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We derive a set of simplified equations that can be used for numerical studies of reduced magnetohydrodynamic turbulence within a small patch of the radially expanding solar wind. We allow the box to be either stationary in the Sun’s frame or to be moving at an arbitrary velocity along the background magnetic-field lines, which we take to be approximately radial. We focus in particular on the case in which the box moves at the same speed as outward-propagating Alfvén waves. To aid in the design and optimization of future numerical simulations, we express the equations in terms of scalar potentials and Clebsch coordinates. The equations we derive will be particularly useful for conducting high-resolution numerical simulations of reflection-driven magnetohydrodynamic turbulence in the solar wind, and may also be useful for studying turbulence within other astrophysical outflows.
In magnetized, stratified environments such as the Sun's corona and solar wind, Alfvénic fluctuations ‘reflect’ from background gradients, enabling nonlinear interactions that allow their energy to dissipate into heat. This process, termed ‘reflection-driven turbulence’, likely plays a key role in coronal heating and solar-wind acceleration, explaining a range of detailed observational correlations and constraints. Building on previous works focused on the inner heliosphere, here we study the basic physics of reflection-driven turbulence using reduced magnetohydrodynamics in an expanding box – the simplest model that can capture local turbulent plasma dynamics in the super-Alfvénic solar wind. Although idealized, our high-resolution simulations and simple theory reveal a rich phenomenology that is consistent with a diverse range of observations. Outwards-propagating fluctuations, which initially have high imbalance (high cross-helicity), decay nonlinearly to heat the plasma, becoming more balanced and magnetically dominated. Despite the high imbalance, the turbulence is strong because Elsässer collisions are suppressed by reflection, leading to ‘anomalous coherence’ between the two Elsässer fields. This coherence, together with linear effects, causes the growth of ‘anastrophy’ (squared magnetic potential) as the turbulence decays, forcing the energy to rush to larger scales and forming a ‘$1/f$-range’ energy spectrum in the process. Eventually, expansion overcomes the nonlinear and Alfvénic physics, forming isolated, magnetically dominated ‘Alfvén vortices’ with minimal nonlinear dissipation. These results can plausibly explain the observed radial and wind-speed dependence of turbulence imbalance (cross-helicity), residual energy, fluctuation amplitudes, plasma heating and fluctuation spectra, as well as making a variety of testable predictions for future observations.
The magnetohydrodynamic (MHD) equations, as a collisional fluid model that remains in local thermodynamic equilibrium (LTE), have long been used to describe turbulence in myriad space and astrophysical plasmas. Yet, the vast majority of these plasmas, from the solar wind to the intracluster medium (ICM) of galaxy clusters, are only weakly collisional at best, meaning that significant deviations from LTE are not only possible but common. Recent studies have demonstrated that the kinetic physics inherent to this weakly collisional regime can fundamentally transform the evolution of such plasmas across a wide range of scales. Here, we explore the consequences of pressure anisotropy and Larmor-scale instabilities for collisionless, $\beta \gg 1$, turbulence, focusing on the role of a self-organizational effect known as ‘magneto-immutability’. We describe this self-organization analytically through a high-$\beta$, reduced ordering of the Chew–Goldberger–Low-MHD (CGL-MHD) equations, finding that it is a robust inertial-range effect that dynamically suppresses magnetic-field-strength fluctuations, anisotropic-pressure stresses and dissipation due to heat fluxes. As a result, the turbulent cascade of Alfvénic fluctuations continues below the putative viscous scale to form a robust, nearly conservative, MHD-like inertial range. These findings are confirmed numerically via Landau-fluid CGL-MHD turbulence simulations that employ a collisional closure to mimic the effects of microinstabilities. We find that microinstabilities occupy a small (${\sim }5\,\%$) volume-filling fraction of the plasma, even when the pressure anisotropy is driven strongly towards its instability thresholds. We discuss these results in the context of recent predictions for ion-vs-electron heating in low-luminosity accretion flows and observations implying suppressed viscosity in ICM turbulence.
Hypertension and depression are increasingly common noncommunicable diseases in Ghana and worldwide, yet both are poorly controlled. We sought to understand how healthcare workers in rural Ghana conceptualize the interaction between hypertension and depression, and how care for these two conditions might best be integrated. We conducted a qualitative descriptive study involving in-depth interviews with 34 healthcare workers in the Kassena-Nankana districts of the Upper East Region of Ghana. We used conventional content analysis to systematically review interview transcripts, code the data content and analyze codes for salient themes. Respondents detailed three discrete conceptual models. Most emphasized depression as causing hypertension: through both emotional distress and unhealthy behavior. Others posited a bidirectional relationship, where cardiovascular morbidity worsened mood, or described a single set of underlying causes for both conditions. Nearly all proposed health interventions targeted their favored root cause of these disorders. In this representative rural Ghanaian community, healthcare workers widely agreed that cardiovascular disease and mental illness are physiologically linked and warrant an integrated care response, but held diverse views regarding precisely how and why. There was widespread support for a single primary care intervention to treat both conditions through counseling and medication.
Understanding the partitioning of turbulent energy between ions and electrons in weakly collisional plasmas is crucial for the accurate interpretation of observations and modelling of various astrophysical phenomena. Many such plasmas are ‘imbalanced’, wherein the large-scale energy input is dominated by Alfvénic fluctuations propagating in a single direction. In this paper, we demonstrate that when strongly-magnetised plasma turbulence is imbalanced, nonlinear conservation laws imply the existence of a critical value of the electron plasma beta (the ratio of the thermal to magnetic pressures) that separates two dramatically different types of turbulence in parameter space. For betas below the critical value, the free energy injected on the largest scales is able to undergo a familiar Kolmogorov-type cascade to small scales where it is dissipated, heating electrons. For betas above the critical value, the system forms a ‘helicity barrier’ that prevents the cascade from proceeding past the ion Larmor radius, causing the majority of the injected free energy to be deposited into ion heating. Physically, the helicity barrier results from the inability of the system to adjust to the disparity between the perpendicular-wavenumber scalings of the free energy and generalised helicity below the ion Larmor radius; restoring finite electron inertia can annul, or even reverse, this disparity, giving rise to the aforementioned critical beta. We relate this physics to the ‘dynamic phase alignment’ mechanism (that operates under yet lower beta conditions and in pair plasmas), and characterise various other important features of the helicity barrier, including the nature of the nonlinear wavenumber-space fluxes, dissipation rates, and energy spectra. The existence of such a critical beta has important implications for heating, as it suggests that the dominant recipient of the turbulent energy, ions or electrons, can depend sensitively on the characteristics of the plasma at large scales.
Wild oat is a long-standing weed problem in Australian grain cropping systems, potentially reducing the yield and quality of winter grain crops significantly. The effective management of wild oat requires an integrated approach comprising diverse control techniques that suit specific crops and cropping situations. This research aimed to construct and validate a bioeconomic model that enables the simulation and integration of weed control technologies for wild oat in grain production systems. The Avena spp. integrated management (AIM) model was developed with a simple interface to provide outputs of biological and economic data (crop yields, weed control costs, emerged weeds, weed seedbank, gross margins) on wild oat management data in a cropping rotation. Uniquely, AIM was validated against real-world data on wild oat management in a wheat and sorghum cropping rotation, where the model was able to reproduce the patterns of wild oat population changes as influenced by weed control and agronomic practices. Correlation coefficients for 12 comparison scenarios ranged between 0.55 and 0.96. With accurate parameterization, AIM is thus able to make useful predictions of the effectiveness of individual and integrated weed management tactics for wild oat control in grain cropping systems.
The Bali myna Leucopsar rothschildi has long suffered heavy trapping, leading to its near extinction in the wild and categorization as Critically Endangered on the IUCN Red List. Decades of conservation breeding, release of birds and post-release management at Bali Barat National Park have, until recently, failed to secure a viable wild population. However, over the past decade, population increases, expansion into new areas of the National Park and beyond, and successful breeding in both artificial and natural nest sites have occurred. These recent successes are associated with a change in approach by the National Park authority from concentrating efforts on the last refugium of the species (an area protected from trapping but with potentially suboptimal habitat) and towards the human-dominated landscapes around the main road through the National Park. Bali mynas tended to favour areas with extensive shorter grass cover and open canopies and to shun denser woodland. Anthropogenic landscapes such as farmland and plantations presumably mimic the original savannah habitat of the species, but nestbox provision has probably been crucial in these areas in the absence of natural cavities. A potential further factor in the increases in myna numbers and range has been a scheme involving local people in commercial breeding of the species, thereby reducing its market price, and working with communities to reduce trapping pressure. We encourage continuing operation of this management strategy inside the National Park and its further extension into adjacent tourist areas, which appear to have myna-friendly socio-ecological conditions.
Pressure anisotropy can strongly influence the dynamics of weakly collisional, high-beta plasmas, but its effects are missed by standard magnetohydrodynamics (MHD). Small changes to the magnetic-field strength generate large pressure-anisotropy forces, heating the plasma, driving instabilities and rearranging flows, even on scales far above the particles’ gyroscales where kinetic effects are traditionally considered most important. Here, we study the influence of pressure anisotropy on turbulent plasmas threaded by a mean magnetic field (Alfvénic turbulence). Extending previous results that were concerned with Braginskii MHD, we consider a wide range of regimes and parameters using a simplified fluid model based on drift kinetics with heat fluxes calculated using a Landau-fluid closure. We show that viscous (pressure-anisotropy) heating dissipates between a quarter (in collisionless regimes) and half (in collisional regimes) of the turbulent-cascade power injected at large scales; this does not depend strongly on either plasma beta or the ion-to-electron temperature ratio. This will in turn influence the plasma's thermodynamics by regulating energy partition between different dissipation channels (e.g. electron and ion heat). Due to the pressure anisotropy's rapid dynamic feedback onto the flows that create it – an effect we term ‘magneto-immutability’ – the viscous heating is confined to a narrow range of scales near the forcing scale, supporting a nearly conservative, MHD-like inertial-range cascade, via which the rest of the energy is transferred to small scales. Despite the simplified model, our results – including the viscous heating rate, distributions and turbulent spectra – compare favourably with recent hybrid-kinetic simulations. This is promising for the more general use of extended-fluid (or even MHD) approaches to model weakly collisional plasmas such as the intracluster medium, hot accretion flows and the solar wind.
With the support of hybrid-kinetic simulations and analytic theory, we describe the nonlinear behaviour of long-wavelength non-propagating (NP) modes and fast magnetosonic waves in high-$\beta$ collisionless plasmas, with particular attention to their excitation of and reaction to kinetic micro-instabilities. The perpendicularly pressure balanced polarization of NP modes produces an excess of perpendicular pressure over parallel pressure in regions where the plasma $\beta$ is increased. For mode amplitudes $|\delta B/B_0| \gtrsim 0.3$, this excess excites the mirror instability. Particle scattering off these micro-scale mirrors frustrates the nonlinear saturation of transit-time damping, ensuring that large-amplitude NP modes continue their decay to small amplitudes. At asymptotically large wavelengths, we predict that the mirror-induced scattering will be large enough to interrupt transit-time damping entirely, isotropizing the pressure perturbations and morphing the collisionless NP mode into the magnetohydrodynamic (MHD) entropy mode. In fast waves, a fluctuating pressure anisotropy drives both mirror and firehose instabilities when the wave amplitude satisfies $|\delta B/B_0| \gtrsim 2\beta ^{-1}$. The induced particle scattering leads to delayed shock formation and MHD-like wave dynamics. Taken alongside prior work on self-interrupting Alfvén waves and self-sustaining ion-acoustic waves, our results establish a foundation for new theories of electromagnetic turbulence in low-collisionality, high-$\beta$ plasmas such as the intracluster medium, radiatively inefficient accretion flows and the near-Earth solar wind.
In a magnetised plasma on scales well above ion kinetic scales, any constant-magnitude magnetic field, accompanied by parallel Alfvénic flows, forms a nonlinear solution in an isobaric, constant-density background. These structures, which are also known as spherically polarised Alfvén waves, are observed ubiquitously in the solar wind, presumably created by the growth of small-amplitude fluctuations as they propagate outwards in the corona. Here, we present a computational method to construct such solutions of arbitrary amplitude with general multidimensional structure, and explore some of their properties. The difficulty lies in computing a zero-divergence, constant-magnitude magnetic field, which leaves a single, quasi-free function to define the solution, while requiring strong constraints on any individual component of the field. Motivated by the physical process of wave growth in the solar wind, our method circumvents this issue by starting from low-amplitude Alfvénic fluctuations dominated by a strong mean field, then ‘growing’ magnetic perturbations into the large-amplitude regime. We present example solutions with non-trivial structure in one, two and three dimensions, demonstrating a clear tendency to form very sharp gradients or discontinuities, unless the solution is one-dimensional. As well as being useful as an input for other calculations, particularly the study of parametric decay, our results provide a natural explanation for the extremely sharp field discontinuities observed across magnetic field switchbacks in the low solar wind.
Acute interstitial pneumonia (AIP) of cattle has been recognized for many decades. While the pathogenesis and risk factors for this condition in pastured cattle are relatively well characterized, there remains a poor understanding of the disease as it occurs in intensively fed cattle such as in beef feedlots. Specifically, in pastured cattle, AIP results from excessive ruminal production of the pneumotoxicant 3-methylindole (3-MI). In feedlot cattle, the evidence to substantiate the role of 3-MI is comparatively deficient and further investigations into the cause, pathogenesis, and control are sorely needed. This review highlights our current understanding of AIP with a focus on the disease as it occurs in feedlot cattle. Additionally, it illustrates the need for further work in understanding the specific animal factors (e.g. the ruminal microbiome, and the role of concurrent diseases), management factors (e.g. animal stocking and vaccination protocols), and dietary factors (e.g. dietary supplements) that may impact the development of AIP and which are relatively unique to the feedlot setting. All stakeholders in the beef industry stand to benefit from a greater understanding of what remains a pressing yet poorly understood issue in beef production.
The zeroth law of turbulence states that, for fixed energy input into large-scale motions, the statistical steady state of a turbulent system is independent of microphysical dissipation properties. This behaviour, which is fundamental to nearly all fluid-like systems from industrial processes to galaxies, occurs because nonlinear processes generate smaller and smaller scales in the flow, until the dissipation – no matter how small – can thermalise the energy input. Using direct numerical simulations and theoretical arguments, we show that in strongly magnetised plasma turbulence such as that recently observed by the Parker Solar Probe spacecraft, the zeroth law is routinely violated. Namely, when such turbulence is ‘imbalanced’ – when the large-scale energy input is dominated by Alfvénic perturbations propagating in one direction (the most common situation in space plasmas) – nonlinear conservation laws imply the existence of a ‘barrier’ at scales near the ion gyroradius. This causes energy to build up over time at large scales. The resulting magnetic-energy spectra bear a strong resemblance to those observed in situ, exhibiting a sharp, steep kinetic transition range above and around the ion-Larmor scale, with flattening at yet smaller scales. The effect thus offers a possible solution to the decade-long puzzle of the position and variability of ion-kinetic spectral breaks in plasma turbulence. The existence of the ‘barrier’ also suggests that, how a plasma is forced at large scales (the imbalance) may have a crucial influence on thermodynamic properties such as the ion-to-electron heating ratio.
While it is well known that every nearly periodic Hamiltonian system possesses an adiabatic invariant, extant methods for computing terms in the adiabatic invariant series are inefficient. The most popular method involves the heavy intermediate calculation of a non-unique near-identity coordinate transformation, even though the adiabatic invariant itself is a uniquely defined scalar. A less well-known method, developed by S. Omohundro, avoids calculating intermediate sequences of coordinate transformations but is also inefficient as it involves its own sequence of complex intermediate calculations. In order to improve the efficiency of future calculations of adiabatic invariants, we derive generally applicable, readily computable formulas for the first several terms in the adiabatic invariant series. To demonstrate the utility of these formulas, we apply them to charged-particle dynamics in a strong magnetic field and magnetic field-line dynamics when the field lines are nearly closed.
Using analytical theory and hybrid-kinetic numerical simulations, we demonstrate that, in a collisionless plasma, long-wavelength ion-acoustic waves (IAWs) with amplitudes $\delta n/n_0 \gtrsim 2/\beta$ (where $\beta \gg {1}$ is the ratio of thermal to magnetic pressure) generate sufficient pressure anisotropy to destabilize the plasma to firehose and mirror instabilities. These kinetic instabilities grow rapidly to reduce the pressure anisotropy by pitch-angle scattering and trapping particles, respectively, thereby impeding the maintenance of Landau resonances that enable such waves’ otherwise potent collisionless damping. The result is wave dynamics that evince a weakly collisional plasma: the ion distribution function is near-Maxwellian, the field-parallel flow of heat resembles its Braginskii form (except in regions where large-amplitude magnetic mirrors strongly suppress particle transport), and the relations between various thermodynamic quantities are more ‘fluid-like’ than kinetic. A nonlinear fluctuation–dissipation relation for self-sustaining IAWs is obtained by solving a plasma-kinetic Langevin problem, which demonstrates suppressed damping, enhanced fluctuation levels and weakly collisional thermodynamics when IAWs with $\delta n/n_0 \gtrsim 2/\beta$ are stochastically driven. We investigate how our results depend upon the scale separation between the wavelength of the IAW and the Larmor radius of the ions, and discuss briefly their implications for our understanding of turbulence and transport in the solar wind and the intracluster medium of galaxy clusters.
The turbulent amplification of cosmic magnetic fields depends upon the material properties of the host plasma. In many hot, dilute astrophysical systems, such as the intracluster medium (ICM) of galaxy clusters, the rarity of particle–particle collisions allows departures from local thermodynamic equilibrium. These departures – pressure anisotropies – exert anisotropic viscous stresses on the plasma motions that inhibit their ability to stretch magnetic-field lines. We present an extensive numerical study of the fluctuation dynamo in a weakly collisional plasma using magnetohydrodynamic (MHD) equations endowed with a field-parallel viscous (Braginskii) stress. When the stress is limited to values consistent with a pressure anisotropy regulated by firehose and mirror instabilities, the Braginskii-MHD dynamo largely resembles its MHD counterpart, particularly when the magnetic field is dynamically weak. If instead the parallel viscous stress is left unabated – a situation relevant to recent kinetic simulations of the fluctuation dynamo and, we argue, to the early stages of the dynamo in a magnetized ICM – the dynamo changes its character, amplifying the magnetic field while exhibiting many characteristics reminiscent of the saturated state of the large-Prandtl-number (${Pm}\gtrsim {1}$) MHD dynamo. We construct an analytic model for the Braginskii-MHD dynamo in this regime, which successfully matches simulated dynamo growth rates and magnetic-energy spectra. A prediction of this model, confirmed by our numerical simulations, is that a Braginskii-MHD plasma without pressure-anisotropy limiters will not support a dynamo if the ratio of perpendicular and parallel viscosities is too small. This ratio reflects the relative allowed rates of field-line stretching and mixing, the latter of which promotes resistive dissipation of the magnetic field. In all cases that do exhibit a viable dynamo, the generated magnetic field is organized into folds that persist into the saturated state and bias the chaotic flow to acquire a scale-dependent spectral anisotropy.
To assess the impact of lisdexamfetamine dimesylate (LDX; Vyvanse®, Shire US Inc.), which is the first long-acting prodrug stimulant indicated for treatment of attention-deficit/hyperactivity disorder (ADHD) in children and adults in the United States, on performance and quality of life (QOL) in adults with ADHD.
Methods
Subjects (n=142; aged 18 to 55 years) with ADHD entered a 4-week open-label dose-optimisation phase, then a 2-week, double-blind crossover phase. The primary efficacy measure was the average postdose total score on the Permanent Product Measure of Performance (PERMP) math test given predose and 2, 4, 8, 10, 12, and 14 hours postdose. The Adult ADHD Impact Module (AIM-A) was self-administered during the dose-optimisation phase. Safety was assessed by monitoring adverse events (AEs).
Results
In the intention-to-treat population (n=105), postdose average PERMP least squares mean (SE) scores were higher (P< .0001) for LDX (312.9 [8.59]) vs placebo (289.5 [8.59]) and at every postdose time point ≥14 hours (P≤.0017 for each). Mean change from baseline scores on AIM-A subscales (n=127) showed improvement (P< .001) with LDX in 6 measured QOL domains (living with ADHD; general wellbeing; work, home, and school performance and daily functioning; relationships and communication; interference with life; and concern caused by symptoms). Treatment-emergent AEs (≥10%) in the dose-optimisation phase were decreased appetite (36.6%), dry mouth (30.3%), headache (19.7%), and insomnia (18.3%).
Conclusions
LDX improved QOL and performance (up to 14 hours) and demonstrated a safety profile consistent with long-acting stimulant use.
Supported by funding from Shire Development Inc., Wayne, PA, US.
The Health Utilities Index-Mark 2 (HUI2), a generic instrument for assessing health status, is an important effectiveness input for pharmacoeconomic modelling. It has not previously been used in patients with attention deficit/hyperactivity disorder (ADHD).
Objective:
To use HUI2 to assess health utility in patients aged 6–17 years with ADHD receiving the prodrug stimulant lisdexamfetamine dimesylate (LDX).
Methods:
SPD489-325 was a 7-week, randomized, double-blind, placebo-controlled trial of LDX, with osmotic-release oral system methylphenidate (OROSMPH) as a reference treatment. Patients’ parents or guardians completed HUI2 questionnaires at baseline and weeks 4 and 7. Utilities were estimated for treatment responders and non-responders, with response defined as a Clinical Global Impressions-Improvement (CGI-I) score of 1 or 2, or a ≥25% or ≥30% reduction in ADHD Rating Scale IV (ADHD-RS-IV) total score.
Results:
Of 336 patients randomized, 317 were included in the full analysis set (LDX, n=104; OROS-MPH, n=107; placebo, n=106) and 196 completed the study. At endpoint, mean HUI2 utility scores across all treatment groups were higher for responders than non-responders when response was based on CGI-I score (responders: 0.896 [SD, 0.0990]; non-responders: 0.838 [0.1421]), on a ≥25% reduction in ADHD-RS-IV score from baseline (responders, 0.899 [0.0969]; non-responders, 0.809 [0.1474]), or on a ≥30% reduction in ADHD-RS-IV score from baseline (responders, 0.902 [0.0938]; non-responders 0.814 [0.1477]).
Conclusions:
The HUI2 instrument is sensitive to treatment response in the child and adolescent ADHD patient population. Health utilities generated using HUI2 are therefore suitable for cost effectiveness evaluations of ADHD medications.
Australian conservation cropping systems are practiced on very large farms (approximately 3,000 ha) where herbicides are relied on for effective and timely weed control. In many fields, though, there are low weed densities (e.g., <1.0 plant 10 m−2) and whole-field herbicide treatments are wasteful. For fallow weed control, commercially available weed detection systems provide the opportunity for site-specific herbicide treatments, removing the need for whole-field treatment of fallow fields with low weed densities. Concern about the sustainability of herbicide-reliant weed management systems remain and there has not been interest in the use of weed detection systems for alternative weed control technologies, such as targeted tillage. In this paper, we discuss the use of a targeted tillage technique for site-specific weed control in large-scale crop production systems. Three small-scale prototypes were used for engineering and weed control efficacy testing across a range of species and growth stages. With confidence established in the design approach and a demonstrated 100% weed-control potential, a 6-m wide pre-commercial prototype, the “Weed Chipper,” was built incorporating commercially available weed-detection cameras for practical field-scale evaluation. This testing confirmed very high (90%) weed control efficacies and associated low levels (1.8%) of soil disturbance where the weed density was fewer than 1.0 plant 10 m−2 in a commercial fallow. These data established the suitability of this mechanical approach to weed control for conservation cropping systems. The development of targeted tillage for fallow weed control represents the introduction of site-specific, nonchemical weed control for conservation cropping systems.
We propose that pressure anisotropy causes weakly collisional turbulent plasmas to self-organize so as to resist changes in magnetic-field strength. We term this effect ‘magneto-immutability’ by analogy with incompressibility (resistance to changes in pressure). The effect is important when the pressure anisotropy becomes comparable to the magnetic pressure, suggesting that in collisionless, weakly magnetized (high-$\unicode[STIX]{x1D6FD}$) plasmas its dynamical relevance is similar to that of incompressibility. Simulations of magnetized turbulence using the weakly collisional Braginskii model show that magneto-immutable turbulence is surprisingly similar, in most statistical measures, to critically balanced magnetohydrodynamic turbulence. However, in order to minimize magnetic-field variation, the flow direction becomes more constrained than in magnetohydrodynamics, and the turbulence is more strongly dominated by magnetic energy (a non-zero ‘residual energy’). These effects represent key differences between pressure-anisotropic and fluid turbulence, and should be observable in the $\unicode[STIX]{x1D6FD}\gtrsim 1$ turbulent solar wind.
In collisionless and weakly collisional plasmas, such as hot accretion flows onto compact objects, the magnetorotational instability (MRI) can differ significantly from the standard (collisional) MRI. In particular, pressure anisotropy with respect to the local magnetic-field direction can both change the linear MRI dispersion relation and cause nonlinear modifications to the mode structure and growth rate, even when the field and flow perturbations are very small. This work studies these pressure-anisotropy-induced nonlinearities in the weakly nonlinear, high-ion-beta regime, before the MRI saturates into strong turbulence. Our goal is to better understand how the saturation of the MRI in a low-collisionality plasma might differ from that in the collisional regime. We focus on two key effects: (i) the direct impact of self-induced pressure-anisotropy nonlinearities on the evolution of an MRI mode, and (ii) the influence of pressure anisotropy on the ‘parasitic instabilities’ that are suspected to cause the mode to break up into turbulence. Our main conclusions are: (i) The mirror instability regulates the pressure anisotropy in such a way that the linear MRI in a collisionless plasma is an approximate nonlinear solution once the mode amplitude becomes larger than the background field (just as in magnetohyrodynamics). This implies that differences between the collisionless and collisional MRI become unimportant at large amplitudes. (ii) The break up of large-amplitude MRI modes into turbulence via parasitic instabilities is similar in collisionless and collisional plasmas. Together, these conclusions suggest that the route to magnetorotational turbulence in a collisionless plasma may well be similar to that in a collisional plasma, as suggested by recent kinetic simulations. As a supplement to these findings, we offer guidance for the design of future kinetic simulations of magnetorotational turbulence.