arXiv subjects

N. W. Watkins

Publications and source records attributed to N. W. Watkins.

23 records · Page 2Linked to original sources

arXiv2001

Ambiguities in Determination Of Self-Affinity in the AE-index Time Series

The interaction between the Earth's magnetic field and the solar wind plasma results in a natural plasma confinement system which stores energy. Dissipation of this energy through Joule heating in the ionosphere can be studied via the Auroral Electrojet (AE) index. The apparent broken power law form of the frequency spectrum of this index has motivated investigation of whether it can be described as fractal coloured noise. One frequently-applied test for self-affinity is to demonstrate linear scaling of the logarithm of the structure function of a time series with the logarithm of the dilation factor $λ$. We point out that, while this is conclusive when applied to signals that are self-affine over many decades in $λ$, such as Brownian motion, the slope deviates from exact linearity and the conclusions become ambiguous when the test is used over shorter ranges of $λ$. We demonstrate that non self-affine time series made up of random pulses can show near-linear scaling over a finite dynamic range such that they could be misinterpreted as being self-affine. In particular we show that pulses with functional forms such as those identified by Weimer within the $AL$ index, from which $AE$ is partly derived, will exhibit nearly linear scaling over ranges similar to those previously shown for $AE$ and $AL$. The value of the slope, related to the Hurst exponent for a self-affine fractal, seems to be a more robust discriminator for fractality, if other information is available.

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arXiv2001

What can we infer about the underlying physics from burst distributions observed in an RMHD simulation ?

We determine that the sizes of bursts in mean-square current density in a reduced magnetohydrodynamic (RMHD)simulation follow power-law probability density function (PDF). The PDFs for burst durations and waiting time between bursts are clearly not exponential and could also be power-law. This suffices to distinguish their behaviour from the original Bak et al. sandpile model which had exponential waiting time PDFs. However, it is not sufficient to distinguish between turbulence, some other SOC-like models, and other red noise sources.

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arXiv2000

Power law burst and inter-burst interval distributions in the solar wind: turbulence or dissipative SOC ?

We calculate for the first time the probability density functions (PDFs) P of burst energy e, duration T and inter-burst interval tau for a known turbulent system in nature. Bursts in the earth-sun component of the Poynting flux at 1 AU in the solar wind were measured using the MFI and SWE experiments on the NASA WIND spacecraft. We find P(e) and P(T) to be power laws, consistent with self-organised criticality (SOC). We find also a power law form for P(tau) that distinguishes this turbulent cascade from the exponential P(tau) of ideal SOC, but not from some other SOC-like sandpile models. We discuss the implications for the relation between SOC and turbulence.

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arXiv2000

Testing the SOC hypothesis for the magnetosphere

As noted by Chang, the hypothesis of Self-Organised Criticality provides a theoretical framework in which the low dimensionality seen in magnetospheric indices can be combined with the scaling seen in their power spectra and the recently-observed plasma bursty bulk flows. As such, it has considerable appeal, describing the aspects of the magnetospheric fuelling:storage:release cycle which are generic to slowly-driven, interaction-dominated, thresholded systems rather than unique to the magnetosphere. In consequence, several recent numerical "sandpile" algorithms have been used with a view to comparison with magnetospheric observables. However, demonstration of SOC in the magnetosphere will require further work in the definition of a set of observable properties which are the unique "fingerprint" of SOC. This is because, for example, a scale-free power spectrum admits several possible explanations other than SOC. A more subtle problem is important for both simulations and data analysis when dealing with multiscale and hence broadband phenomena such as SOC. This is that finite length systems such as the magnetosphere or magnetotail will by definition give information over a small range of orders of magnitude, and so scaling will tend to be narrowband. Here we develop a simple framework in which previous descriptions of magnetospheric dynamics can be described and contrasted. We then review existing observations which are indicative of SOC, and ask if they are sufficient to demonstrate it unambiguously, and if not, what new observations need to be made?

astro-ph↗

arXiv1999

Signatures of dual scaling regimes in a simple avalanche model for magnetospheric activity

Recently, the paradigm that the dynamic magnetosphere displays sandpile-type phenomenology has been advanced, in which energy dissipation is by means of avalanches which do not have an intrinsic scale. This may in turn imply that the system is in a self organised critical (SOC) state. Indicators of internal processes are consistent with this, examples are the power law dependence of the power spectrum of auroral indices, and in-situ magnetic field observations in the earth's geotail. An apparent paradox is that, rather than power laws, substorm statistics exhibit probability distributions with characteristic scales. Here we discuss a simple sandpile model which yields for energy discharges due to internal reorganization a probability distribution that is a power law, whereas systemwide discharges (flow of "sand" out of the system) form a distinct group whose probability distribution has a well defined mean. We analyse the model over a wide dynamic range whereupon two regimes having different inverse power law statistics emerge, corresponding to reconfigurations over two distinct scaling regions: short scale sizes sensitive to the discrete nature of the sandpile model, and long scale sized up to the system size which correspond to the continuous limit of the model. The latter are anticipated to correspond to large scale systems such as the magnetosphere. Since the energy inflow may be highly variable, we examined the response of the model under strong or variable loading and established that the power law signature of the large scale internal events persists. The interval distribution of these events is also discussed.

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