(* Synchrotron radiation *)

(* Time structure of the radiated power at a point in the xy plane. Change beta and observe the peaking and the shortening of the pulse *)

Manipulate[Plot[(beta+ Sin[varphi])^2 / (1+ beta Sin[varphi])^6, {varphi, - Pi, Pi}, PlotRange -> All], {beta,0,1}]

(* The total power radiated in the xy plane, as a function of beta. Note that in spite of the pulse width shortening, the net power still grows sharply at large beta. *)

Plot[NIntegrate[ (beta+ Sin[varphi])^2 / (1+ beta Sin[varphi])^6, {varphi, - Pi, Pi}], {beta,0, 0.9}, PlotRange -> All]

Manipulate[SphericalPlot3D[(1 - Sin[theta]^2 Cos[phi]^2  (1 - beta^2) /  (1 - beta Cos[theta])^2) / (1 - beta Cos[theta]^3), {theta,0,Pi}, {phi,0,2 Pi} , PlotRange -> All], {beta,0,1}]