Kinetic Investigation Of Spontaneous Rotation Driven By Electromagnetic Turbulence In Tokamak Plasmas

Tokamak is one of the most promising magnetic confinement fusion(MCF)devices to achieve artificial controllable nuclear fusion.Improving the confinement performance of tokamak plasma is crucial for realizing commericilization of fusion reactor.Plasma toroidal rotation can significantly improve plasma confinement performance via stabilizing macroscopic magnetohydrodynamic(MHD)instabilities and suppressing mircoturbulence.However,for future fusion reactors like International Thermonuclear Experimental Reactor(ITER),external driven sources are not needed any more after self-controlled heating is achieved,so understanding the generation mechanisms of spontaneous rotation is particularly important for furture reactors.Existing results from experiments and simulations found that electromagnetic effects can significantly affect spontaneous rotation.Therefore,it is important to investigate the spontaneous rotation driven by electromagnetic turbulence in tokamak plasmas.Gyrokinetic theory has provided theoretical foundations for studing the lowfrequency and small-scale microturbulence in tokamak plasmas.We analytically derived the mean field evolution equation of the plasma parallel rotation velocity with considering electromagnetic ion temperature gradient(ITG)turbulence in slab geometry.It is shown that both kinetic stress and cross Maxwell stress,which are directly related to magnetic perturbation,can make contribution to the generation of spontaneous rotation.This is analogous to the usual residual stress.In addition,there are two terms named turbulent acceleration which cannot be written as a divergence of stress.Therfore,they can act as a local source/sink of spontaneous rotation.Except the turbulent acceleration term obtained in electrostatic condition,we also obtain an electromagnetic turbulent acceleration term driven by the equilibrium ion pressure gradient along radial perturbed magnetic field in electromagnetic condition.The total turbulent acceleration driven by the correlation between the density fluctuation and the pressure gradient along the total magnetic field line is obtained by combing these two terms.The quasilinear expressions for all the intrinsic torqure terms are calculated,showing that electromagnetic effects have great influence on intrinsic torque.To clarify the influence coming from electromagnetic effects,we estimated these intrinsic torque therms by taking the typical plasma parameters from the pedestal top region on DIII-D,in which the dominant turbulence mode is the electromagnetic ITG mode.Comparing to the results obtained in electrostatic condition,electromagnetic effects can reduce the non-resonant stress force and even reverse its sign,but enhance the resonant stress force.Meanwhile,both the non-resonant and resonant turbulent acceleration terms are also enhanced by electromagnetic effects.Because of the flat density profile in the pedestal top region,the characterstic frequency of the eIectromagnetic ITG mode is comparable to the ion transit frequency,leading to very strong resonant effects.Thus,the resonant intrinsic torque is also important and it is comparable to the non-resonant intrinsic torque.By changing the sequence of taking flux average and decoupling ion desnity and rotation velocity,we use two different methods to obtain the same mean field evolution equation of the plasma parallel rotation velocity in slab geometry.It is proved that the presence of turbulent acceleration does not result from regrouping terms.The turbulent acceleration really exsits in physical nature.Meanwhile,we also derive two kinds of gyrocenter momentum conservation equations,and obtain similar results in particle space by pull-back operation.We point out that the conserved quantity corresponding to the axial symmetry of tokamak is the total canonical momentum carried by both species or the total momentum including the ion kinematic momentum and the electromagnetic fields momentum,but not the ion kinematic momentum,even not the ion rotation velocity.Therefore,the turbulent acceleration in the evolution equation of the ion mean rotation velocity does not break the momentum conservation law,but is consistent with the momentum conservation law.We also extend the results in the pedestal top region to the steep gradient region of pedestal with considering radial equilibrium electric field and toroidal effects.Because of the large density gradient in this region,the characteristic frequency of the electromagnetic instability is much larger than the magnetic drift frequency and the electron diamagnetic drift frequency,making the resonant effects negligible.Simultaneously,the magnetic drift frequency is much less than the electron diamagnetic drift frequency,so the toroidal effects coming from magnetic drift frequency make little contribution to the intrinsicn torque of plasma.However,according to the radial force balance equation of ions,the radial equilibrium electric field shoulde be taken inton consideration due to the strong pressure gradient.The quasilinear results are estimated by taking the typical plasma parameters from the steep gradient region of pedestal on DIII-D.It is found that the intrinsic torque obtained with considering radial equilibrium electric field is much smaller than that without considering radial equilibrium electric field,even neglecting the suppression effects on turbulence intensity due to radial equilibrium electric field.This reason may be that the radial equilibrium electric field can not only suppress the turbulence intensity,but also reduce the correlation coefficient between fluctuations,then leading to the reduction of intrinsic torqure driven by turbulence.Moreover,electromagnetic effects can significantly enhance the non-resonant residual stress force but reduce the non-resonant turbulent acceleration in the steep gradient region regardless of the presence of radial equilibrium electric field,resulting in a negligible total non-resonant turbulen acceleration.Therefore,the spontaneous rotation is mainly driven by non-resonant stress force,which is different from the case of pedestal top region.In a word,the influence of electromagnetic effects on plasma spontaneous rotation is non-negligible in pedestal region.Taking into account the electromagnetic effects and turbulent acceleration is necessary for accurate understanding and prediction of spontaneous rotation.