A Universal Planetary Substorm Model

Lead Research Organisation: University of Bath
Department Name: Electronic and Electrical Engineering

Abstract

The sun continuously emits a stream of electrically charged particles, known as the solar wind, into space. This wind, travelling at 100s to 1000s km/s, propagates throughout the solar system and all the planets move through it as they orbit the sun. Planets like the Earth are protected from the dangers of the solar wind since the charged particles that it consists of are hindered from striking the surface by a strong internally generated magnetic field. Without this field, the solar wind would strip away the atmosphere and cause enormous damage to living cells, making macroscopic life as we understand it impossible. Although the surface is protected, the solar wind does have important effects, the largest of which is the distortion of Earth's magnetic field, which becomes compressed on the up-stream side of the solar wind and stretched into a long "magnetotail" on the down-stream side. This magnetotail extends beyond the orbit of the moon to a distance over 1,000 times the radius of Earth itself. Events in the magnetotail known as "substorms" accelerate particles from space into Earth's upper atmosphere where they have numerous impacts, the most spectacular of which is the triggering of the Aurora Borealis and Aurora Australis. There are also numerous technological impacts, including electrical charging and increased drag on spacecraft in Low Earth Orbit, which can lead to reduced operational lifetime of the satellites.

Substorms can be described as a simple electrical circuit with a generator in the magnetotail and a resistor in the upper atmosphere linked by "wires" following lines of magnetic force, however the effects of this circuit are not easily predictable because the generator is not creating a steady current. Instead the current varies depending on the "weather conditions" of the solar wind, which provides the energy source for the circuit.

Mercury, Saturn and Jupiter have magnetotails similar in form to that of Earth and also experience substorms. At Mercury the substorm circuit generator is driven by the solar wind, as it is at Earth but at Saturn and Jupiter there is another source of energy for the generator - the planets' own rapid rotation. Jupiter's substorm circuit generator is dominated by this rotational energy source but is still influenced by the solar wind. At Saturn the substorm generator's energy is supplied in significant amounts by both rotational and solar wind inputs.

The aim of this project is to model the substorm electrical circuit for any planet with a magnetotail similar to that of Earth or Jupiter with the intent of understanding the circumstances when substorms are present, when they occur in a predictable, periodic fashion and when they exhibit chaotic, unpredictable behaviour in terms of the energy input from the solar wind and rotational sources. This will allow limits to be placed on the timescale that forecasting of the effects of the substorm circuit is possible for, in the same way that limits can be calculated for the useful timescale of a weather forecast.

Because the model will not be limited to any one set of planetary characteristics (particularly rotational speed, magnetic field strength and orbital distance) or specific set of solar wind conditions, it will not be limited to just one planet but instead can be used for any planet with a magnetotail like Earth's. This means it can be used to make predictions about planets outside the solar system which in turn can be used to help understand the habitability of these planets of from the perspective of protection of the surface from stellar wind particles.

Publications

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Title Mechanical Analogue of Earth-like Planetary Mangetotail Dynamics 
Description A relaxation oscillator model of Earth-like magnetotail dynamics, applicable to Mercury, Earth, Jupiter, Saturn and hypothetical exoplanet cases. The model is analogous to a dripping tap and provides good qualitative agreement with observations of the dynamical behaviour of Earth-like magnetotails. The model is capable of incorporating the Dungey Cycle and the Vasyliunas Cycle, unlike any previous low dimensional model of magnetotail dynamics. The model also incorporates adjustable levels and types of dynamical noise, also not previously incorporated in this type of model. 
Type Of Material Computer model/algorithm 
Year Produced 2018 
Provided To Others? No  
Impact The model explains the observed global behaviour of Earth's magnetotail under varying levels of solar wind driving. The dynamics can be switched from periodic to deterministically chaotic by increasing the level of driving. The impact of dynamical noise (noisy variations in driving) has been shown to be qualitatively distinct from the impact of instrument noise (measurement error). 
 
Title New method of estimating Correlation dimension from many Takens embeddings of data 
Description It is now possible to generate many (order of hundreds) Takens embeddings of the same data in a short time frame (hours) instead of attempting to guess the optimal embedding parameters and only doing in the region of 10 embeddings. This is useful as no reliable method of establishing optimal embedding parameters a priori has been discovered. It leads to the problem of determining what the scaling region is from so many embeddings, rather than being uncertain if the small number of embeddings previously available were truly representative. A solution has been developed, tested and found to be reliable. The technique is to take a histogram of the results across the whole embedding, without attempting to distinguish a scaling region. Repeat for all embeddings, adding the results to the same histogram. The resulting histogram has a clear global maximum which is taken to be the Correlation dimension of the data. Tests against simulations of systems with known Correlation dimension show good results. 
Type Of Material Data analysis technique 
Year Produced 2022 
Provided To Others? No  
Impact Application to experimental data not yet complete. 
 
Title Rapid near-neighbour searching 
Description Finding "near neighbours" (data points within a specified distance of some reference datum in an abstract or physical space) has many uses, not least in non-linear time series analysis, dynamical system analysis and noise reduction. Traditionally, this has been slow due to computing speed and memory limitations. To mitigate this, "box assisted" search techniques are employed to cut down the number of calculations required. All such techniques are superceded by a new and extremely simple Matlab algorithm which calculates all inter-point distances for a given data set, two orders of magnitude faster than the standard box-assisted algorithm. This brings new opportunities in regard to such analysis techniques as Correlation dimension and Information dimension estimation, largest Lyapunov exponent estimation and non-linear noise reduction, since it is now possible to search the parameter spaces of these techniques and select optimal results a posteriori, instead of attempting (unreliably) to a priori select the best parameter values. A paper describing the algorithm has been submitted for publication but not yet accepted. 
Type Of Material Computer model/algorithm 
Year Produced 2021 
Provided To Others? No  
Impact Application of these algorithms is under way