Q:

Why are Ion thrusters so energy hungry? 

Ion thrusters need a lot of energy.  But I don't understand why.  So, one thing I understand is that it takes a lot of energy to take achieve a high exhaust velocity ( since kinetic energy is proportional to velocity squared) but we get little momentum.  This is all great.  But, the energy required is coming from the grids.  The charge present on these grids doesn't change (due to ion optics), hence they can accelerate particles forever as long as the ionization chamber has sufficient pressure to let the ions enter the grid space.  Now, it takes energy to ionize the gas.  But when I calculated it, its not in Kilowatts obviously.  The chambers walls are positively charged.  The walls act like an anode and take in the electrons from the plasma.  So, the thing that I was wondering about was whether the constant charging of these walls could take up that much energy.  I then tried to calculate the energy needed to do this through the knowledge of the metals work function and found out that it requires less than 100 watts of energy.  I AM PRETTY SURE THIS IS WRONG, but I don't understand why ion thrusters are so energy hungry.  

A:

An idealized ion thruster might work like this: 
First we make some gas that is neutral and non-conducting, conductive.  That takes some energy.  Then we charge the conductive gas positively, that takes some energy.  
If there happens to be an electric field, maybe caused by some charged grids, in that place where the gas that we are charging is located, then the gas starts to feel a force after becoming charged. 
As we are charging the gas, that takes energy.  As we are not charging any grids, we are not using any energy to charge any grids. 
How do we charge a conductive gas positively?  We connect the positive terminal of a voltage source on it.  When the voltage source is charging the gas, it is using energy. 
Now we would like to know how much energy the charging takes. " Charging" means cramming a lot of similar charges in a small volume.  We can charge some gas positively near a negative grid without using much energy, while near a positively charged grid charging some gas positively takes quite a lot energy. 
It happens to be so that we want the positively charged gas to be near a positively charged grid, and far from a negatively charged grid, so that the positively charged gas will spend quite long time accelerating away from the positive grid and towards the negative grid.  And that is why the voltage source that is charging the gas has to use quite a lot of energy.