Would it be possible to have an electron-less solid? We can create plasmas quite easily, indeed you can buy a plasma cutter and generate it all day long for less than $500. Would it be possible to trap a plasma, say magnetically, and cool it so much that it became a solid/liquid/gas without allowing it to receive electrons? Or would the energy requirement exceed what is possible?
I'm mostly curious about how the nuclei would interact with each other in the absence of electrons as a solid or liquid. Is there some principle that makes such an endeavor impossible?
 A: Well you could replace the electrons with something else, such as muons.  That is essentially what is proposed for this, although in extremely small quantities.  Muons in this case replace some electrons, but very very few compared to the total:
http://en.wikipedia.org/wiki/Muon-catalyzed_fusion
Obviously, this is fraught with difficulties because there is a good reason we live in the world defined by electrons.  You would have to scale up this idea beyond the fusion proposal dramatically, and even if you did, the fact that it can induce fusion is a problem... well, a big problem.  Maybe you could replace the electrons with something other than muons, that isn't as heavy.  But probably not.
If you're interested in how nuclei would interact with each other, you could consider a neutron star.  That is rather like a big nucleus, but it's held together by gravity.  It still doesn't have the electrons stripped out.  As I understand, the electrons are still mixed in the mass.
Let's say you just took ordinary matter and removed the electrons.  Let's look at a tennis ball sized thing, with a diameter of $6.7 cm$.  The nuclei are now repelling each other.  How much?  Let's calculate the energy, with the electric analog to the gravitational binding energy.
$$    U = \frac{3GM^2}{5r} $$
here:
$$ U = \frac{ 3 k Q^2 }{5 r} $$
We can very simply find Q from the nuclei alone.  If we assume the ball is the density of water and solid (unlike the tennis ball) then we find it weighs about $1.25 kg$.  Let's assume it's Carbon-ish in terms of the formula mass.  Divide by the formula mass, multiply by the electron charge (which is the same as the proton charge), and I find about 10.1 million Coulombs.  Here is the total calculation string in Google, but i won't take the time to prettify it right now.
(8.987551e9 N*m^2/C^2)3((1.0 g/cm^3)*4/3*Pi*(6.7 cm)^3 *(electron charge) / (12 amu))^2/(5*6.7 cm)
This comes out to $8.258 \times 10^{24} J$.  This is about 2.0 petatons of TNT equivalent.  The Tsar Bomba was 100 megatons TNT equivalent.  The KT extinction event was 100 million megatons of TNT, or 100 teratons of TNT.
A ball stripped of electrons would have so much energy it would possibly destroy life on Earth as we know it.  That is how the nuclei would interact with each other.
