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 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.
I am talking about what we are using energy for, and how it translates into the ion beam energy. Like ionization, etc; not how to calculate the energy needed.