Weak turbulence theory for collisional plasmas

Plasma is an ionized gas in which the collective behavior dominates over the individual particle interactions. For this reason, plasma is often treated as collisionless or collision-free. However, the discrete nature of the particles can be important, and often, the description of plasmas is incomplete without properly taking the discrete particle effects into account. The weak turbulence theory is a perturbative nonlinear theory, whose essential formalism was developed in the late 1950s and 1960s and continued on through the early 1980s. However, the standard material found in the literature does not treat the discrete particle effects and the associated fluctuations emitted spontaneously by thermal particles completely. Plasma particles emit electromagnetic fluctuations in all frequencies and wave vectors, but in the standard literature, the fluctuations are approximately treated by considering only those frequency-wave number regimes corresponding to the eigenmodes (or normal modes) satisfying the dispersion relations, while ignoring contributions from noneigenmodes. The present paper shows that the noneigenmode fluctuations modify the particle kinetic equation so that the generalized equation includes the Balescu-Lénard-Landau collision integral and also modify the wave kinetic equation to include not only the collisional damping term but also a term that depicts the bremsstrahlung emission of plasma normal modes

Two dimensional time evolution of beam-plasma instability in the presence of binary collisions

Energetic electrons produced during solar flares are known to be responsible for generating solar type III radio bursts. The radio emission is a byproduct of Langmuir wave generation via beam-plasma interaction and nonlinear wave-wave and wave-particle interaction processes. In addition to type III radio bursts, electrons traveling downwards toward the chromosphere lead to the hard X-ray emission via electron-ion collisions. Recently, the role of Langmuir waves on the X-ray-producing electrons has been identified as important, because Langmuir waves may alter the electron distribution, thereby affecting the X-ray profile. Both Coulomb collisions and wave-particle interactions lead electrons to scattering and energy exchange that necessitates considering the two-dimensional (2D) problem in velocity space. The present paper investigates the influence of binary collisions on the beam-plasma instability development in 2D in order to elucidate the nonlinear dynamics of Langmuir waves and binary collisions. The significance of the present findings in the context of solar physics is discussed

A Rigorous Derivation of the Functional Renormalisation Group Equation

The functional renormalisation group equation is derived in a mathematically rigorous fashion in a framework suitable for the Osterwalder-Schrader formulation of quantum field theory. To this end, we devise a very general regularisation scheme and give precise conditions for the involved regulators guaranteeing physical boundary conditions. Furthermore, it is shown how the classical limit is altered by the regularisation process leading to an inevitable breaking of translation invariance. We also give precise conditions for the convergence of the obtained theories upon removal of the regularisation

θ\theta-splitting Densities and Reflection Positivity

A simple condition is given that is sufficient to determine whether a measure that is absolutely continuous with respect to a Gau{\ss}ian measure on the space of distributions is reflection positive. It readily generalises conventional lattice results to an abstract setting, enabling the construction of many reflection positive measures that are not supported on lattices

Generation of Suprathermal Electrons by Collective Processes in Collisional Plasma

The ubiquity of high-energy tails in the charged particle velocity distribution functions observed in space plasmas suggests the existence of an underlying process responsible for taking a fraction of the charged particle population out of thermal equilibrium and redistributing it to suprathermal velocity and energy ranges. The present Letter focuses on a new and fundamental physical explanation for the origin of suprathermal electron distribution function in a highly collisional plasma. This process involves a newly discovered electrostatic bremsstrahlung emission that is effective in a plasma in which binary collisions are present. The steady-state electron velocity distribution function dictated by such a process corresponds to a Maxwellian core plus a quasi-inverse power-law tail, which is a feature commonly observed in many space plasma environment. In order to demonstrate this, the system of self-consistent particle- and wave- kinetic equations are numerically solved with an initially Maxwellian electron velocity distribution and Langmuir wave spectral intensity, which is a state that does not reflect the presence of electrostatic bremsstrahlung process, and hence not in force balance. The electrostatic bremsstrahlung term subsequently drives the system to a new force-balanced steady state. After a long integration period it is demonstrated the initial Langmuir fluctuation spectrum is modified, which in turn distorts the initial Maxwellian electron distribution into a velocity distribution that resembles the said core-suprathermal velocity distribution. Such a mechanism may thus be operative at the coronal source region, which is characterized by high collisionality.Comment: 7 pages, 2 figures. Published at: The Astrophysical Journal Letters, Volume 849, Number 2, L30. url: https://doi.org/10.3847/2041-8213/aa956

Embedding career climate skills broadly into Australian degrees

One of the emerging barriers to climate action in Australia, and globally, is having enough people with the skills and interest to accelerate decarbonisation across the economy. While universities have a critical role to play in addressing these skills issues, many degrees are not currently geared towards developing a workforce suitably equipped to address climate change. Likewise, building the knowledge and skills necessary to address climate change - including understanding the challenges and opportunities for innovation - are often too narrowly defined or considered. Growing breadth of conception will be key to successfully nurturing future leaders in this regard

The functional renormalisation group, its mathematics and applications to asymptotic safety

We present a regularisation scheme for scalar Quantum Field theories that enables a flexible and mathematically consistent formulation of interacting theories in arbitrary dimensions. In contrast to a lattice approach, it retains the smooth features of spacetime and the infinite de- grees of freedom such that, in particular, the rotational symmetry can be left unbroken. In this framework, we give a mathematically rigorous derivation of the Wetterich equation as well as sufficient conditions for the passage to the limit of vanishing regularisation. We also introduce an iterative construction procedure for exact solutions to the Wetterich equation that works by producing higher-order correlation functions form the renormalisation group flow of lower order correlators. Then a generalisation of Quantum Electrodynamics is considered in the asymptotic safety framework and particular solutions are found that reproduce physical results in a low-energy regime. Finally, the applicability of the introduced regularisation scheme to the ϕ4 theory is proved. It follows from an integrability statement that can be thought of as a generalisation of Fernique’s theorem on exponential tails of Gaußian measures