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If my back of the napkin calculations are right, and If he can scale it up by a billion-fold (i.e., to 35,000 Newtons), a million kilogram ship (i.e., one of respectable size), starting at an initial velocity of zero, would travel about one kilometer towards Mars in a week’s time

Uh, no. a = 35e3/1e6 = 35e-3 m/sec².

It would take about 28.6 sec per meter per second -- so a day's thrust would give you around 3 km/sec of delta-V.

Arghh! Man, I can't even duplicate what I did on that napkin now.

I was using:

d = (1/2)at²

and somehow got a travel distance of only one kilometer after 604,800 seconds (1 week). But now I'm getting 10,584 km, still woefully inadequate to get you to Mars in a reasonable amount of time.

'Course, in reality, the initial velocity isn't zero either. So it's not as bad as I'm making it out to be. But still, he's going to have to scale up the power of his invention by a factor of much, much more than a billion.

More power to him.