# What limit the maximum magnetic and electric fields usable for particle acceleration?

Progress in acceleration of particle is quite steady but slow, at least in my opinion. I was wondering what are the fundamental roadblocks to develop larger electric fields gradients (in any material) to accelerate and large magnetic fields to keep particle in round trajectory for storage/collision.

Electric and magnetic fields end up limiting the achievable energies in particle accelerators and I wanted to know what are the fundamental limits to them in ordinary (metals, liquids, ... ) and extra-ordinary materials (plasma, lasers, rare metals from planet Krypton ...)

I can certainly see how materials imperfections can : 1) lead to instabilities such as discharges from sharp objects, or 2) get amplified and give rise to alterations of the materials due to a too strong magnetic field, that would start messing up the lattice structure of a metallic magnet (or anything similar at a larger length scale)

I am sure there is much more to say ... thanks for your inputs!

• Explain the downvote please. Jan 3 '18 at 16:34
• @annav As a last message in the form of comment (the website seems to complain about the length of this discussion), I wanted to remark that linear acceleration seems to give rise to radiation colinear with the charged particle accelerated, so it does not alter the direction of motion, just speed is lost due to radiation. On the contrary, when orthogonal acceleration is applied the particles change direction, making them go out of orbit. This seems to me a significant difference. Jan 4 '18 at 16:36
• In other words, If I want to re-accelerate the lost speed in a linear accelerator I can just add one more stage of acceleration along the same line (a predictable location), whereas for a circular accelerator I would have to put my re-acceleration stretch on a different orbit, which is different for every amount of radiation loss and angle of emission. To me this makes a great difference. I would say that if we had far greater acceleration capabilities we can easily compensate for parallel acceleration bremsstrahlung loss. So in the end the limitations seems to arise max accelerating field Jan 4 '18 at 16:40

Have you read the wiki article on particle accelerators? The limits do not come from the fields themselves:

Due to the high voltage ceiling imposed by electrical discharge, in order to accelerate particles to higher energies, techniques involving dynamic fields rather than static fields are used.

It is electrical discharge that imposes a limit to the design of static accelerators and thus one goes to dynamical accelerations for high energy particle beams .

Also excessive loss of energy due to radiation from the accelerated particles is a large factor. The proposed future linear collider for e+e- is supported because of the advantage of less energy loss and so less input energy needed. There is no problem with the electric and magnetic field magnitudes to present a limit in the progress, as you suppose. It is energy losses and consequent costs that set limits.

• Electrical discharge imposes a limit on accelerators that use static fields (like a Van de Graaff generator). Modern high energy (anything above about $100~\rm keV$) particle accelerators don't use static fields, so that isn't really relevant to the question.
– Chris
Jan 4 '18 at 5:42
• @Chris you might notice that the quote is about dynamical designs . Maybe I should qualify. Jan 4 '18 at 8:04
• Thanks to both, as you read in my question discharges are mentioned, but it seems to me they are a key factor only for acceleration, not for storage, which requires magnetic field. Any input on what is the trouble when one tries to make larger magnetic field (superconducting) magnets? why is so hard to go from present few-10 T to say 100 T ? Jan 4 '18 at 15:44
• I would like also to reprise @annav comment on energy loss due to radiation. I suppose that applies to circular designs only, so I can take it out from the discussion by choosing a linear accelerator design. Still we struggle to make progress on enahncing energy of linear colliders. This I presume originates from the difficulty to have large field gradients (needed for acceleration) over large lengths (needed to go to fractions of TeV energy per beam). From what I read so far discharges (even in non-static fields) are the limiting issue, aren't they? Jan 4 '18 at 15:49
• Not discharges, synchrotron radiation . They have not reached the limits in electric and magnetic fields, they just need longer and longer routes for acceleration so that the synchrotron radiation is under control. Have a look at the design en.wikipedia.org/wiki/International_Linear_Collider#Design . The length is so as to control the loss in radiation from too large accelerations. Jan 4 '18 at 16:01