Theoretical And Numerical Research On Transport In The Stochastic Magnetic Field In Tokamak Plasmas

The stochastic field can induce the anomalous transport in tokamak plasmas,which reduces the confinement of tokamak.Numerical gyro-kinetic simulation is a powerful method to investigate the turbulence transport.Simulations can compute the particle flux and the heat flux.Generally,the transport fluxes contain the diagonal diffusive term and the off-diagonal convective term.It is important to understand the turbulence transport by distinguishing each term.However,these two terms can be hardly dis-tinguished from the simulations at present.The method that computing the fluxes by using the phase-space transport matrix can distinguish the two terms.In this thesis,we calculate the second-order Hamiltonian of gyro-kinetic theory with full electromagnetic potential perturbations by using the Lie-transform method,then improve the guiding-center(GC)orbit code GYCAVA;then we develop a numerical code,based on the im-proved GYCAVA,to compute the phase-space transport matrix by integrating along the full orbit of GC.In the first work,the second-order gyro-kinetic Hamiltonianin,in the low fre-quency electromagnetic field,is investigated in detail by using the two-step Lie-transform method.The result shows that the main term of the second-order transformed Hamil-tonian is 1/2?A?2 for any magnetic perturbation in the long-wave-length limit.And the result is due to the little difference of the magnetic moment ?? between the magnetic moment in gyrocenter coordinates and that in guiding-center coordinates.And it is the corresponding Hamiltonian ??B0 that cancels the 1/2?A?2,where B0 is the equilibrium magnetic field.The GC orbit code NLT and GYCAVA are improved,based on the the-ory,to compute the GC orbit of particles in TFTR with a ripple field and to simulate the collisionless stochastic diffusion of energetic particles.And the simulation result of the stochastic diffusion area of the energetic particles agrees well with GWB theory result for TFTR.In the second work,we develop a numerical code,based on the improved GY-CAVA,to compute the phase-space transport matrix by integrating along the full orbit of GC.Two test simulations are carried out to validate the code to compute the phase-space transport matrix.One is the scaling relations between De and v?,|?A|,where De is collisionless diffusion coefficient of passing electrons in a tokamak with the stochas-tic magnetic field,v? is the parallel velocity of electrons and |?A| is the amplitude of perturbation fields.The scaling relations are De ?|v?|;De ?|?A|2.The other one is the relation between Drv? and Drr and the relation between Dv?v? and Drr,where Drv?is the cross-correlation between the parallel velocity excursion ?v? and the radial excur-sion of guiding centers ?r and Dv?v? is the auto-correlation of ?v? And the simulation result agree with the theory result.Then the code is used to verify the |v?| cut-off of the auto-correlation of the parallel velocity excursion ?v?.The code also computes the Lagrangian correlation function to obtain the Lagrangian correlation time and the tur-bulence correlation length.For the case of stochastic magnetic field,we find that the order of magnitude of the parallel correlation length can be estimated by qR0,where q and R0 are the safety factor and the major radius,respectively.