# How to confine electric charges

by Gerenuk
Tags: charges, confine, electric
 P: 1,060 What sort of field do you need to confine electric charges? Is an electric field alone possible? Do the charges have to circle or can they be stationary? What parameters are important for this to work.
 P: 4,663 A central electric field can confine electric charges without circular motion. A single proton will confine a single electron in a bound state without orbital angular momentum (i.e., not in a "circle"). A helium nucleus will confine two. A magnetic bottle will simultaneously confine moving charges of both polarities in helical orbits. See http://en.wikipedia.org/wiki/Magnetic_mirror Bob S [added] Actually, a single proton can confine two electrons. The binding energy of the "valence" electron is only about 0.75 eV, and can be detached with an IR laser (wavelength < ~10,000 Angstroms). H-minus ions are often used as a source of protons in proton accelerators.
 P: 1,060 I'd like to confine lots of protons. Do you mean I need a strong negatively charged wire? Which other possibilites do you have? Can I set up a magnet mirror to confine a bunch of protons in a limited space?
P: 4,663
How to confine electric charges

 Quote by Gerenuk I'd like to confine lots of protons. Do you mean I need a strong negatively charged wire?
No.
 Can I set up a magnet mirror to confine a bunch of protons in a limited space?
The magnetic bottle can confine orbiting charged particles of either polarity. See
http://en.wikipedia.org/wiki/Magnetic_mirror
Solenoidal magnetic fields with magnetic "caps" on the ends have been used to do precision elementary particle physics experiments. The magnetic "caps' confine the charged particles axially-confined helical orbits.
Bob S
P: 1,060
 Quote by Bob S Solenoidal magnetic fields with magnetic "caps" on the ends have been used to do precision elementary particle physics experiments. The magnetic "caps' confine the charged particles axially-confined helical orbits. Bob S
Just to make sure: there is no sensible way to do this with electrostatic fields alone?

Do I need to set up a particular motion of the charges in order to confine them in an magnetic bottle?

(I mean just putting in a bunch of protons won't work... in all directions?!)

There is no way to confine a bunch of protons with random directions?
 P: 4,663 The Penning trap uses a solenoidal magnetic field combiled with electrostatic fields to confine particles axially: http://titan.triumf.ca/equipment/pen...ap/index.shtml Here is a purely electrostatic ion beam trap http://www.astro.columbia.edu/~savin...s/massspec.pdf Bob S [added] See also http://fisica.unicam.it/quele/docs/p...trap_paper.pdf [added #2] There is a class of microwave tubes called crossed-field tubes (crossed E and B), of which the simplest is the magnetron. In this tube, elecrons emitted from a hot cathode are accelerated toward an anode, and in the process are deflected by an axial magnetic field. The result is that the electrons undergo cycloidal (~cyclotron) motion at microwave frequencies. See http://en.wikipedia.org/wiki/Cavity_magnetron In principle, protons could also undergo a similar motion in a cylindrical-radial electric field and an axial magnetic field. The best source for the theory of a magnetron could be found in EE textbooks.
P: 5,539
 Quote by Gerenuk What sort of field do you need to confine electric charges? Is an electric field alone possible? Do the charges have to circle or can they be stationary? What parameters are important for this to work.
Maybe I'm missing the point, but isn't that what a capacitor does? Likewise, a battery or electrolytic solution- say, an acid with pH <7?
P: 1,060
 Quote by Andy Resnick Maybe I'm missing the point, but isn't that what a capacitor does? Likewise, a battery or electrolytic solution- say, an acid with pH <7?
I suppose if you have enough attractive charges, then the particles cannot espace. Probably when the sum of kinetic energies does not exceed the espace energy for a single particle, right?

Edit: But wait, arent the partners particles acting repulsively too. Why in fact does a capacitor not lose particles?
P: 250
 Quote by Gerenuk What sort of field do you need to confine electric charges? Is an electric field alone possible? Do the charges have to circle or can they be stationary? What parameters are important for this to work.
According to "The Feynman Lectures on Physics", V2, Sect. 5-2, "There are no points of stable equilibrium in any electrostatic field --- except right on top of another charge."
P: 1,060
 Quote by GRDixon According to "The Feynman Lectures on Physics", V2, Sect. 5-2, "There are no points of stable equilibrium in any electrostatic field --- except right on top of another charge."
I didn't realize. So when a normal particle is confined in some container with wall, it's due to quantum mechanical effects at the walls? Electrostatics cant explain why a container is sealed?
P: 250
 Quote by Gerenuk I didn't realize. So when a normal particle is confined in some container with wall, it's due to quantum mechanical effects at the walls? Electrostatics cant explain why a container is sealed?
My take on the Feynman quote is that the author was talking about a disconnect between the concept of "normal" particles and Maxwell's theory. In general, texts routinely posit stable distributions of charge ... spherical shells of constant radii, etc. ... but Maxwell's theory provides no explanation for how such stable distributions can persist in time. In view of the Feynman quote, when we talk about a spherical shell of charge (for example), we must implicitly assume some non-electromagnetic agent is preventing the distribution from dissipating into space. It's a nasty little assumption that's rarely mentioned in EM texts.
PF Gold
P: 3,225
 Quote by Gerenuk I didn't realize. So when a normal particle is confined in some container with wall, it's due to quantum mechanical effects at the walls? Electrostatics cant explain why a container is sealed?
Maybe Feynman made an allusion to Earnshaw's theorem? http://en.wikipedia.org/wiki/Earnshaw%27s_theorem
P: 1,060
 Quote by GRDixon According to "The Feynman Lectures on Physics", V2, Sect. 5-2, "There are no points of stable equilibrium in any electrostatic field --- except right on top of another charge."
An idea: does the situation change if we allow for dynamics? I mean can atom cores with orbiting electrons create a stable structure?
P: 250
 Quote by Gerenuk I didn't realize. So when a normal particle is confined in some container with wall, it's due to quantum mechanical effects at the walls? Electrostatics cant explain why a container is sealed?
To my knowledge even classical electrodynamics can't produce such a confinement. If the particles are accelerating, they classically emit radiant energy. The confinement of electrons in atoms was of course the motivation for inventing quantum theory.
P: 250
 Quote by fluidistic Maybe Feynman made an allusion to Earnshaw's theorem? http://en.wikipedia.org/wiki/Earnshaw%27s_theorem
In a way, yes. But my impression is that the Feynman quote refers to a continuous distribution of charge (e.g. a spherical shell of charge), whereas Earnshaw refers to multiple point charges which are themselves somehow kept from "evaporating" into space.
P: 185
 Quote by GRDixon My take on the Feynman quote is that the author was talking about a disconnect between the concept of "normal" particles and Maxwell's theory. In general, texts routinely posit stable distributions of charge ... spherical shells of constant radii, etc. ... but Maxwell's theory provides no explanation for how such stable distributions can persist in time. In view of the Feynman quote, when we talk about a spherical shell of charge (for example), we must implicitly assume some non-electromagnetic agent is preventing the distribution from dissipating into space. It's a nasty little assumption that's rarely mentioned in EM texts.
A spherical shell of charge has no effect on the stuff inside it anyway, so you don't even have to make that assumption. Remember that inside the shell, the voltage is constant, so there is no force on a particle of either charge. Therefore no confining 'in a certain place' (other than the whole shell) going on. Once a particle reached the edge of the sphere after just drifting, it would either shoot out or get sucked back in, depending on the charge. So I guess some charges will be kept in there but they aren't kept in a specific spot they will drift in the interior.
P: 250
 Quote by Prologue A spherical shell of charge has no effect on the stuff inside it anyway, so you don't even have to make that assumption. Remember that inside the shell, the voltage is constant, so there is no force on a particle of either charge. Therefore no confining 'in a certain place' (other than the whole shell) going on. Once a particle reached the edge of the sphere after just drifting, it would either shoot out or get sucked back in, depending on the charge. So I guess some charges will be kept in there but they aren't kept in a specific spot they will drift in the interior.
I agree. The spherical shell was a poor choice. A solid sphere of charge might have been a better one. Somewhere in his texts Feynman, in the course of discussing the electric field right AT a surface charge, suggests that it's the average just "in front of" and "in back of" the sheet. In the context of the spherical shell he might have argued that the E field at a point right IN the shell is q^2/(2)(pi)(eps0)(R^2). That being the case, every increment of charge in the shell might be expected to experience an increment of outward pointing force, and we might expect the shell would expand with time (in the absence of some other, constraining, implied, non-electromagnetic, inward pointing force increments).
 P: 185 I have a problem with the average argument. Any time I have seen it, it has been in the context of a parallel plate capacitor, and the average argument just 'happens' to be correct there. The average is E/2, where E is the field inside the capacitor. This quantity is correct but there is a real reason for why that is, rather than 'it is the average'. The real reason is that the surface can't apply a force to itself in the normal direction, so the only thing that contributes to the force (therefore the field) is the other plate on the capacitor. Since the field doesn't vary with distance, it is merely half of the original E field in the capacitor (this is because the E field in the capacitor is a sum of the two fields from the plates, each plate with E/2). If you have an example that shows why the average argument is true in a general case, I would love to see it, I just can't believe that it is true without that though.

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