Answer to Question #492 in Molecular Physics | Thermodynamics for Gina

Question

Consider heating the plasma through the adiabatic compression. Because of the invariance of μ, with the increasing of B the value of kT must also grow. But the magnetic field can not accelerate particles, since the Lorentz force qv×B is always perpendicular to the velocity. Then how do the particles get energy?

Answer 1

When a particle is moving in a non-uniform magnetic field its magnetic moment remains constant, ie invariant.

μ=12mv⊥2B=kTB

The magnetic field is perpendicular to the velocity of a particle and can not do a work changing its energy, but when it changes, as follows from Maxwell's equations, induced electric field emerges. It is perpendicular to the magnetic field, which means that there exists a component parallel to the particle velocity. Exactly this electric field will change the energy of the particles. If the magnetic field increases adiabatically slowly, then the field E is small, but the integral action of this field in the times exceeding Larmor will be noticeable. The invariance of the magnetic moment allows finding an increase of the particle energy without considering the process of averaging.