quasiequilibrium" medium are by the formation of current sheets or by the excitation of very low-frequency Alfvén resonances. Both processes lead to singular current densities in the ideal limit, and both may result from the excitation of very low- (or zero-) frequency shear Alfvén resonances. Thus, understanding the conditions under which zero-frequency Alfvén resonances can occur may ultimately be important in understanding coronal heating. This paper examines shear Alfvén resonances in line-tied magnetic geometries, with special attention being paid to geometries with discontinuities in the field line mapping as candidates for having zero-frequency Alfvén resonances. Two such geometries have been examined in detail: a two-dimensional X-point and a three-dimensional magnetic null. Qualitative differences in the two spectra are observed. The X-point geometry has Alfvén resonances of vanishing frequency, whereas the magnetic null geometry has a finite cutoff in resonant frequency for all field lines in the system. The Alfvén continuum for a null depends on its geometry, however, and much lower (though still nonzero) resonant frequencies are found when the flux surfaces are moderately eccentric. Consequently, a subset of magnetic nulls in complex, line tied geometries may have flux surfaces that can be driven resonantly by a driver of much lower frequency than for similar media without nulls. To the extent that nulls are generic features of complex magnetic geometries {and there is some reason to... [ABSTRACT FROM AUTHOR]

Toroidal calculations on m = 2 magnetic feedback are presented. These calculations are performed using a coupled Δ' formulation and show that the feedback can have a pronounced effect on the sideband (m = 1 and 3) content. [ABSTRACT FROM AUTHOR]

The separation of the cylindrical tearing mode stability problem into a resistive resonant layer calculation and an external marginal ideal magnetohydrodynamic (MHD) calculation (Δ’ calculation) is generalized to axisymmetric toroidal geometry. The general structure of this separation is analyzed and the marginal ideal MHD information (the toroidal generalization of Δ’) required to discuss stability is isolated. This can then, in principle, be combined with relevant resonant layer calculations to determine tearing mode growth rates in realistic situations. Two examples are given: the first is an analytic treatment of toroidally coupled (m=1, n=1) and (m=2, n=1) tearing modes in a large aspect ratio torus; the second, a numerical treatment of the toroidal coupling of three tearing modes through finite pressure effects in a large aspect ratio torus. In addition, the use of a coupling integral approach for determining the stability of coupled tearing modes is discussed. Finally, the possibility of using initial value resistive MHD codes in realistic toroidal geometry to determine the necessary information from the ideal MHD marginal solution is discussed. [ABSTRACT FROM AUTHOR]

This paper examines the stability of tearing modes in a sheared slab when the width of the tearing layer is much smaller than the ion Larmor radius. The ion response is nonlocal, and the quasineutrality retains its full integral form. An expansion procedure is introduced to solve the quasineutrality equation in powers of the width of the tearing layer over the ion Larmor radius. The expansion procedure is applied to the collisionless and semicollisional tearing modes. It is found that first-order terms in the expansion are strongly stabilizing. The physics of the mode and of the stabilization are discussed. Tearing modes are observed in experiments even though the slab theory predicts stability. It is proposed that these modes grow from an equilibrium with islands at the rational surfaces. If the equilibrium islands are wider than the ion Larmor radius, the mode is unstable when δ' is positive. [ABSTRACT FROM AUTHOR]

The usual kinetic description of a plasma is extended to include variables to describe the nuclear spin. The distribution function, over phase space and the new spin variables, provides a sufficient description of a spin-polarized plasma. The evolution for the distribution function is given. The equations derived are used to calculate depolarization caused by four processes: inhomogeneous fields, collisions, collisions in inhomogeneous fields, and waves. It is found that depolarization by field inhomogeneity on scales large compared with the gyroradius is totally negligible. The same is true for collisional depolarization. Collisions in inhomogeneous fields yield a depolarization rate of order 10-3 sec-1 for deuterons and a negligible rate for tritons in a typical fusion reactor design. This is still sufficiently small on reactor time scales. However, small-amplitude magnetic fluctuations (of order 1 G) resonant with the spin precession frequency can lead to significant depolarization (depolarizes triton in 10 sec and deuteron in 100 sec). [ABSTRACT FROM AUTHOR]

Using a simple model for the layer of the tearing mode, it is demonstrated that toroidally coupled tearing modes with two rational surfaces are most unstable when the ω*’s of the electrons at the rational surfaces are equal. The onset of instability may then occur because of the tuning of ω* rather than the passage of Δ’-like quantities through zero. This mechanism for the onset of instability is sharp since the resonance is narrow. The effect of toroidal rotation is also discussed. [ABSTRACT FROM AUTHOR]

Slow dynamical changes in magnetic-field strength and invariance of the particles’ magnetic moments generate ubiquitous pressure anisotropies in weakly collisional, magnetized astrophysical plasmas. This renders them unstable to fast, small-scale mirror and firehose instabilities, which are capable of exerting feedback on the macroscale dynamics of the system. By way of a new asymptotic theory of the early non-linear evolution of the mirror instability in a plasma subject to slow shearing or compression, we show that the instability does not saturate quasi-linearly at a steady, low-amplitude level. Instead, the trapping of particles in small-scale mirrors leads to non-linear secular growth of magnetic perturbations, δB/B ∝ t2/3. Our theory explains recent collisionless simulation results, provides a prediction of the mirror evolution in weakly collisional plasmas and establishes a foundation for a theory of non-linear mirror dynamics with trapping, valid up to δB/B = O(1). [ABSTRACT FROM PUBLISHER]

Calculations of tearing mode stability in tokamaks split conveniently into one in an external region, where marginally stable ideal magnetohydrodynamics (MHD) is applicable, and one in a resonant layer around the rational surface where sophisticated kinetic physics is needed. These two regions are coupled by the stability parameter Δ′. Axisymmetric pressure and current perturbations localized around the rational surface significantly alter Δ′. Equations governing the changes in the external solution and Δ′ are derived for arbitrary perturbations in axisymmetric toroidal geometry. These equations can be used in two ways: (i) the Δ′ can be calculated for a physically occurring perturbation to the pressure or current; (ii) alternatively we can use these equations to calculate Δ′ for profiles with a pressure gradient at the rational surface in terms of the value when the perturbation removes this gradient. It is the second application we focus on here since resistive magnetohydrodynamics (MHD) codes do not contain the appropriate layer physics and therefore cannot predict stability for realistic hot plasma directly. They can, however, be used to calculate Δ′. Existing methods (Ham et al 2012 Plasma Phys. Control. Fusion54 025009) for extracting Δ′ from resistive codes are unsatisfactory when there is a finite pressure gradient at the rational surface and favourable average curvature because of the Glasser stabilizing effect (Glasser et al 1975 Phys. Fluids18 875). To overcome this difficulty we introduce a specific artificial pressure flattening function that allows the earlier approach to be used. The technique is first tested numerically in cylindrical geometry with an artificial favourable curvature. Its application to toroidal geometry is then demonstrated using the toroidal tokamak tearing mode stability code T7 (Fitzpatrick et al 1993 Nucl. Fusion33 1533) which employs an approximate analytic equilibrium. The prospects for applying this approach to resistive MHD codes such as MARS-F (Liu et al 2000 Phys. Plasmas7 3681) which utilize a fully toroidal equilibrium are discussed. [ABSTRACT FROM AUTHOR]

A theoretical framework for low-frequency electromagnetic (drift-)kinetic turbulence in a collisionless, multi-species plasma is presented. The result generalises reduced magnetohydrodynamics (RMHD) and kinetic RMHD (Schekochihin et al., Astrophys. J. Suppl. Ser., vol. 182, 2009, pp. 310–377) to the case where the mean distribution function of the plasma is pressure-anisotropic and different ion species are allowed to drift with respect to each other – a situation routinely encountered in the solar wind and presumably ubiquitous in hot dilute astrophysical plasmas such as the intracluster medium. Two main objectives are achieved. First, in a non-Maxwellian plasma, the relationships between fluctuating fields (e.g. the Alfvén ratio) are order-unity modified compared to the more commonly considered Maxwellian case, and so a quantitative theory is developed to support quantitative measurements now possible in the solar wind. Beyond these order-unity corrections, the main physical feature of low-frequency plasma turbulence survives the generalisation to non-Maxwellian distributions: Alfvénic and compressive fluctuations are energetically decoupled, with the latter passively advected by the former; the Alfvénic cascade is fluid, satisfying RMHD equations (with the Alfvén speed modified by pressure anisotropy and species drifts), whereas the compressive cascade is kinetic and subject to collisionless damping (and for a bi-Maxwellian plasma splits into three independent collisionless cascades). Secondly, the organising principle of this turbulence is elucidated in the form of a conservation law for the appropriately generalised kinetic free energy. It is shown that non-Maxwellian features in the distribution function reduce the rate of phase mixing and the efficacy of magnetic stresses, and that these changes influence the partitioning of free energy amongst the various cascade channels. As the firehose or mirror instability thresholds are approached, the dynamics of the plasma are modified so as to reduce the energetic cost of bending magnetic-field lines or of compressing/rarefying them. Finally, it is shown that this theory can be derived as a long-wavelength limit of non-Maxwellian slab gyrokinetics. [ABSTRACT FROM PUBLISHER]

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.

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

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.

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.

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.