Gyrokinetic theories, even ‘global’ models, typically rely on a separation in scale (in perpendicular wavelength) between the fluctuations and the system scale. In such models direct simulation of system-scale dynamics like magnetohydrodynamic (MHD) motion is formally not consistent. Drift-kinetic theory, on the other hand, may be directly applied to model system-scale MHD-ordered behaviour. I review the long-wavelength limit of standard gyrokinetics and drift kinetics to present the relationships between these theories in an elementary fashion. This provides a pathway to global gyrokinetic modelling, resulting in an approach that is structurally similar to kinetic MHD, and I present dynamical equations for solving global field evolution in this framework. Departures from certain earlier global gyrokinetic theories include the appearance of magnetosonic (fast) modes, and the cross-coupling of the parallel and perpendicular currents with perpendicular and parallel magnetic field components. A periodic two-dimensional testcase is outlined as a benchmarking and implementation target, to help clarify practical aspects of these theories, with minimal complexity in terms of boundary conditions, and a proof-of-principle implementation of a field-solver is exhibited. To motivate this work, I first illustrate certain limitations of existing global gyrokinetic frameworks and directly identify how scale separation approximations lead to certain ‘missing’ system-scale field terms in global gyrokinetics, largely as a result of simplifications associated with the field representation in terms of $A_{\|}$ and $B_{\|}$. As a result, the currents in the gyrokinetic Ampère's law resulting from a gyrokinetic equilibrium distribution do not match the currents implied by Ampère's law in a force-balance MHD equilibrium. I present a simple choice of equilibrium distribution function whose drift-kinetic currents are consistent with MHD currents; a specific Grad–Shafranov equilibrium is used to illustrate the size of the components of the parallel currents.

Colliding collisionless shocks appear in a great variety of astrophysical phenomena and are thought to be possible sources of particle acceleration in the Universe. We have previously investigated particle acceleration induced by single super-critical shocks (whose magnetosonic Mach number is higher than the critical value of 2.7) (Yao et al., Nat. Phys., vol. 17, issue 10, 2021, pp. 1177–1182; Yao et al., Matter Radiat. Extrem., vol. 7, issue 1, 2022, 014402), as well as the collision of two sub-critical shocks (Fazzini et al., Astron. Astrophys., vol. 665, 2022, A87). Here, we propose to make measurements of accelerated particles from interpenetrating super-critical shocks to observe the ‘phase-locking effect’ (Fazzini et al., Astron. Astrophys., vol. 665, 2022, A87) from such an event. This effect is predicted to significantly boost the energy spectrum of the energized ions compared with a single super-critical collisionless shock. We thus anticipate that the results obtained in the proposed experiment could have a significant impact on our understanding of one type of primary source (acceleration of thermal ions as opposed to secondary acceleration mechanisms of already energetic ions) of ion energization of particles in the Universe.

The understanding of cross-field transport is crucial for optimizing the properties of magnetic confinement in fusion devices. In this work, a two-dimensional, simplified model is used to study the turbulent dynamics in the region of the scrape-off layer. The numerical model, based on the reduced Braginskii equations, is able to describe the formation and the evolution of blob-like structures. The dynamics has been investigated by using both classical Eulerian analysis and the Lagrangian approach, by varying the ambient conditions of the plasma. The major goals are (i) a detailed and systematic study of turbulence by varying the plasma jump conditions in the edge tokamaks plasmas and (ii) a Lagrangian diffusion study of the edge turbulence by using an appropriate Braginskii model. It has been found that both the magnetic shear and the plasma mean profiles of density and temperature are crucial for setting the properties of the transport. By following fluid tracers, diffusive transients for the radial transport are observed, at length scales larger than the typical blob size. This work is relevant for the comprehension of the turbulent transport at tokamaks edges.