Theory - The Larmor formula

The Larmor formula is a fundamental concept in classical electromagnetism that describes the power radiated by an accelerated charged particle. Its physical meaning can be understood by breaking down its components and implications:
(Under non-relativistic conditions)

$$\mathrm{P}=\frac{q^2{a}^2}{6\pi {\epsilon }_0{c}^3}$$

In SI Units, Where:
P is the total power radiated.
ε₀ is the permeability of free space.
q is the charge of the particle.
a is the acceleration of the particle.
c is the speed of light in a vacuum.

If a standing still system accelerates a beam of electron to a high speed, both the standing system and the beam will get opposite momentum.

However, if the electron beam is forced to track a curved acceleration, according the Larmor formula, the beam of electron could radiate energe to space out of the standing system.

As a result, the speed of the beam will slow down, and thus lose its momentum, while the standing system keep the opposite moment.

The whole system including the electron beam will gain net momentum