Our team from Rhodes College will be performing an experiment in
microgravity aboard NASA's "Vomit Comet" in August.  For our
experiment to come off successfully, we need to know how well
electrical charge persists on a metallic, spherical object (radius of
about 1.5 cm) at high altitudes.

To answer this question, we would specifically like quantitative data
showing how the following affect the dielectric strength (i.e. the
electric field at which breakdown occurs) of air:

1. air pressure
2. humidity
3. cosmic ray intensity

We suspect that low humidity may increase dielectric strength and high
cosmic ray intensity may decrease it, but we would like more specific
information about all three of the above factors.  Any suggestions
about how to prevent electrical discharge at high altitudes would also
be appreciated.

Note that we need this information by the first week of August at the latest.

---

Request for Question Clarification by hedgie-ga on 21 Jul 2006 04:52 PDT

This is a fairly complex problem. You would have  to estimate
ion density - and the 'cosmic rays' may have to be better defined.

For price shown, you can get couple references, like this one:
http://www.blazelabs.com/l-vacuum.asp

not a complete answer. Are you interested?

---

Clarification of Question by rhodescollegephysics-ga on 26 Jul 2006 11:57 PDT

Let me clear up two issues: the amount of charge on each of the two
metal spheres we'll use, and the definition of cosmic rays.

1. We will use two different-sized spheres (1.5 and 6.5 cm radii),
both of which will be at a voltage of 30 kV.  Using V = k*q/R to
calculate the charge q, we expect 217 nC on the large sphere and 50 nC
on the small sphere.  Dividing by the surface area of each, we obtain
0.4 and 1.8 nC/m^2 for the large and small spheres.  So there you have
the surface charge densities.  These distributions aren't exactly
uniform in practice, but for the purposes of this question we can
assume they are.

2. We were warned by another college that cosmic rays are more intense
at high altitudes (at least 25,000 feet) and could hinder us from
keeping charge on our spheres.  By cosmic rays, I mean radiation
(mainly protons) streaming from space into Earth's atmosphere.

One of the most significant contributors to electrical discharge is
the relative humidity.  Generally speaking, the lower the RH, the more
likely it will be to have an electrostatic discharge (ESD).  In many
labs where ESD events would be an issue (i.e. computer chip
manufacturing plants), RH levels are closely monitored at all times. 
If they drop below some threshold (usually around 30%), work ceases
immediately.  So, if you don't want ESD events, humidify the heck out
of that cabin.  Hard to do, since most airplane cabins are drier
than...well, you can finish that yourself.

There is a wealth of knowledge available on ionization chambers used
for radiation detection and measurement.  You are in some ways
creating a giant radiation detector.  Study how they work with respect
to humidity, voltage and air pressure and you may have you answer.

If this information isn't already in 'the literature,' I'd be
surprised.  There are probably oodles of experimental measures of
air's dielectric constant as a function of (pressure, humidity).  That
should be pretty sufficient phenomenological in roads.  There may be
not be as many as a function of "cosmic rays."  I haven't thought much
about it, but I'd physically intuit that this means (since you
mentioned protons) that there's some charge flux density in the
surrounding air and well that's proportional to the dielectric
constant...

There are a lot of ways you could solve these problems: isobaric
chamber, EM shielding (like faraday cage or something),
(de)humidifiers-- all of various cost and effectiveness.  Or just take
pressure, humidity, and cosmic ray measurements... and then compensate
for them in the calculations based on whatever dependence of air's
dielectric constant you find.

But sorry, I have no specifics not for $35, heh.  Hope this helps, though...