Theoretical Studies Of Collisionless Trapped Electron Modes In Tokamak Plasmas

Collisionless trapped-electron mode(CTEM)turbulence is considered to be one of the im-portant mechanisms responsible for the anomalous transports in tokamak plasmas[1].Although investigated extensively for decades,the nonlinear dynamics of CTEMs are still an active topic in tokamak physics research[1-4].In this dissertation,by employing the nonlinear gyrokinetic equation and the ballooning-mode representation,we have studied various linear and nonlinear properties of CTEMs.First,we introduce basic features of the magnetic field in tokamaks and its associated guiding center dynamics,emphasizing the mechanisms of anomalous transports induced by microscopic turbulences.The classical nonlinear gyrokinetic theory and its basic contents together with the well-known ballooning-mode representation are also briefly introduced.Second,we give a step-by-step guide for the excitation mechanisms and the classification of the collisionless trapped-electron mode.By assuming ’fluid ions + kinetic trapped-electrons’ and including the effects of finite radial envelope modulations(i.e.,finite θk effects),we derive the corresponding eigenmode equation for CTEMs.To numerically solve the eigenmode equation,we further present a numerical algorithm based on the generalized argument principle.Numerical results of the linear eigenmode equation indicate that the finite radial envelope modulation effects can affect the linear CTEM stability both qualitatively and quantitatively,through the significant modifications in the associated eigenmode structures.Specifically,in the case without radial en-velope modulations(i.e.,θk = 0),the toroidicity-induced modes relevant to the trapped-electron instability can be categorized into two types:the strong toroidicity-induced modes peaking around the outboard(i.e.,η=0)of the tokamak,and the weak toroidicity-induced modes peaking away from the η=0 outboard.When the finite θk effect is taken into account,the most unstable even parity strong toroidicity-induced modes center at θk = 0.The linear growth rates of the even parity weak toroidicity-induced modes and the odd parity weak/strong toroidicity-induced modes,however,peak at a finite θk,with the parity being referred to the limit of θk = 0.Third,we investigate a specific case of nonlinear mode-coupling processes in the CTEM turbulence,i.e.,the spectral cascading process in toroidal mode numbers due to the nonlinear s-cattering effects,and focus on its dependence on the physical parameters.We firstly explain the theoretical framework of weak turbulence theory via a local theory of the spectral cascading pro-cesses.The results indicate that the spectral cascading processes are dominated by the inverse spectral cascading processes in toroidal mode numbers due to local ion-induced scatterings,and resonant particles mainly exchange generalized toroidal angular momentum with CTEM plasmons in these processess.Then the spectral cascading effects in toroidal mode numbers are systemat-ically investigated in the toroidal geometry by using the nonlinear gyrokinetic equations and the ballooning-mode representation.It is found that the finite radial envelope modulations can signifi-cantly affect the scattering effects via the nonlinear coupling coefficient,the overlapping between mode structures parallel to the confining magnetic field and the modification in the wave-particle resonance due to the ion magnetic drift.For the typical parameters of the present-day tokamak experiments,the trapped-electron-induced scattering dominates when the quasi-mode phase ve-locity is along the trapped-electron toroidal precession direction,while the ion-induced scattering,due to the finite radial envelope modulation effects,dominates when the quasi-mode phase veloc-ity is along the ion magnetic drift direction.Furthermore,the spectral cascading direction in the toroidal mode numbers is found to depend on the value of the ion and trapped-electron temperature gradients.