Particle transport, acceleration and energization are phenomena of major importance for both space and laboratory plasmas. Despite years of study, an accurate theoretical description of these effects is still lacking. Validating models with self-consistent, kinetic simulations represents today a new challenge for the description of weakly collisional, turbulent plasmas. We perform simulations of steady state turbulence in the 2.5-dimensional approximation (three-dimensional fields that depend only on two-dimensional spatial directions). The chosen plasma parameters allow to span different systems, going from the solar corona to the solar wind, from the Earth’s magnetosheath to confinement devices. To describe the ion diffusion we adapted the nonlinear guiding centre (NLGC) theory to the two-dimensional case. Finally, we investigated the local influence of coherent structures on particle energization and acceleration: current sheets play an important role if the ions’ Larmor radii are of the order of the current sheet’s size. This resonance-like process leads to the violation of the magnetic moment conservation, eventually enhancing the velocity-space diffusion.

]]>The effect of electrostatic microturbulence on fast particles rapidly decreases at high energy, but can be significant at moderate energy. Previous studies found that, in addition to changes in the energetic particle density, this results in non-trivial changes to the equilibrium velocity distribution. These effects have implications for plasma heating and the stability of Alfvén eigenmodes, but make multiscale simulations much more difficult without further approximations. Here, several related analytic model distribution functions are derived from first principles. A single dimensionless parameter characterizes the relative strength of turbulence relative to collisions, and this parameter appears as an exponent in the model distribution functions. Even the most simple of these models reproduces key features of the numerical phase-space transport solution and provides a useful a priori heuristic for determining how strong the effect of turbulence is on the redistribution of energetic particles in toroidal plasmas.

]]>The time-independent projection-operator formalism of Brey et al. (Physica A, vol. 109, 1981, pp. 425–444) for the derivation of Burnett equations is extended and considered in the context of multispecies and magnetized plasmas. The procedure provides specific formulas for transport coefficients in terms of two-time correlation functions involving both two and three phase-space points. It is shown how to calculate those correlation functions in the limit of weak coupling. The results are used to demonstrate, with the aid of a particular non-trivial example, that the Chapman–Enskog methodology employed by Catto & Simakov (CS) (Phys. Plasmas, vol. 11, 2004, pp. 90–102) to calculate the contributions to the parallel viscosity driven by temperature gradients is consistent with formulas previously derived from the two-time formalism by Brey (J. Chem. Phys., vol. 79, 1983, pp. 4585–4598). The work serves to unify previous work on plasma kinetic theory with formalism usually applied to turbulence. Additional contributions include discussions of (i) Braginskii-order interspecies momentum exchange from the point of view of two-time correlations; and (ii) a simple stochastic model, unrelated to many-body theory, that exhibits Burnett effects. Insights from that model emphasize the role of non-Gaussian statistics in the evaluation of Burnett transport coefficients, including the effects calculated by CS that stem from the nonlinear collision operator. Together, Parts 1 and 2 of this series provide an introduction to projection-operator methods that should be broadly useful in theoretical plasma physics.

]]>The drift surfaces of minority heated ions differ from flux surfaces due to finite poloidal gyroradius effects. As the minority poloidal gyroradius approaches radial scale lengths in the plasma, the difference between drift and flux surfaces can modify the heating and lead to a symmetric spectrum minority counter-current being driven. In response, a corresponding overall net co-current of comparable size is driven. This beneficial symmetric spectrum current drive in a tokamak is due to the parallel velocity asymmetry in the drift departure from a flux surface. As this new source of driven current is a side effect of minority heating it comes without any additional economic cost to reactor power balance. The symmetric spectrum current driven for near Maxwellian minorities is evaluated by an adjoint method and found to be modest. However, minority heating typically results in strong non-Maxwellian features on minority distributions so it may be possible to drive a significantly larger co-current. A related evaluation is performed for alpha particles in a deuterium minority heated plasma with a tritium majority. The low density of the alphas tends to keep this driven symmetric spectrum current small, but at very high heating levels a significant co-current might be driven. Other mechanisms to drive co-current with a symmetric spectrum are discussed and estimated, including asymmetric electron drag and focusing of the applied minority heating radio frequency fields.

]]>Azimuthal surface waves are eigenmodes of cylindrical plasma–dielectric–metal structures both in the presence of and without an axial static magnetic field. They are actively studied due to possible applications in plasma electronics, nanotechnologies and biomedical diagnostics. Higher radial modes are known to propagate at higher frequencies and shorter wavelengths compared to those of the zeroth mode, a feature which is of interest for practical applications. To gain the advantage of the excitation of higher radial modes of azimuthal surface waves one has first to know their dispersion properties. This paper generalizes the results of earlier papers by including a static axial magnetic field and considering the higher radial modes. The presence of the constant axial magnetic field removes the degeneracy in the wave spectrum with respect to the sign of the azimuthal wavenumber.

]]>Collisionless shocks follow the Rankine–Hugoniot jump conditions to a good approximation. However, for a shock propagating parallel to a magnetic field, magnetohydrodynamics states that the shock properties are independent of the field strength, whereas recent particle-in-cell simulations reveal a significant departure from magnetohydrodynamics behaviour for such shocks in the collisionless regime. This departure is found to be caused by a field-driven anisotropy in the downstream pressure, but the functional dependence of this anisotropy on the field strength is yet to be determined. Here, we present a non-relativistic model of the plasma evolution through the shock front, allowing for a derivation of the downstream anisotropy in terms of the field strength. Our scenario assumes double adiabatic evolution of a pair plasma through the shock front. As a result, the perpendicular temperature is conserved. If the resulting downstream is firehose stable, then the plasma remains in this state. If unstable, it migrates towards the firehose stability threshold. In both cases, the conservation equations, together with the relevant hypothesis made on the temperature, allows a full determination of the downstream anisotropy in terms of the field strength.

]]>Accurate modelling of the interaction between fast electrons and partially ionized atoms is important for evaluating tokamak disruption mitigation schemes based on material injection. This requires accounting for the effect of screening of the impurity nuclei by the cloud of bound electrons. In this paper, we generalize the Fokker–Planck operator in a fully ionized plasma by accounting for the effect of screening. We detail the derivation of this generalized operator, and calculate the effective ion length scales, needed in the components of the collision operator, for a number of ion species commonly appearing in fusion experiments. We show that for high electric fields, the secondary runaway growth rate can be substantially larger than in a fully ionized plasma with the same effective charge, although the growth rate is significantly reduced at near-critical electric fields. Furthermore, by comparison with the Boltzmann collision operator, we show that the Fokker–Planck formalism is accurate even for large impurity content.

]]>Gyrokinetic stability of plasmas in different magnetic geometries is studied numerically using the GENE code. We examine the stability of plasmas, varying the mass ratio between the positive and negative charge carriers, from conventional hydrogen plasmas through to electron–positron plasmas. Stability is studied for prescribed temperature and density gradients in different magnetic geometries: (i) An axisymmetric, circular flux surface, low (tokamak) configuration. (ii) A non-axisymmetric quasi-isodynamic (optimised stellarator) configuration using the geometry of the stellarator Wendelstein 7-X. We also present the analytic theory of trapped particle modes in electron–positron plasmas. We found similar behaviour of the growth rate and real frequency compared to previous studies on the tokamak case. We are able to identify two distinct regimes dominated by modes propagating in the electron diamagnetic direction and modes propagating in the ion/positron diamagnetic direction, depending on the mass ratio. In both the tokamak and the stellarator case we observe that the real frequency tends to zero as the mass ratio approaches unity and are able to explain this using gyrokinetic theory.

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