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
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
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
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.
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.
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
more on how this kind of modeling works,
see the “Particle
For those who do plasma simulations for a
living, here ’s some additional information.
We use a variant of a Boris pusher to update
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
given the number of particles involved
(and the fact that we currently only use fields that can be expressed as simple
decided that on-the-fly calculations
- 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
motion. As a result, we cap the
of the particles to keep things from going too haywire. This is really only
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
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.