Peeling-ballooning stability of tokamak plasmas with applied 3D magnetic fields

The poloidal harmonics of the toroidal normal modes of an unstable axisymmetric tokamak plasma are employed as basis functions for the minimisation of the 3D energy functional. This approach presents a natural extension of the perturbative method considered in Anastopoulos Tzanis et al (2019 Nucl. Fusion 59 126028). This variational formulation is applied to the stability of tokamak plasmas subject to external non-axisymmetric magnetic fields. A comparison of the variational and perturbative methods shows that for D-shaped, high β N plasmas, the coupling of normal modes becomes strong at experimentally relevant applied 3D fields, leading to violation of the assumptions that justify a perturbative analysis. The variational analysis employed here addresses strong coupling, minimising energy with respect to both toroidal and poloidal Fourier coefficients. In general, it is observed that ballooning unstable modes are further destabilised by the applied 3D fields and field-aligned localisation of the perturbation takes place, as local ballooning theory suggests. For D-shaped high β N plasmas, relevant to experimental cases, it is observed that the existence of intermediate n unstable peeling-ballooning modes, where a maximum in the growth rate spectrum typically occurs, leads to a destabilising synergistic coupling that strongly degrades the stability of the 3D system

Large-scale phenotyping of patients with long COVID post-hospitalization reveals mechanistic subtypes of disease

One in ten severe acute respiratory syndrome coronavirus 2 infections result in prolonged symptoms termed long coronavirus disease (COVID), yet disease phenotypes and mechanisms are poorly understood1. Here we profiled 368 plasma proteins in 657 participants ≥3 months following hospitalization. Of these, 426 had at least one long COVID symptom and 233 had fully recovered. Elevated markers of myeloid inflammation and complement activation were associated with long COVID. IL-1R2, MATN2 and COLEC12 were associated with cardiorespiratory symptoms, fatigue and anxiety/depression; MATN2, CSF3 and C1QA were elevated in gastrointestinal symptoms and C1QA was elevated in cognitive impairment. Additional markers of alterations in nerve tissue repair (SPON-1 and NFASC) were elevated in those with cognitive impairment and SCG3, suggestive of brain–gut axis disturbance, was elevated in gastrointestinal symptoms. Severe acute respiratory syndrome coronavirus 2-specific immunoglobulin G (IgG) was persistently elevated in some individuals with long COVID, but virus was not detected in sputum. Analysis of inflammatory markers in nasal fluids showed no association with symptoms. Our study aimed to understand inflammatory processes that underlie long COVID and was not designed for biomarker discovery. Our findings suggest that specific inflammatory pathways related to tissue damage are implicated in subtypes of long COVID, which might be targeted in future therapeutic trials