Influence of canonical angular momentum spread on the synchrotron radiation spectrum for a relativistic plasma

The influence of canonical angular momentum spread on the incoherent synchrotron radiation spectrum Il(ω) is calculated for a relativistic low-density (ω2p/ω2c≪1) plasma column that rotates about an axis of symmetry aligned parallel to a uniform magnetic field B0êz. The analysis is carried out for the class of spatially nonuniform Vlasov equilibria described by f0e(x,p) =const×F1(H/mc2)exp{−(Pϑ −P0)2/2Δ2}δ (pz), where P0 and Δ are positive constants, H is the energy, Pϑ is the canonical angular momentum, and pz is the axial momentum. A detailed parameter study is presented which shows that Il(ω) exhibits a sensitive dependence on canonical angular momentum spread Δ. For Δ=0, and smooth energy distribution F1(H/mc2), the lth harmonic spectrum Il(ω) is characterized by a sudden onset of emission for ω⩽lωc/γ0, where ωc=eB0/mc and γ20=1+2ωcP0/mc2. For sufficiently large Δ, however, there is a continuous onset of emission for ω⩽lωc. The analysis also reveals a strong dependence of electron density profile ne0(r) on canonical angular momentum spread Δ. In particular, small Δ corresponds to a hollow beam equilibrium, whereas sufficiently large Δ corresponds to an electron density profile peaked on axis.