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Using magnetic fields to fire plasma bolts

Physics Asked by ArborianSerpent on June 17, 2021

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?

2 Answers

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 $dvec{x}$ is $dW = vec{F} cdot dvec{x}$; since $dvec{x}$ 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:

$dW = q vec{E} cdot dvec{x}$.

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

Answered by Sebastian on June 17, 2021

You can accelerate charged particles using electric fields, and you can create electric fields by various methods, including for example by a making time-varying magnetic field.

There is a lot of sophisticated knowledge about this, mainly in two communities: the particle accelerator community which supports high energy physics experiments at CERN and elsewhere, and the plasma physics community which supports research into nuclear fusion among other things.

One of the most efficient ways to pass energy into a fusion plasma is by a microwave method that excites the plasma. One of the most efficient ways to accelerate charged particles in a single direction is the laser wake field method, where a high intensity laser creates a rapidly moving intense electric field, with some clever plasma physics also involved. This is just a brief answer to point you in the right direction.

Answered by Andrew Steane on June 17, 2021

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