The attached file gives reasons to expect that the axel Doppler shift changes the number of observed particles in a beam. This is non-relativistic shift due the motion of a enser or observer relative to a stationary point the beam passes through.
I think you got it the other way around: The Doppler does not influence the particle motion, it is a result of it. The higher the kinetic energy of the particles the more Doppler shifted your spectral lines will be. If you have a low pressure plasma, i.e. one with only few collisions, the classical current density continuity will hold:
j = n*v*q = const. where n is the charge density, v the charge velocity and q the particle charge. Since SDoppler ~ v and higher velocity forces lower density in order to keep j = const. you will observe larger Doppler shifts at lower densities.
That the chicken or the egg problem. Doppler shifts change observed particle fluxes in add dimensions (velocity and observation angle) to almost all differential relationships of the plasma (Faraday-maxwell law for one). But as you say an addition or subtraction to kinetic energy in plasma doe change the Doppler shifts.
See the attached files for a more complete discussion of the axial shifts impacts.
The blue shift does make particles have a greater observed individual energy and increases the number observed passing though a stationary area by a moving sensor or observer. Of cause one could also accelerate part of a plasma to have that part have a greater Doppler shift.
A blue shift (if the plasma is the observer) of an incoming electromagnetic wave makes the plasma get greater acceleration from that wave relative to it's reference plane.