I was reading up on electrostatic particle accelerators when I read a statistic stating the efficiency of converting wall electrical power (the electrical power from the outlet) into beam power in an accelerator. I tried finding out why this was the case and doing some first cut calculations. The most I could come up with was a lot of the power gets wasted by particles not being efficiently collimated, I.E. most of the accelerated particles hit the wall. Now, I'm pretty sure that is not the only reason, I assume depending on the quality of the vacuum, scattering by the leftover gas molecules would also contribute to the lost beam power, as well as losses via emitted radiation from focusing the charged particles with magnetic fields.

Am I getting this right? Or am I missing some huge power draw that sucks most of the power away from the beam? I know the efficiency depends somewhat on the beam maximum energy (since higher energy beams have higher brehmstrahlung and cyclotron radiation losses), I'm looking at the power efficiency of a 10 MeV electrostatic electron beam accelerator.

Why are 10 MeV electron electrostatic particle accelerators so inefficient?

  • $\begingroup$ You have to maintain a large electrostatic potential difference, right? What does the circuit that does that look like? How much power does it take to run? Remember to allow for various leakage currents. (Just guessing, BTW, I've never worked it out myself.) $\endgroup$ Sep 8, 2015 at 2:31
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    $\begingroup$ Can you cite the source? For the most part electrostatic accelerators have gone out of favor many decades ago. There is no inherent reason why they can't be made reasonably efficient, probably similar to a klystron based AC machine. Beam collimation shouldn't waste much, if any power. UHV is not a problem these days, either. Can you tell us what you want to do with a 10MeV machine that requires efficiency? $\endgroup$
    – CuriousOne
    Sep 8, 2015 at 5:12
  • $\begingroup$ Yes, I'm look to see if it can power a free electron laser for converting visible light into gamma rays for transmitting solar energy from near the sun to Earth orbit. The efficiency is needed (at least 30% of visible light energy becomes gamma rays) so that the platform can deliver enough power to be profitable (within a year of operation) $\endgroup$
    – user11377
    Sep 8, 2015 at 6:40
  • $\begingroup$ @CuriousOne - Electrostatic accelerators have fallen out of favor for particle physics, but the ubiquity of SEMs, TEMs, FIBs, ion implanters, and whatnot suggests there are plenty still around. UHV is not a problem, but is not exactly energy efficient. For the poster - very little beam will hit the walls (if run properly). However, for high stability voltage control you have current flowing down a string of high-precision resistors on the column to establish the potential gradient. This has to be a high % of beam current to be effective. Then all the ancillary equipment adds up fast. $\endgroup$
    – Jon Custer
    Sep 8, 2015 at 14:07
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    $\begingroup$ @CuriousOne - as the owner of an ion beam laboratory, I can only say that I fully understand all the different accelerator designs. And Cockroft-Walton type designs are still quite common, particularly over 50kV. Linacs are clearly the way to go for 10MeV electrons, but I wouldn't say they are very efficient (or else my building would need a lot less cooling water...) $\endgroup$
    – Jon Custer
    Sep 8, 2015 at 15:50

2 Answers 2


As one data point for linac efficiency, I found a nice presentation from a Jefferson Lab meeting (where CEBAF is - Continuous Electron Beam Accelerator Facility). This is from Googling 'energy efficient linac'. In it, they quote that the CEBAF klystrons are about 25-28% efficient, while their new solid state amplifier proposal (an SBIR, can see at Far-Tech, I have no affiliation other than Googling them) is 55% efficient. This is at 1497 MHz, and 6.5kW linear mode amplification.

Now, that ignores efficiencies in the electron source, focusing elements, steering plates, and all the vacuum components (a 300 liter/sec turbo plus backing runs about 700W). It also ignores production of cooling water and so forth, that will contribute to the overall (in)efficiency (and you will need lots of cooling of whatever target you are trying to get gammas out of). We won't even go in to the electron-to-gamma conversion efficiency, much less how you are realistically going to extract energy from the gamma beam on the other end.

  • $\begingroup$ The fact that is hard to transfer power from the wall to the beam is an undisputed fact. The weird point here is that DC is much less efficient than RF... It also sounds a weird comparison to me as their applications are pretty much different. $\endgroup$
    – DarioP
    Sep 16, 2015 at 9:24
  • $\begingroup$ I'm not sure that DC is much less efficient than rf as a rule. Part of it is what you mean by efficiency. For example, rf systems are pretty bad on the front end, that is, getting the source ions into the system in the first place (while bunching helps, it is far from 'efficient'). I'd claim a DC accelerator gets more beam power on target per unit power in. But, you won't get 100's of MeV or >GeV beams out of it... $\endgroup$
    – Jon Custer
    Sep 16, 2015 at 15:40
  • $\begingroup$ By efficiency I mean what stated in the question: the fraction of wall plug power that ends up into the beam. I think that the question is flawed, after all the OP didn't provide any reference for that. $\endgroup$
    – DarioP
    Sep 16, 2015 at 17:52

The 'electrostatic' accelerators don't recycle the current, I suspect. This would be a pelletron or Van de Graaf design, and current going through the free electron laser magnet structure (undulator) then hits a target and dissipates all the energy it didn't lose in radiation. Hitting the target dumps all the kinetic energy.

A synchrotron, on the other hand, takes bunches of relativistic charges and moves them through that same undulator once per cycle, circulating at near lightspeed, so a tiny amount of the beam kinetic energy can be lost due to radiation reaction, but built back up by the accelerator sections elsewhere in the apparatus. Those sections use timed RF in the right phase to re-accelerate the bunches back to full speed, and until the charges hit gas molecules and scatter into a beamtube wall, that beam can remain circulating for hours between fills.

A static field just makes a current from HV to ground.

Circulating is more efficient use of fast-moving particles than dumping them into a grounded target; the synchrotron electron gun can be turned off after startup, but the Van de Graaff has to put new electrons out continuously.


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