Producing EB Waves: Accelerating and Decelerating Particles

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A charged particle produces an electromagnetic (EB) wave when it accelerates or decelerates due to an external force. The energy of the EB wave originates from the particle's kinetic energy or the work done by the external force. When a particle decelerates, it still emits EB waves, indicating energy loss. In circular accelerators like synchrotrons, this radiated energy contributes to increased electric power costs. Understanding these dynamics is crucial for optimizing particle acceleration and energy efficiency in such systems.
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How does a charged particle, that is accelerating or de-accelerating, produce an EB wave? What is actualy happening when an EB wave is produced? The EB wave has energy, what is happening to the energy of the charged particle? Is the charged particle slowing down, if so why is an EB wave produced for a de-accelerating particle as well?
 
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Charged particles don't accelerate or decelerate by themselves. They do so in response to some external force. So the energy that is radiated away can come either from some of the particle's kinetic energy, or from work done by the external agent, or both.

In a circular electron accelerator (synchrotron) or storage ring, the radiated energy shows up in the accelerator's electric power bill.
 
Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?

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