It's far too late to edit my original post, but I want to add a disclaimer here. I still don't see how this system can work, but (as suggested by T-A in a brief comment in that earlier thread) there's at least some chance that the details of plasma physics make it function. My current sense is still that one way or another it doesn't work out (I'll spell that out in a bit more detail in a response to one of my later comments here where I was flat out wrong about how plasma screening might work), but I am not remotely an expert in plasma physics: maybe there's some subtle dynamical effect that really does save the day. (If that's the key, though, then I'm pretty sure that the plasma details are essential for making it work: none of the arguments I've seen in that earlier thread or in this one make the case.)
> there's at least some chance that the details of plasma physics make it function. My current sense is still that one way or another it doesn't work out
You really should learn to read papers before trying to debunk them. Zubrin's paper has Debye length all over it; it's a crucial consideration.
All right, weekend fun: let's look up the closed form expression for the electric field of a capacitor immersed in a plasma. This is old stuff, it was worked out many decades ago, and can be found e.g. in
The internal field is given by Eq. 12 and depicted in Fig. 2 (looks roughly like a catenary, sagging between the plates), the external field is given by Eqs. 6 and 8, Fig. 1.
We only need to concern ourselves with the simple case of zero frequency, in which case the external electric field E at distance r from a plate with surface field E_0 is
E = E_0 * exp( -r / l_D )
with l_D denoting Debye length. The internal field at distance z from the left plate (at the origin) for plate spacing d is
E = E_0 * ( sinh( (d - z) / l_D ) + sinh( z / l_D ) ) / sinh( d / l_D )
It sags more in the middle for larger d, but it has the nice property that it never reverses sign (as can happen for non-zero frequencies) so there's no risk of the ion getting trapped uselessly inside the capacitor.
To get the energy lost by a positive unit charge entering through the anode and then exiting through the cathode, integrate the external field from r = 0 to infinity and multiply by two. Total loss: 2 * E_0 * l_D
To get the energy gained by the same unit charge between the plates, integrate the internal field from z = 0 to d. Total gain: 2 * E_0 * l_D * ( exp( d / l_D ) - 1 ) / ( exp( d / l_D ) + 1 )
Subtract loss from gain and you have the net kinetic energy gain,
which is positive for d > l_D * ln(2) ~ 0.693 * l_D and grows asymptotically toward 2 * E_0 * l_D as d -> infinity (in practice, there is little difference beyond d = 5 * l_D).
So, it works, and you can space the two "plates" (actually meshes of conducting wires, each 0.1 mm wide, in Zubrin's paper) as far apart as you want, but there is little to be gained (other than the flexibility of working across a larger altitude range) from spacing them more than 5 Debye lengths apart.
... except I just realized that the final expression for gain minus loss is wrong: redoing the calculation I get
-4 * E_0 * l_D / ( exp( d / l_D ) + 1 )
So charges traversing the whole thing lose energy. You still get a net momentum due to the mass difference between electrons and protons, but in the opposite direction. :/