Bremsstrahlung collision contribution to entropy generation and attendant radial expansion in a self-pinched high-power relativistic electron beam propagating in a neutral gas

Abstract

In the Bennett-Nordsieck self-pinched regime of high power REB propagation in a neutral atmosphere, radial expansion is generally associated with transverse entropy generation caused by elastic electron-neutral multiple scattering: LN ∝ 1/s′⊥ elast, where LN is the Nordsieck length, the distance for one e-folding of beam radius, and where s′⊥ elast is the elastic collision space rate of transverse mean entropy per particle.For ultrarelativistic beams (γ ≳ 100), the bremsstrahlung, which is the dominant energy loss process, also plays an essential rôle in the radial expansion.A general treatment could be based on the proper time evolution equation of the beam electron pressure 4-tensor pλμ (λ, μ = 0, 1, 2, 3) where source terms linked to elastic, inelastic and bremsstrahlung collisions are introduced, as is also a closure relation. This approach is currently being studied at LPPG.When the various implied scale lengths have clearly different orders of magnitude, a much simpler approximate description may be given.In the λmbrems < z < λstrbrems propagation distance range, where λmbrems is the depth threshold beyond which bremsstrahlung scattering becomes multiple, and λstrbrems a characteristic distance for bremsstrahlung straggling, the rôle of bremsstrahlung in radial expansion is similar to that of elastic multiple scattering. The calculated s′⊥ brems/s′⊥ elast increases rapidly with both propagation distance and beam electron energy. For γ ≫ 103, the bremsstrahlung transverse entropy source term s′⊥ brems is no more negligible before s′⊥ elast.In the z > λstrbrems propagation distance range, where bremsstrahlung straggling is dominant, an evaluation of its effect is deduced by applying the Haftel–Lampe–Aviles criterion to a statistical study of this straggling. A completely different estimation, based on an oversimplified version of the above-cited general thermodynamic method, gives a result which is in rather good agreement.