Ion Engine Efficency: What Mass is Optimal?

[flatmaster]

I was arguing with my NASA friend the other day about what would make a more efficent propellent for an ion engine. Is it a lighter ion or a heavier ion. THis was what I derived.

Assume a charge q of mass m is accelerated through a potential V. The mass of the ship is M. Working through the problem with the tools an intro physics student could comprehend, I arrived at an equation that gives you the change in velocity for the ship after consuming ONE available ion.

v = Sqrt[2qVm/(M^2)]



I'm pretty confident in this. The units work out and all variables are in the correct place intuitively.

i'm confused on one point. I already have velocity as a function of mass of one particle. Do I need to divide by mass of one particle to get to velocity change per unit mass?

I think I'm confusing particle mass with bulk mass somehow.

 

[Redbelly98]

You're equation is correct. Not sure why the velocity change per unit mass would be useful here. If we assume a certain number of ions are generated per unit time, then multiply your equation by the rate at which ions are generated to get the acceleration.

 

[flatmaster]

Well, you want to carry as little propellent to keep the weight down. A higher change in velocity per unit mass would allow you to carry less propellent to achieve the same change in velocity.

 

[Redbelly98]

Thinking about this a little more, and I am thinking the quantity of interest is the velocity change due to burning a fixed mass of fuel, since the "energy budget" would include a certain amount of fuel by mass.

Multiplying your v expression times the number of particles in a total fuel mass m_f would give Δv for that mass of fuel. This number of particles is simply m_f/m, so we have

Δv = Sqrt[2qVm_f² / (m²M²)] = Sqrt[2qV] m_f/(mM)​

I guess this is pretty much what you were getting at ... essentially divide by the mass m to get the velocity change per unit mass of fuel.

EDIT:
I posted this before reading your post #3. (Yes, I had this edit window open and in progress for nearly an hour.) I agree with what you said.

So it appears that a smaller particle mass results in a greater thrust.

 

[flatmaster]

Well, if that's the case, why are they using xenon? It's heavy. Is xenon particularly easy to ionize multiple times? I mean, all that you need this particle to do is get ionized and fly out the back. Other than ease of storage, all other properties are irrelevant.