The short answer is "in practice, not in this case". In Sigmond's derivation d is the z- (usually vertical) distance traveled by the single ion under study. Since the highest density of ions takes the shortest route, for most (but not all) lifter designs one can make the approximation of the same z-distance d (the gap length) for all ions, hence the I*d/mu thrust formula obtained by summing all the q*d/mu momentums contributed by all the ions crossing the gap in one second. In those lifters the exact shape of the collector doesn't matter, whether wing shaped or round tube or plane mesh.
But there are exceptions, e.g. in my trough shaped mesh design as I explained the ions fan out, so they travel very different z-distances, so the X-to-plane I*d/mu formula doesn't apply. If you do the (simple) maths you find: Thrust(line to half cylinder) = 2/pi * I*d/mu Michel P.S. You seem quite interested in this matter Harry, are you planning a lifter construction project? ----- Original Message ----- From: "Harry Veeder" <[EMAIL PROTECTED]> To: <[email protected]> Sent: Saturday, February 24, 2007 8:45 AM Subject: [Vo]: Lifter electrode geometries > > Michel, > > Reading your attachment, I noticed the derived formula for the force on the > ions appears to be specific to a particular anode and cathode geometry. > > i.e. It says "d = distance point-plane", which I take to mean > the gap between a wire-like anode and the upper edge of skirt-like cathode. > > Since the geometry of the cathode is different in the tubular lifter > wouldn't the derived formula be different too? > > Harry >
