Collisions are an important dissipation mechanism in plasmas. When approximating collision operators numerically, it is important to preserve their mathematical structure in order to retain the laws of thermodynamics at the discrete level. This is particularly challenging when considering particle methods. A simple but commonly used collision operator is the Lenard–Bernstein operator, or its modified energy- and momentum-conserving counterpart. In this work, we present a macro-particle discretisation of this operator that is provably energy and momentum preserving.
In a recent publication (Toler et al., J. Plasma Phys., vol. 89, issue 2, 2023, p. 905890210), we demonstrated that for axisymmetric geometries, the Kapur–Rokhlin quadrature rule provided an efficient and high-order accurate method for computing the normal component, on the plasma surface, of the magnetic field due to the toroidal current flowing in the plasma, via the virtual-casing principle. The calculation was indirect, as it required the prior computation of the magnetic vector potential from the virtual-casing principle, followed by the computation of its tangential derivative by Fourier differentiation, to obtain the normal component of the magnetic field. Our approach did not provide the other components of the virtual-casing magnetic field. In this letter, we show that a more direct and more general approach is available for the computation of the virtual-casing magnetic field. The Kapur–Rokhlin quadrature rule accurately calculates the principal value integrals in the expression for all the components of the magnetic field on the plasma boundary, and the numerical error converges at a rate nearly as high as the indirect method we presented previously.
In this paper, we investigate the kinetic stability of classical, collisional plasma – that is, plasma in which the mean-free-path 
$lambda$ of constituent particles is short compared with the length scale 
$L$ over which fields and bulk motions in the plasma vary macroscopically, and the collision time is short compared with the evolution time. Fluid equations are typically used to describe such plasmas, since their distribution functions are close to being Maxwellian. The small deviations from the Maxwellian distribution are calculated via the Chapman–Enskog (CE) expansion in 
$lambda /L ll 1$, and determine macroscopic momentum and heat fluxes in the plasma. Such a calculation is only valid if the underlying CE distribution function is stable at collisionless length scales and/or time scales. We find that at sufficiently high plasma 
$beta$, the CE distribution function can be subject to numerous microinstabilities across a wide range of scales. For a particular form of the CE distribution function arising in strongly magnetised plasma (viz. plasma in which the Larmor periods of particles are much smaller than collision times), we provide a detailed analytic characterisation of all significant microinstabilities, including peak growth rates and their associated wavenumbers. Of specific note is the discovery of several new microinstabilities, including one at sub-electron-Larmor scales (the ‘whisper instability’) whose growth rate in certain parameter regimes is large compared with other instabilities. Our approach enables us to construct the kinetic stability maps of classical, two-species collisional plasma in terms of 
Linearized gravity around a rotating black hole or compact object introduces the concept of a gravitomagnetic field, which originates from the matter–current in the rotating object. Plasma in proximity to this object is subsequently subjected to motion guided by this gravitomagnetic term (where mass serves as the effective charge) in addition to the conventional magnetic field. Such an interplay of fields complicates the accessible plasma waves of the system and thus merits exploration to delineate this interplay, to identify any observable signatures of the gravitomagnetic field in weakly magnetized systems, and to motivate future numerical work in a fully relativistic setting where the effects may be stronger. In this work we analyse the dispersion of the upper and lower hybrid electrostatic waves in a plasma immersed in both magnetic and gravitomagnetic fields. In particular, we discuss the effective augmentation or cancellation of the two fields under the right conditions for the upper hybrid wave. In contrast, the lower hybrid wave experiences a frequency up-shift from the gravitomagnetic field regardless of whether it is parallel or antiparallel to the magnetic field for the studied field strengths.
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