Bounce effects in the negative mass instability

Bounce effects on the cyclotron instability caused by trapped alpha particles in tokamak reactors

“…It is evident that Ac3 B /to b > 1. Therefore, it follows from the above that bounce effects must be taken into account not only in the theory of electrostatic instabilities considered in Refs [4][5][6][7][8][9] but also in…”

“…The cyclotron build-up of waves by trapped particles has also been considered in connection with the problem of plasma confinement in adiabatic traps [4][5][6][7][8][9]. In contrast to Refs [1][2][3], the excitation ofpotential (electrostatic) perturbations is investigated in Refs [4][5][6][7][8][9], Here the authors allowed not only for the non-monotony of the energy distribution, taken into account in Refs [1][2][3], but also for anisotropy of the particle velocity distribution. It was shown that resonance interaction of the type shown in expression (1.1) between anisotropic trapped ions and electrostatic perturbations may lead to a hydrodynamictype instability called the modified negative-mass instability.…”

“…Apart from the modified negative-mass instability due to ion anisotropy, which is hardly of relevance to the dynamics of alpha particles in a tokamak, Refs [4][5][6][7][8][9] also brought to light electrostatic instabilities which, like the fast magneto-acoustic wave instability considered in Refs [1][2][3], are caused by non-monotony of the transverse velocity distribution function. References [4][5][6][7][8][9] investigated not only resonances of the type described in expression (1.1), which were analysed in Refs [1][2][3], but also resonances of the type co = ncog + 2pco b (1.4) where co b = 27T/T is the bounce frequency and p is an integer.…”

“…Apart from the modified negative-mass instability due to ion anisotropy, which is hardly of relevance to the dynamics of alpha particles in a tokamak, Refs [4][5][6][7][8][9] also brought to light electrostatic instabilities which, like the fast magneto-acoustic wave instability considered in Refs [1][2][3], are caused by non-monotony of the transverse velocity distribution function. References [4][5][6][7][8][9] investigated not only resonances of the type described in expression (1.1), which were analysed in Refs [1][2][3], but also resonances of the type co = ncog + 2pco b (1.4) where co b = 27T/T is the bounce frequency and p is an integer. From the analysis performed it follows that allowance for resonances of the type described in expression (1.4) (called bounce resonances) and the effects associated with them (bounce effects) is important if the scatter of the averaged cyclotron frequencies co B for particles with different degrees of trapping (a different ratio of magnetic moment to energy) is not small compared with their characteristic bounce frequency:…”