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Trajectories of Charged Particles in the Jovian Magnetic Field

##### Students from Kings College Maths School and Dr Dimitrios Millas

Magnetospheres are bubbles around planets (and sometimes moons!) that are created by the magnetic field of the planet. Jupiter's strong magnetic field, very rapid rotation (a Jupiter day is less than 10 hours long) and volcanic moon Io, lead Jupiter to produce the largest magnetosphere in the solar system. If you could see this structure with your eyes, you would see an object in the night sky that appeared to be 6 times the size of the moon (although it is much larger than this, but much further away). This huge magnetosphere provides a laboratory in space to explore how particles behave in magnetic fields across the Universe. The image below illustrates what you would see in the sky if you had magical magnetospheric glasses.

Illustration of the size of Jupiter’s magnetosphere in the night sky if it could be seen by human eye [Credit: NASA/ESA]

For this project, we examined the motion of charged particles in the magnetic field of Jupiter. To achieve this, we used a simple 2-dimensional magnetic field profile of Jupiter's magnetosphere and a numerical code which traces different particles in this environment.

For the necessary theoretical background, we first introduced the case of Earth's magnetic field and discussed the differences that we must take into account when we shift our attention to the Jupiter case. In addition, we explored the motion of charged particles in some simple magnetic field profiles, where the equations of motion can be solved analytically, either in 2D or in 3D.

For the numerical part of the project, we started by establishing the necessity of using numerical solutions in problems where an analytical solution cannot be obtained – even in seemingly simple cases. Then, we experimented with codes that were used to verify the analytical predictions for some simple problems; these involved the trajectory of the Earth around the Sun and the motion of charged particles in the simple cases that were shown during the theoretical part.

The core of the project was the examination of the motion of charged particles for different parameters. In particular, we examined the motion of protons, electrons and heavier ions (O+, O++, S+, S++, S+++ - Jupiter's moon Io produces lots of Oxygen and Sulphur from its volcanic eruptions) for different values of initial energy, position and pitch angle. We repeated the numerical investigation using two different models of the Jovian magnetosphere, representing a compressed or an expanded state.

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