On the Two Approaches to Incorporate Wave‐Particle Resonant Effects Into Global Test Particle Simulations

Energetic electron dynamics in the Earth's radiation belts and near-Earth plasma sheet are controlled by multiple processes operating on very different time scales: from storm-time magnetic field reconfiguration on a timescale of hours to individual resonant wave-particle interactions on a timescale of milliseconds. The most advanced models for such dynamics either include test particle simulations in electromagnetic fields from global magnetospheric models, or those that solve the Fokker-Plank equation for long-term effects of wave-particle resonant interactions. The most prospective method, however, would be to combine these two classes of models, to allow the inclusion of resonant electron scattering into simulations of electron motion in global magnetospheric fields. However, there are still significant outstanding challenges that remain regarding how to incorporate the long term effects of wave-particle interactions in test-particle simulations. In this paper, we describe in details two approaches that incorporate electron scattering in test particle simulations: stochastic differential equation (SDE) approach and the mapping technique. Both approaches assume that wave-particle interactions can be described as a probabilistic process that changes electron energy, pitch-angle, and thus modifies the test particle dynamics. To compare these approaches, we model electron resonant interactions with field-aligned whistler-mode waves in dipole magnetic fields. This comparison shows advantages of the mapping technique in simulating the nonlinear resonant effects, but also underlines that more significant computational resources are needed for this technique in comparison with the SDE approach. We further discuss applications of both approaches in improving existing models of energetic electron dynamics

From one-dimensional fields to Vlasov equilibria: theory and application of Hermite polynomials

We consider the theory and application of a solution method for the inverse problem in collisionless equilibria, namely that of calculating a Vlasov–Maxwell equilibrium for a given macroscopic (fluid) equilibrium. Using Jeans’ theorem, the equilibrium distribution functions are expressed as functions of the constants of motion, in the form of a Maxwellian multiplied by an unknown function of the canonical momenta. In this case it is possible to reduce the inverse problem to inverting Weierstrass transforms, which we achieve by using expansions over Hermite polynomials. A sufficient condition on the pressure tensor is found which guarantees the convergence and the boundedness of the candidate solution, when satisfied. This condition is obtained by elementary means, and it is clear how to put it into practice. We also argue that for a given pressure tensor for which our method applies, there always exists a positive distribution function solution for a sufficiently magnetised plasma. Illustrative examples of the use of this method with both force-free and non-force-free macroscopic equilibria are presented, including the full verification of a recently derived distribution function for the force-free Harris sheet (Allanson et al., Phys. Plasmas, vol. 22 (10), 2015, 102116). In the effort to model equilibria with lower values of the plasma beta, solutions for the same macroscopic equilibrium in a new gauge are calculated, with numerical results presented for beta=0.05

An exact collisionless equilibrium for the force-free Harris sheet with low plasma beta

We present a first discussion and analysis of the physical properties of a new exact collisionless equilibrium for a one-dimensional nonlinear force-free magnetic field, namely, the force-free Harris sheet. The solution allows any value of the plasma beta, and crucially below unity, which previous nonlinear force-free collisionless equilibria could not. The distribution function involves infinite series of Hermite polynomials in the canonical momenta, of which the important mathematical properties of convergence and non-negativity have recently been proven. Plots of the distribution function are presented for the plasma beta modestly below unity, and we compare the shape of the distribution function in two of the velocity directions to a Maxwellian distribution

Neutral and non-neutral collisionless plasma equilibria for twisted flux tubes: the Gold-Hoyle model in a background field

We calculate exact one-dimensional collisionless plasma equilibria for a continuum of flux tube models, for which the total magnetic field is made up of the “force-free” Gold-Hoyle magnetic flux tube embedded in a uniform and anti-parallel background magnetic field. For a sufficiently weak background magnetic field, the axial component of the total magnetic field reverses at some finite radius. The presence of the background magnetic field means that the total system is not exactly force-free, but by reducing its magnitude, the departure from force-free can be made as small as desired. The distribution function for each species is a function of the three constants of motion; namely, the Hamiltonian and the canonical momenta in the axial and azimuthal directions. Poisson's equation and Ampère's law are solved exactly, and the solution allows either electrically neutral or non-neutral configurations, depending on the values of the bulk ion and electron flows. These equilibria have possible applications in various solar, space, and astrophysical contexts, as well as in the laboratory

Evidence-based decision support for pediatric rheumatology reduces diagnostic errors.

BACKGROUND: The number of trained specialists world-wide is insufficient to serve all children with pediatric rheumatologic disorders, even in the countries with robust medical resources. We evaluated the potential of diagnostic decision support software (DDSS) to alleviate this shortage by assessing the ability of such software to improve the diagnostic accuracy of non-specialists. METHODS: Using vignettes of actual clinical cases, clinician testers generated a differential diagnosis before and after using diagnostic decision support software. The evaluation used the SimulConsult® DDSS tool, based on Bayesian pattern matching with temporal onset of each finding in each disease. The tool covered 5405 diseases (averaging 22 findings per disease). Rheumatology content in the database was developed using both primary references and textbooks. The frequency, timing, age of onset and age of disappearance of findings, as well as their incidence, treatability, and heritability were taken into account in order to guide diagnostic decision making. These capabilities allowed key information such as pertinent negatives and evolution over time to be used in the computations. Efficacy was measured by comparing whether the correct condition was included in the differential diagnosis generated by clinicians before using the software ( unaided ), versus after use of the DDSS ( aided ). RESULTS: The 26 clinicians demonstrated a significant reduction in diagnostic errors following introduction of the software, from 28% errors while unaided to 15% using decision support (p \u3c 0.0001). Improvement was greatest for emergency medicine physicians (p = 0.013) and clinicians in practice for less than 10 years (p = 0.012). This error reduction occurred despite the fact that testers employed an open book approach to generate their initial lists of potential diagnoses, spending an average of 8.6 min using printed and electronic sources of medical information before using the diagnostic software. CONCLUSIONS: These findings suggest that decision support can reduce diagnostic errors and improve use of relevant information by generalists. Such assistance could potentially help relieve the shortage of experts in pediatric rheumatology and similarly underserved specialties by improving generalists\u27 ability to evaluate and diagnose patients presenting with musculoskeletal complaints. TRIAL REGISTRATION: ClinicalTrials.gov ID: NCT02205086

The development of a space climatology: 3. Models of the evolution of distributions of space weather variables with timescale

We study how the probability distribution functions of power input to the magnetosphere Pα and of the geomagnetic ap and Dst indices vary with averaging timescale, , between 3 hours and 1 year. From this we develop and present algorithms to empirically model the distributions for a given and a given annual mean value. We show that lognormal distributions work well for ap, but because of the spread of Dst for low activity conditions, the optimum formulation for Dst leads to distributions better described by something like the Weibull formulation. Annual means can be estimated using telescope observations of sunspots and modelling, and so this allows the distributions to be estimated at any given between 3 hour and 1 year for any of the past 400 years, which is another important step towards a useful space weather climatology. The algorithms apply to the core of the distributions and can be used to predict the occurrence rate of “large” events (in the top 5% of activity levels): they may contain some, albeit limited, information relevant to characterizing the much rarer “superstorm” events with extreme value statistics. The algorithm for the Dst index is the more complex one because, unlike ap, Dst can take on either sign and future improvements to it are suggested

The development of a space climatology: 1. solar-wind magnetosphere coupling as a function of timescale and the effect of data gaps

Different terrestrial space weather indicators (such as geomagnetic indices, transpolar voltage, and ring current particle content) depend on different “coupling functions” (combinations of near-Earth solar wind parameters) and previous studies also reported a dependence on the averaging timescale, {\tau}. We study the relationships of the am and SME geomagnetic indices to the power input into the magnetosphere P_{\alpha}, estimated using the optimum coupling exponent {\alpha} for a range of {\tau} between 1 min and 1 year. The effect of missing data is investigated by introducing synthetic gaps into near-continuous data and the best method for dealing with them when deriving the coupling function, is formally defined. Using P_{\alpha}, we show that gaps in data recorded before 1995 have introduced considerable errors into coupling functions. From the near-continuous solar wind data for 1996-2016, we find {\alpha} = 0.44 plus/minus 0.02 and no significant evidence that {\alpha} depends on {\tau}, yielding P_{\alpha} = B^0.88 Vsw^1.90 (mswNsw)^0.23 sin4({\theta}/2), where B is the Interplanetary Magnetic Field (IMF), Nsw the solar wind number density, msw its mean ion mass, Vsw its velocity and {\theta} is the IMF clock angle in the Geocentric Solar Magnetospheric reference frame. Values of P_{\alpha} that are accurate to within plus/minus 5% for 1996-2016 have an availability of 83.8% and the correlation between P_{\alpha} and am for these data is shown to be 0.990 (between 0.972 and 0.997 at the 2{\sigma} uncertainty level), 0.897 plus/minus 0.004, and 0.790 plus/minus 0.03, for {\tau} of 1 year, 1 day and 3 hours, respectively, and that between P_{alpha} and SME at {\tau} of 1 min. is 0.7046 plus/minus 0.0004

Particle-in-cell experiments examine electron diffusion by whistler-mode waves: 2. Quasilinear and nonlinear dynamics

Test-particle codes indicate that electron dynamics due to interactions with low amplitude incoherent whistler mode-waves can be adequately described by quasilinear theory. However there is significant evidence indicating that higher amplitude waves cause electron dynamics not adequately described using quasilinear theory. Using the method that was introduced in Allanson et al. (2019, https://dx.doi.org/10.1029/2019JA027088), we track the dynamical response of electrons due to interactions with incoherent whistler-mode waves, across all energy and pitch angle space. We conduct 5 experiments each with different values of the electromagnetic wave amplitude. We find that the electron dynamics agree well with the quasilinear theory diffusion coefficients for low amplitude incoherent waves with $(B_{\text{w,rms}}/B_0)^2\approx 3.7\cdot 10^{-10}$, over a timescale $T$ of the order of 1000 gyroperiods. However the resonant interactions with higher amplitude waves cause significant non-diffusive dynamics as well as diffusive dynamics. When electron dynamics are extracted and analyzed over timescales shorter than $T$, we are able to isolate both the diffusive and non-diffusive (advective) dynamics. Interestingly, when considered over these appropriately shorter timescales (of the order of hundreds or tens of gyroperiods), the diffusive component of the dynamics agrees well with the predictions of quasilinear theory, even for wave amplitudes up to $(B_{\text{w,rms}}/B_0)^2\approx 5.8\cdot 10^{-6}$. Quasilinear theory is based on fundamentally diffusive dynamics, but the evidence presented herein also indicates the existence of a distinct advective component. Therefore, the proper description of electron dynamics in response to wave-particle interactions with higher amplitude whistler-mode waves may require Fokker-Planck equations that incorporate diffusive and advective terms