Note: I am describing this question using cylindrical coordinates $\hat{r}$, $\hat{\theta}$, $\hat{z}$.
I've been looking into how you could slow down a plasma moving downstream in a pipe using magnetic fields. Subsequently, this idea that using a radial magnetic field to impart an azimuthal force on the plasma, will make it slow in the $z$-direction, kept popping up.
My next question was, how an azimuthal force could possibly cause an acceleration in the $z$-direction. The answer I found was that, since the azimuthal force causes the particles in the plasma to start moving in $\hat{\theta}$, conservation of momentum (C.O.M.) would cause the $\hat{z}$ velocity to decrease. However, conservation of momentum doesn't apply when there are external forces on the system.
After reading further, I found that the logic that would cause conservation of momentum to apply is that, since the Lorentz force is acting on the particles within the plasma, when looking at the plasma holistically, the Lorentz force can be treated as an internal force, and the $\hat{z}$ momentum of the whole plasma would decrease.
Is any of this true? Would it be more accurate to say that the particles within the plasma are exerting a force back on the object, that generates the magnetic field, and that's how C.O.M. is achieved? Please help!
