Ion cyclotron emission due to the newly-born fusion products induced fast Alfven wave radiative instabilities in tokamaks

The velocity distribution functions of the newly born (t = 0) charged fusion products of tokamak discharges can be approximated by a monoenergetic ring distribution with a finite vparallel such that vperpendicular ∼ vparallel ∼ vj where (MjVj2/2) = Ej, the directed birth energy of the charged fusion product species j of mass Mj. As the time t progresses these distribution functions will evolve into a Gaussian in velocity with thermal spreadings given by the perpendicular and parallel temperatures Tperpendicularj(t) = Tparallelj(t) with Tj(t) increasing as t increases and finally reaches an isotropic saturation value of Tperpendicularj(t ∼ τj) = Tparallelj(t ∼ τj) = Tj(t ∼ τj) ∼ [MjTdEj/(Mj + M)]1/2, where Td is the temperature of the background deuterium plasma ions, M is the mass of a triton or a neutron for j = protons and alpha particles, respectively, and τj ∼ τsj/4 is the thermalization time of the fusion product species j in the background deuterium plasma and τsj is the slowing-down time. For times t of the order of τj their distributions can be approximated by a Gaussian in their total energy. Then for times t ≥ τsj the velocity distributions of these fusion products will relax towards their appropriate slowing-down distributions. Here the authors will examine the radiative stability of all these distributions. The ion cyclotron emission from energetic ion produced by fusion reactions or neutral beam injection promises to be a useful diagnostic tool