# Using magnetic fields to fire plasma bolts

I very recently asked this question: Could you use magnetic fields to direct a bolt of lightning?

As it doesn't seem feasible for what I have in mind, I decided I would instead ask if it's possible to simply accelerate electrons using magnetic fields, until they have enough kinetic energy to turn the air they travel through into a beam of plasma.

If this could be done, how powerful would the magnets and potential other equipment need to be? What equipment would I need?

• Not exactly what you're describing, but look up "Z-pinch". Actually, any plasma magnetic confinement device acts essentially like "directing a bolt of lightning." A bolt of lightning is a current in ionized gas, and currents experience forces from magnetic fields. – pwf Jan 13 '17 at 16:44

A general rule is that magnetic fields can't do work, which follows from the Lorentz force law for the force on a particle with charge $q$ moving with velocity $\vec{v}$:

$\vec{F} = q \vec{E} + q \vec{v} \times \vec{B}$.

The work on the particle during a small displacement $d\vec{x}$ is $dW = \vec{F} \cdot d\vec{x}$; since $d\vec{x}$ is parallel to $\vec{v}$, the cross product vanishes when the dot product is taken (since $\vec{v} \times \vec{B}$ is perpendicular to $\vec{v}$ by properties of the cross product, and therefore its dot product with anything parallel to $\vec{v}$ vanishes). Therefore only the electric field does work on the particle:

$dW = q \vec{E} \cdot d\vec{x}$.

The upshot is that, since accelerating a particle would require doing work on it, any magnetic field alone cannot be used to accelerate anything.

• Don't railguns use magnetic fields to accelerate projectiles? – ArborianSerpent Jan 12 '17 at 22:14
• They use changing magnetic fields, which generate electric fields (or electromotive forces, if you prefer). It's those electric fields that do the actual accelerating. It's a little less obvious that magnetic fields can't do work when considering macroscopic objects, because the charges within those objects need not move in the same way as the object as a whole. But if considering only a single charged particle (as in your question), the Lorentz force law makes it very clear that a magnetic field can't do work. – Sebastian Jan 13 '17 at 12:15
• Could one use the same principle as in the railgun to accelerate charged particles? Alternatively, could the particles not be charged and still generate the sort of plasma effect I'm looking for? – ArborianSerpent Jan 13 '17 at 14:03
• Sure, but in the trivial sense that (on a microscopic level) it's electric fields that do the accelerating; so applying "the same principle" to charged particles just means accelerating them with an electric field. If your goal is just to ionize air, however, then it's true that uncharged particles (e.g. gamma rays) can do the trick as well. But (if I recall correctly) they don't work nearly as well as charged particles, and you'd need a very large amount of radiation to have the same effect. – Sebastian Jan 13 '17 at 16:34