In turbulent high-beta astrophysical plasmas (exemplified by the galaxy cluster plasmas), pressure-anisotropy-driven firehose and mirror fluctuations grow nonlinearly to large amplitudes, deltaB/B approximately 1, on a time scale comparable to the turnover time of the turbulent motions. The principle of their nonlinear evolution is to generate secularly growing small-scale magnetic fluctuations that on average cancel the temporal change in the large-scale magnetic field responsible for the pressure anisotropies. The presence of small-scale magnetic fluctuations may dramatically affect the transport properties and, thereby, the large-scale dynamics of the high-beta astrophysical plasmas.

Both global dynamics and turbulence in magnetized weakly collisional cosmic plasmas are described by general magnetofluid equations that contain pressure anisotropies and heat fluxes that must be calculated from microscopic plasma kinetic theory. It is shown that even without a detailed calculation of the pressure anisotropy or the heat fluxes, one finds the macroscale dynamics to be generically unstable to microscale Alfvénically polarized fluctuations. Two instabilities that can be treated this way are considered in detail: the parallel firehose instability (including the finite Larmor radius effects that determine the growth rate and scale of the fastest growing mode) and the gyrothermal instability (GTI). The latter is a new result – it is shown that a parallel ion heat flux destabilizes Alfvénically polarized fluctuations even in the absence of the negative pressure anisotropy required for the firehose. The main physical conclusion is that both pressure anisotropies and heat fluxes associated with the macroscale dynamics trigger plasma microinstabilities and, therefore, their values will likely be set by the non‐linear evolution of these instabilities. Ideas for understanding this non‐linear evolution are discussed. It is argued that cosmic plasmas will generically be ‘three‐scale systems’, comprising global dynamics, mesoscale turbulence and microscale plasma fluctuations. The astrophysical example of cool cores of galaxy clusters is considered quantitatively and it is noted that observations point to turbulence in clusters (velocity, magnetic and temperature fluctuations) being in a marginal state with respect to plasma microinstabilities and so it is the plasma microphysics that is likely to set the heating and conduction properties of the intracluster medium. In particular, a lower bound on the scale of temperature fluctuations implied by the GTI is derived.

Weakly collisional magnetized cosmic plasmas have a dynamical tendency to develop pressure anisotropies with respect to the local direction of the magnetic field. These anisotropies trigger plasma instabilities at scales just above the ion Larmor radius ρ i and much below the mean free path λ mfp . They have growth rates of a fraction of the ion cyclotron frequency, which is much faster than either the global dynamics or even local turbulence. Despite their microscopic nature, these instabilities dramatically modify the transport properties and, therefore, the macroscopic dynamics of the plasma. The non-linear evolution of these instabilities is expected to drive pressure anisotropies towards marginal stability values, controlled by the plasma beta β i . Here this non-linear evolution is worked out in an ab initio kinetic calculation for the simplest analytically tractable example -the parallel (k ⊥ = 0) firehose instability in a highbeta plasma. An asymptotic theory is constructed, based on a particular physical ordering and leading to a closed non-linear equation for the firehose turbulence. In the non-linear regime, both the analytical theory and the numerical solution predict secular (∝t) growth of magnetic fluctuations. The fluctuations develop a k −3 spectrum, extending from scales somewhat larger than ρ i to the maximum scale that grows secularly with time (∝t 1/2 ); the relative pressure anisotropy (p ⊥ − p )/p tends to the marginal value −2/β i . The marginal state is achieved via changes in the magnetic field, not particle scattering. When a parallel ion heat flux is present, the parallel firehose mutates into the new gyrothermal instability (GTI), which continues to exist up to firehose-stable values of pressure anisotropy, which can be positive and are limited by the magnitude of the ion heat flux. The non-linear evolution of the GTI also features secular growth of magnetic fluctuations, but the fluctuation spectrum is eventually dominated by modes around a maximal scale ∼ρ i l T /λ mfp , where l T is the scale of the parallel temperature variation. Implications for momentum and heat transport are speculated about. This study is motivated by our interest in the dynamics of galaxy cluster plasmas (which are used as the main astrophysical example), but its relevance to solar wind and accretion flow plasmas is also briefly discussed.

As an emerging field of theory, research, and practice, STEAM (Science, Technology, Engineering, Arts, and Mathematics) has received attention for its efforts to incorporate the arts into the rubric of STEM (Science, Technology, Engineering, and Mathematics) learning. In particular, many informal educators have embraced it as an inclusive and authentic approach to engaging young people with STEM. Yet, as with many nascent fields, the conceptualization and usage of STEAM is somewhat ambivalent and weakly theorized. On the one hand, STEAM offers significant promise through its focus on multiple ways of knowing and new pathways to equitable learning. On the other hand, it is often deployed in theory, pedagogy, and practice in ambiguous or potentially problematic ways toward varying ends. This paper attempts to disentangle some of the key tensions and contradictions of the STEAM concept as currently operationalized in educational research, policy, and practice. We pay particular attention to the transformative learning potential supported by contexts where STEAM is conceptualized as both pedagogical and mutually instrumental. That is, neither STEM nor arts are privileged over the other, but both are equally in play. We link the possibilities suggested by this approach to emerging theories for understanding how designing for and surfacing epistemic practices linked to the relevant disciplines being integrated into STEAM programs may point the way toward resolving tensions in inter‐ and transdisciplinary learning approaches.

This article presents a new formulation of the solution for fully nonlinear and unsteady planar flow of an electron beam in a diode. Using characteristic variables (i.e., variables that follow particle paths) the solution is expressed through an exact analytic, but implicit, formula for any choice of incoming velocity v(0), electric field E(0), and current J(0). For steady solutions, this approach clarifies the origin of the maximal current J(max), derived by Child and Langmuir for v(0) = 0 and by Jaffe for v(0) > 0. The implicit formulation is used to find (1) unsteady solutions having constant incoming flux J(0) > J(max), which leads to formation of a virtual cathode, and (2) time-periodic solutions whose average flux exceeds the adiabatic average of J(max).