Ion Cyclotron Emission Due To The Newly-born Fusion Products Induced Fast Alfvén Wave Radiative Instabilities In Tokamaks
Author: V. Arunasalam
The velocity distribution functions of the newly born (t = 0) charged fusion products (protons in DD and alpha particles in DT plasmas) of tokamak discharges can be approximated by a monoenergetic ring distribution with a finite v|| such that v^ Å v|| Å 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 (i.e., a drifting Maxwellian type) with thermal spreadings given by the perpendicular and parallel temperatures T^j(t) = T||j(t) with Tj(t) increasing as t increases and finally reaches an isotropic saturation value of T^j(t Å tj) = T||j(t Å tj) = Tj(t Å tj) Å [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 tj Å tsj/4 is the thermalization time of the fusion product species j in the background deuterium plasma and tsj is the slowing-down time. For times t of the order of tj their distributions can be approximated by a Gaussian in their total energy (i.e., a Brysk type). Then for times t ³ tsj the velocity distributions of these fusion products will relax towards their appropriate slowing-down distributions. Here we will examine the radiative stability of all these (i.e., a monoenergetic ring, a Gaussian in velocity, a Gaussian in energy, and the slowing-down) distributions.