The magnetic field also deflects the electrons. The quantum mechanical consequence is the Landau levels. I would guess that in an inhomogeneous magnetic field we have distorted, nonuniform Landau levels. The higher the field, the higher the Landau level energies, so that creates a force repelling electrons away from the high field. This is known in classical physics, where electrons spiraling in a magnetic field are reflected from the high field region. It's why Earth's radiation belt remains confined while the electrons spiral back and forth between the magnetic poles. -- Gene From: Warren D Smith <warren.wds@gmail.com> To: math-fun <math-fun@mailman.xmission.com> Sent: Thursday, June 4, 2015 1:56 PM Subject: [math-fun] Can a strong magnetic field create electron-positron pairs? Here is an argument, which seems absolutely indisputable, that an INHOMOGENOUS magnetic field can and will create pairs. Let the field be of form (Bx,By,Bz) = (0, 0, K*x) incidentally arising from vector potential (Ax,Ay,Az) = (0, K*x*x/2, 0). We know from the Stern-Gerlach effect that an electron (positron also) in such a field will be sucked in either the +x or -x direction depending on its spin. And the force sucking it will be F = mu_e * K. And this is experimentally confirmed, not mere theorizing. Therefore, if the distance L we can go in the x direction obeys L*F > m*c^2 then the total energy from all that sucking is enough to create an electron. A pair could be created at x=0, then suck distance L, and then have regained enough energy to pay for the pair creation. Therefore, pairs will be created. And if a distance L <= hbar/(m*c) suffices, then this creation process should be very fast. I don't see how anybody can possibly argue with this. Now any real-world magnetic field is NOT uniform, and it must go to 0 someplace. Therefore, any real magnetic field with enough strength, specifically if max strength B>m*c^2/mu_e, will generate pairs at a nonzero rate. Then the only question, it seems to me, is "what is that rate?" And how does the rate depend on the specific geometry of the field, for example on grad|B|? Optimally, we would express the pair generation rate (pairs/second) in terms of some triple integral of some function (or functional) of the magnetic field. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)