Thanks for the nice pair of related questions.
The main answer is that the simple principle of "electrical currents
follow the path of least resistance" is guiding the path of the
electrical discharge, but that the path of least resistance depends on
where the electricity has already flowed, giving an interesting an
nonlinear feedback situation. We'll explain:
discharge releases energy by neutralizing opposite charges which have
built up between clouds or between a cloud and the earth during a
thunderstorm. These charges build up over large volumes of air and
ground. As the voltage difference increases between the clouds and the
ground, it eventually rises to the point where electrons can be torn
away from the negatively charged ions and fly through the air. The
built-up electric field between the cloud and the ground provides the
energy. As an electron travels through the field, it is accelerated. If
the electron collides hard enough with a gas molecule, it can knock
some of the molecule's electrons loose, and the process repeats in an
avalanche-like manner. The end result is a tube of plasma, a gas
consisting of positive and negative ions (in addition to remaining
unionized gas molecules). The electrical resistivity in the plasma is
much less than that of ordinary air because of the presence of charged
particles which are free to move. Once this tube has been established,
electrical currents will flow very easily along it.
lightning strike may consist of many separate discharges, all down the
same tube of ionized air. But some areas of charge buildup may not lie
directly on the ends of the tube, but instead are off to the sides. The
path of least resistance is for the current to stay in the main bolt as
long as possible, but then branch off to the region where the opposite
charge buildup is, taking a short side path. It's a little like
planning a trip in a car. You follow small branch roads to find the
nearest interstate freeway (which offers the fastest travel with the
least resistance). You follow that as long as you can, and then branch
off again on small roads to go to your eventual destination. The
nonlinear feedback here is that people will drive their cars the most
where people have driven their cars before, which caused the interstate
freeway to be built in the first place.
The same sorts of
rules apply to many instances of self-organizing distribution networks.
These include: blood vessels in animals, tree trunks and branches and
roots, and rivers and streams. These all follow crazy, jagged paths,
which are needed to distribute a mobile substance either from or to a
volume. This happens when the distribution channels have a lower
dimension than that in which they are distributing their cargo.
Lightning bolts and blood vessels are effectively one-dimensional, but
they must distribute electrical charge or blood to a three-dimensional
volume, and therefore must take jagged, branching paths to fill up the
space in the most efficient manner. The same principles apply to
crystal growth. Snowflakes develop by attaching water molecules on the
ends of frozen crystals, and the easiest place to make new ice is at
the free ends. The raw material, water in the gaseous phase, is
distributed in three dimensions around the snowflake and each molecule
attaches to the closest part of the currently existing ice crystal.
Snowflakes and other crystals therefore often have branches and
dendrites on their ends.
The discharges in a plasma ball obey
essentially the same rules -- charge travels the easiest down already
established conducting plasma discharge paths, and then fork out to the
places where the charge needs to go. You raise the very interesting
question of "how does the discharge decide where to make the plasma
path in the first place, if the electric field is spherically
symmetrical?" The answer is a very interesting topic in its own right,
with the name "spontaneous symmetry breaking." A symmetrical equation
can have a non-symmetrical solution. The electrical discharge in a
plasma ball just picks a direction or directions at random when it is
turned on, if it is truly symmetrical. The same sort of thing happens
if you push down on on a ruler that is held vertically in contact with
a table. The system is left-right symmetric, but if you push hard
enough, the ruler will bow to the left or right.
If there are
asymmetries in the plasma ball, such as someone's hand touching the
glass, then the discharge paths are affected by the asymmetry.
Here is an explanation of why the discharges in a plasma ball head for your hands when you touch the glass
Tom, Mike, and Nigel
(published on 10/22/2007)