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

The velocity distribution functions of 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⊥≈v∥ ≈Vj, where ½MjV2j =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 spreads given by the perpendicular and parallel temperatures T⊥j(t) =T∥j(t), with Tj(t) increasing as t increases and finally reaching an isotropic saturation value offormula hereHere 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≈¼τsj is the thermalization time of the fusion product species j in the background deuterium plasma, with τsj the slowing-down time. For times t of the order of τj, the distributions can be approximated by a Gaussian in the total energy (i.e. a Brysk type). Then, for times t[ges ]τsj, the velocity distributions of the fusion products will relax towards their appropriate slowing-down distributions. Here we shall 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.