Frequently Asked Questions about Magneto Golf and Magneto Bowling The Golf and Bowling games both deal with the motion of charged particles in magnetic fields. Here are a few questions that come up. What’s a field? You know what a magnet is. And you know that it can attract some things, like pieces of iron. A physicist would say that the magnet creates a magnetic field that extends away from it. The piece of iron reacts to that field, and is pulled toward the magnet. So scientists don’t think about the magnet attracting the iron: instead, the magnet makes a field, and the field moves the iron. Where do the fields come from? Space is full of magnetic fields. They’re almost all made by electric currents: there are electrical currents in the Sun, and electrical currents deep in the molten core of Earth and most other planets. Those currents create magnetic fields, just like magnets do. I thought space was empty. Space is almost a vacuum, but not quite. Depending on where you are, there might be a single atom in every cubic centimeter or so of space (around 15 per cubic inch). That’s not a lot: right now you’re breathing more like 10,000,000,000,000,000,000 atoms per cubic centimeter. But even those few particles in space can add up when you start looking at huge volumes, 10 or 100 times wider than Earth. What are these particles you’re talking about? Everything around you is made of atoms. Atoms are made of protons and neutrons, surrounded by electrons. Atoms in space can be hit by light from the Sun, which can knock off their electrons. The electron then moves along, separate from its parent atom. If most of the atoms have lost one or more electrons, we call it an ionized gas or plasma. Most of what’s in space is hydrogen, which consists only of one proton and one electron. When the electron is knocked off, you end up with a plasma of protons and electrons moving independently. Plasmas behave completely differently from a normal gas. The protons and electrons have electric charges – positive for the proton, negative for the electron. Because they have charge, they are influenced by magnetic fields. Also because they have charge, when they move they form an electric current (that’s what a current is: a flow of charged particles). But that current can make its own magnetic field, which makes things complicated: charged particles, moving in magnetic fields, generating new magnetic fields which influence their motion! More on plasmas. How do the Golf and Bowling games know how to move the particles? These games are actually tiny little computer simulations of a plasma. They solve the equations of motion for a charged particle (a proton) in fixed magnetic and electric fields. They make a few approximations so that they can run at reasonable speeds: The protons don’t generate electrical currents that affect the fields: the magnetic field is static. Only a few protons are run: these are sometimes called “tracer” particles… they just give you an idea of how particles behave, instead of trying to fill space with a realistic number of them. Normally, if the proton speeds up, you might want to slow down the simulation (do more calculations) so you can follow its motion carefully. We don’t do that in golf, so if the protons start moving too fast, the motion will become inaccurate. We’re not worrying too much about the actual field strengths and particle masses: it’s intended to give a qualitative sense of how things move. The protons are actually moving in three dimensions (not just in the plane of the computer screen), but we don’t show you that extra dimension. If you let things run a very long time, you might notice odd things that resulted from motion in that third dimension. For instance, particles in Earth’s field can slowly orbit around Earth, forming a “ring current”. For more on how this kind of modeling works, see the “Particle modeling” section. Technical notes For those who do plasma simulations for a living, here ’s some additional information. We use a variant of a Boris pusher to update the particles. The fields at each particle are calculated from a set of equations at each time step (instead of interpolating from a grid). We have implemented a grid solution as well, but given the number of particles involved (and the fact that we currently only use fields that can be expressed as simple equations), we decided that on-the-fly calculations were preferable. The time step is fixed: we could make it adaptive, but that would alter the speed of the animation and introduce misconceptions about the time dependence of the particle motion. As a result, we cap the energy of the particles to keep things from going too haywire. This is really only visible if you pass very near the x-line in some of the later holes. The code is fully 3D (it’s possible to see a ring current form). We chose not to do 3D visualization, because we thought it would detract from our ability to meet our primary learning goals. We could consider adding more holes to this course, or doing other modifications. If you have suggestions (for instance, interesting field models), please contact us.