Theoretical And Numerical Research On Particle Transport Induced By Resonant Magnetic Perturbations In Tokamaks

In tokamak,the overlapping of magnetic islands generated by resonant magnetic perturbations?RMPs?are able to induce the stochasticity of field lines at the edge,thus RMPs lead to strong particle transport.In this paper,the quasi-linear particle transport in stochastic magnetic field induced by RMPs is studied through the I-transform theory and the transport theory of steady homogeneous turbulence of plasmas.In the first work,the quasi-linear transport of passing electrons neglecting the mag-netic drift is studied through the I-transform theory,which is based on the Lie-transform perturbation method.Without the existence of the radial electric field?E_r?,the "field-line" model?Rechester&Rosenbluth,1978?can be recovered by our theory.From the"field-line" model we can see that the diffusion coefficient of particles in stochastic magnetic field is proportional to the magnitude of the parallel velocity.Thus due to the large ion-to-electron mass ratio,the diffusion coefficient of electrons is much larger than that of ions,which leads to charge separation and the formation of the ambipolar radial electric field.As is shown in our theory calculation and the test particle simu-lation data,in the stochastic magnetic field with the existence of E_r,the excursion of the kinetic energy of the guiding-center?GC??K and the excursion of the radial posi-tion of the GC ?r are correlated,i.e.,?K = q_sE_r?r,with q_s the charge of particle s.This correlation leads to a relation of the the transport coefficients in phase space,i.e.,DrK = q_sE_rDrr,which induces a convective particle flux??q_sE_r/Ts,with Ts the tem-perature of particle s?.We theoretically calculate the particle flux of electrons and ions with the existence of E_r.By using the ambipolar condition ?er=?ir and the profile data of TEXTOR,we obtain the magnitude and the direction of the ambipolar electric field,which are qualitatively consistent with the experimental observation on TEXTOR.In the second work,the quasi-linear transport of passing particles including the finite-Larmor-radius?FLR?effect and the radial electric field is studied by using the transport theory of steady homogeneous turbulence of plasmas.Both of the "field-line"model and the quasi-linear theory keeping only the poloidal magnetic drift?Myra&Catto,1993?can be recovered from our theory.The theoretical calculation shows that,the re-duced wave-particle resonance condition is m-nq-m?v?E =0,with m the poloidal mode number,n the toroidal mode number,q the safety factor,?v the direction of par-allel velocity v?,???,B0 and R0 are the magnetic field and the major radius at the magnetic axis,respectively,r the radial position.From the resonance condition we can see that,E_r can shift the wave-particle resonance position?E_r-shift effect?and the shift distance is???,with s the magnetic shear.The E_r-shift direction is dependent on the direction of v? and the direction of E_r,thus when the resonance position is shifted to a position where the perturbation magnitude is smaller,the diffusion coefficient is reduced and vise versa;the E_r-shift distance is reversely proportional to the magnitude of the parallel velocity,thus the E_r-shift effect mainly modifies the diffusion coefficient of ions.By using the experimental profile data of DIII-D,we numerically calculate the particle flux of electrons ?er and the particle flux of deuterons ?_deu^r with the existence of different E_r.And by using the ambipolar condi-tion ?er=?_deu^r,we obtain the profile of the ambipolar radial electric field and the profile of the total particle flux at the edge.We find that,since the E_r-shift effect mainly re-duces the coefficient of deuterons,the reduction of the deuteron particle flux at the edge leads to a reduction of the total flux at the edge.The total flux at the edge is one order of magnitude smaller than that calculated by the "field-line" model,which is qualita-tively consistent with the experimental observation.The effective diffusion coefficient of electrons estimated from our model??0.05?0.1?m²s^-1 is of the same order of magnitude as the experimental observation?0.2m²s^-1.