A point charge oscillates with the trajectory r0(t ) a cos( 0 t)z Find the angular distribution of power radiated into the m th harmonic, dP m d, during one period of the motion Which harmonics dominate in the non relativistic limit Two Bessel function identities will be useful Jm(x) im 2 2 T d expli(mp x cos 4) and Jm 1(x) Jm 1(x) (2m x) Jm (x)

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Question: A point charge oscillates with the trajectory r0(t ) = a cos( 0 t)z. Find the angular distribution of power radiated into the m th

A point charge oscillates with the trajectory r0(t ) = a cos(ω₀t)ẑ. Find the angular distribution of power radiated into the m^th harmonic, dP_m/dΩ, during one period of the motion. Which harmonics dominate in the non-relativistic limit? Two Bessel function identities will be useful:

Jm(x)= im 2 2.T [ d expli(mp - x cos 4)] and

Jm(x)= im 2 2.T [ d expli(mp - x cos 4)] and Jm+1(x) + Jm-1(x) = (2m/x) Jm (x).

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