Hybrid simulation of q=1 high-order harmonics driven by passing energetic particles in tokamak plasmas

High-order harmonics q(ψ_(s))=1 energetic particle modes(EPMs)have been observed in toroidal plasmas experiments with neutral beam injection.To investigate these phenomena,linear properties and nonlinear dynamics of these EPMs driven by passing energetic particles(EPs)are studied via the global hybrid kinetic-magnetohydrodynamic code M3D-K.Simulation results demonstrate that passing EPs'effects on high mode-number harmonics(q(ψ_(s))=m/n=2/2,3/3,4/4)instability are more obvious than the q(ψ_(s))=1/1 mode,especially when q-profile is sufficiently flat in the core region.Furthermore,the effects of the pitch angleΛ_0 and beam ion pressure P_(hot)/P_(total)on the features of high n components are also analyzed specifically.It is found that there exists only one resonant condition for these EPMs.In the nonlinear phase,these high mode-number harmonics can induce significant energetic ions redistribution and chirping up phenomena,which differs from the classical fishbone excited by passing EPs.These discoveries are conducive to better apprehend the underlying physical mechanisms of the highorder harmonics driven by passing EPs.

Influence of adiabatic response of passing energetic ions on high-frequency fishbone

Adiabatic response effects on high-frequency flshbone instability driven by passing energetic ions are studied.With flnite orbit width effects,the adiabatic contributionδW_(hf)is derived analytically for purely passing energetic ions.By approximating the adiabatic contribution to the flrst order of the reverse aspect ratioε,we derive one of its analytic expressions,which is expected to be more accurate than that in a previous work(Graves J P 2004 Phys.Rev.Lett.92185003).For high-frequency flshbone instability,nonadiabatic response is usually dominant over adiabatic response,but under certain circumstances the latter plays an important role,comparable to the former.With a more generalized distribution function by introducing Gaussian-type factors representing their pitch and radial dependences and using a slowing-down equilibrium distribution for the energy of energetic ions,numerical analysis indicates that the adiabatic contribution is conducive to stabilization of the mode and causes a decrease in mode frequency.In addition,we flnd that the adiabatic contribution has a weak stabilizing effect on the flshbone instability when the flnite orbit width effect is taken into account.We further analyze the dependence of the adiabatic contribution on the characteristic parameters of the distribution function.When the neutral beam has either a larger deviation from the plasma axis or a larger radial proflle,the adiabatic contribution has a more evident effect on the flshbone instability.When the neutral beam has a relatively small critical energy,the adiabatic contribution has a greater effect on the mode instability.