A Ponderomotive force and conservation of momentum

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A charged particle in an inhomogeneous, oscillating electric field experiences ponderomotive force, accelerating away from regions of stronger field intensity. When a charged particle is positioned off-center in a laser beam, it moves toward weaker field areas. This movement affects the laser beam's momentum, as described by a theorem analogous to Poynting's theorem, which states that changes in the particle's momentum result in equal and opposite changes in the electromagnetic field's momentum. The interaction highlights the conservation of momentum between the particle and the electromagnetic field. Understanding this relationship is crucial for applications in laser physics and particle dynamics.
Philip Koeck
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According to https://en.wikipedia.org/wiki/Ponderomotive_force a charge in an inhomogeneous, oscillating electric field will be accelerated in the direction where the field gets weaker.

One could think of a charged particle placed slightly off-center inside a laser beam.
If I read the Wikipedia page correctly this particle should be accelerated away from the center of the beam.

What would happen to the laser beam during this process?
 
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There is a theorem like Poynting’s theorem, but for momentum. As the momentum of the particle changes, the momentum of the EM field changes in the equal and opposite direction.
 
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