MIST

By Oliver Allanson (University of Reading)

The Earth's outer radiation belt is a dynamic and extended radiation environment within the inner magnetosphere, composed of energetic plasma that is trapped by the geomagnetic field. The size and location of the outer radiation belt varies dramatically in response to solar wind variability - orders of magnitude changes in the electron flux can occur on short timescales (~hours). However, it is very challenging to accurately predict, or model, fluxes within the radiation belt. This is a pressing concern given the hundreds of satellites that orbit within this hazardous environment, and so the prediction of its variability is a key goal of the magnetospheric space weather community (e.g. see Horne et al., 2013).

Most physics-based computer models of particle dynamics in the radiation belts rely upon the assumption of slow perturbations to electron distributions due to interactions with low amplitude electromagnetic waves. However, satellite observations have shown that high amplitude waves and correspondingly large changes in electron distributions are not rare (e.g. see a recent example with observations from the ARASE satellite in Kurita et al., 2018). In our novel electromagnetic particle-in-cell numerical experiments, we analyse the diffusion in energy and pitch angle space of 100 million individual high-energy electrons in conditions typical of the radiation belt environment - due to interactions with externally driven electromagnetic waves. The method is illustrated in Figure 1. We present two main conclusions:

(i) On very short timescales (~0.1 second) we observe an initial ‘anomalous’ electron response, for which the rate of diffusion is nonlinear in time.

(ii) After the initial transient phase we observe a normal diffusive response that is consistent with quasilinear theory.

Figure 1: A schematic illustrating the particle-in-cell numerical experiment.

 The results demonstrate the exciting capabilities of our new experimental technique. Here we prove the concept for conditions that are unlikely to deviate from standard theory, and in future experiments this framework will allow us to investigate the changing nature of the electron response with increased electromagnetic wave amplitude.

For more information, please see the paper:

Allanson, O.,  Watt, C. E. J.,  Ratcliffe, H.,  Meredith, N. P.,  Allison, H. J.,  Bentley, S. N., et al. ( 2019).  Particle‐in‐cell experiments examine electron diffusion by whistler‐mode waves: 1. Benchmarking with a cold plasma. Journal of Geophysical Research: Space Physics,  124. https://doi.org/10.1029/2019JA027088 

by Georgios Nicolaou (MSSL, UCL)

The effective polytropic index of space plasmas γ is crucial for understanding the dynamics of the plasma particles. For instance, numerous theoretical descriptions and simulations of plasmas, demand the knowledge of the effective polytropic index for accurate calculations.  

Several studies, determined γ within different plasma regions, using single spacecraft observations of the plasma density n and temperature T. The effective polytropic index γ is typically determined from a linear chi-squared minimization fitting of lnT as a function of lnn.

In this paper, we investigate the accuracy of γ calculations based on the standard fitting analysis, considering plasma n and T measurements with a certain level of uncertainty σ_n and σ_T respectively (see Figure 1). We model typical plasmas, and we show that uncertainty in the plasma density measurements introduces a systematic error in the calculation of γ, and potentially leads to artificial isothermal indices (Figure 1, left). On the other hand, uncertainty in the plasma temperature measurements introduces a statistical error in the calculation of γ (Figure 1, right). We analyze Wind spacecraft observations of solar wind protons in order to investigate the propagated uncertainties in real plasma applications, confirming our model predictions (Figure 1).

These results highlight how uncertainties in plasma measurements can lead to erroneous values of the poytropic index. In this study we present a new data-analysis approach for reducing the number of erroneous data-points from future analyses.

Figure 1. Normalized histograms of (left) γ as a function of σ_n/n, for σ_T/T < 15% and (right) γ as a function of σ_T/T, for σ_n/n < 1%. The white line is the mean value of the histogram in each column. We display only the range of uncertainties for which we have more than 100 data points. On each panel, we show the predictions of our model (red) for plasma parameters corresponding to the mode values of each parameter for the analyzed intervals.

For more information, please see the paper:

Nicolaou, G., G. Livadiotis, R. T. Wicks (2019). On the Calculation of the Effective Polytropic Index in Space Plasmas. Entropy, 21, 997. https://doi.org/10.3390/e21100997.

by Georgios Nicolaou (MSSL, UCL)

The polytropic process determines a relationship between the plasma density and temperature, during the transition of the plasma from one equilibrium state to another under constant specific heat. This process is described by the effective polytropic index, which can be determined by the analysis of plasma density and temperature measurements, and is a crucial parameter in determining the dynamics of the plasma.

Over the last few decades numerous studies have shown that the velocities of the plasma particles often follow kappa distribution functions. The kappa index that labels and governs these distributions also becomes a key parameter to understand the plasma dynamics.

Interestingly, recent studies have shown that the polytropic indices and kappa indices of space plasmas are related, in the presence of potential energy. Moreover, the relationship between the two indices defines the potential degrees of freedom.

This is the first statistical study to analyze Wind spacecraft observations to derive the polytropic index and the kappa index of solar wind protons and investigate their relationship, over the last two solar cycles. We show that, most of the time, the two indices are related, exactly as predicted by the theory. When able, we quantify the relation in order to derive the potential degrees of freedom. Among others, we show that an enhanced solar activity and/or interplanetary magnetic field, reduces the potential degrees of freedom, and decrease the dimensionality of a typical electric field potential from d_r = 3 in solar minimum, to d_r = 2 in solar maximum (Figure 1).

Overall, these results identify fundamental properties of the solar wind plasma, that demonstrate clear dependences on solar cycle.

Figure 1. Dimensionality d_r for a typical interplanetary potential as a function of sunspot number S_n. The linear fit to data points (black dash) is also shown. The results indicate that the potential dimensionality d_r reduces with increasing S_n.

For more information, please see the paper:

Nicolaou G. and G. Livadiotis (2019). Long-term correlations of polytropic indices with Kappa distributions in solar wind plasma near 1 AU. The Astrophysical Journal, 884:52, https://iopscience.iop.org/article/10.3847/1538-4357/ab31ad/meta 

By Carl Haines (University of Reading)

Variability in the near-Earth solar wind conditions can adversely affect a number of ground- and space-based technologies.  Some of these space weather impacts on ground infrastructure are expected to increase primarily with geomagnetic storm intensity, but also storm duration, through time-integrated effects. Forecasting storm duration is also necessary for scheduling the resumption of safe operating of affected infrastructure. It is therefore important to understand the degree to which storm intensity and duration are related.

In this study, we use the recently recalibrated aa index, aa_H, which provides a global measure of the level of geomagnetic disturbance. We analyse the relationship between geomagnetic storm intensity and storm duration over the past 150 years, further adding to our understanding of the climatology of geomagnetic activity. In particular, we construct and test a simple probabilistic forecast of storm duration based on storm intensity. Using a peak-above-threshold approach to define storms, we observe that more intense storms do indeed last longer but with a non-linear relationship (See Figure 1a).

Figure 1 (a) The mean duration (red) and number of storms (blue) plotted as a function of storm intensity. (b) The probability that a storm will last at least 24 hours plotted as a function of storm intensity. The black line shows the observed probability and the red line shows the model output.

Next, we analysed the distribution of storm durations in different intensity classes. We found them to be approximately lognormal, with parameters depending on the storm intensity. On this basis we created a method to probabilistically predict storm duration given peak intensity. Equations are given to find lognormal parameters as a function of storm peak intensity. From these, a distribution of duration can be created and hence a probabilistic estimate of the duration of this storm is available. This can be used to predict the probability a storm will last at least e.g. 24 hours. Figure 1b shows the output of the model for a range of storm peak intensity compared against a test set of the aa_H index. The model has good agreement with the observations and provides a robust method for estimating geomagnetic storm duration. The results demonstrate significant advancements in not only understanding the properties and structure of storms, but also how we can predict and forecast these dynamic and hazardous events.

For more information, please see the paper:

Haines, C., Owens, M.J., Barnard, L. et al. Sol Phys (2019) 294: 154. https://doi.org/10.1007/s11207-019-1546-z