The Model Studies Of The Interactions Between Transport Of Turbulence Intensity And Temperature Profiles

In tokamak plasmas, energy transport (i.e, heat diffusion) process obeys Gyro-Bohm (GB) scaling according to turbulence transport models modulated by zonal flows. However, in some edge modulated experiments, it is observed that the core temperature of plasma responds fast to the edge injected "cold pulse" and "heat pulse" within a very short time. The characteristic time scale of such responses is much smaller than that of the typical heat diffusion time predicted by GB scaling, thus it can be seen as a transient transport in GB scaling regime. And it is also observed that the chracteristic length scale of such transient responses is greater than the correlation length but smaller than the system size or the mean temperature gradient length, thus it can also be seen as a nonlocal transport in GB scaling regime. Such mismatches suggest breaking of GB scaling, and a new scaling on meso-scales is needed to completely explain the mechanism of transient nonlocal transport.To understand the transient nonlocal transport on meso-scales, there are two basic mechanisms in theory, nonlinear mode coupling mechanism and self-organized criticality (SOC) mechanism. However, in the previous nonlinear models of turbulence transport, such as K-ε, Fokker-Planck (F-P), and Critical Gradient (CG) models, the nonlinear noise or incoherent source term and the self-consistent electric field shear feedback on turbulence are all neglected in all the models. In this thesis, according to nonlinear mode coupling mechanism, a model of turbulence intensity spreading with self-consistent nonlinear noise is derived via triad mode nonlinear coupling processes. The effects of the nonlinear noise on turbulence spreading are studied. Another simple two-field CG model consisting of coupled nonlinear reaction-diffusion equations for both turbulence intensity and heat transport is proposed according to SOC mechanism. Supression of self-consistent E×B shear feedback on turbulence intensity growth and transport is also included in the model. In the approach of heat flux-driven turbulence, the model has been used to elucidate several aspects of transient nonlocal transport dynamics, such as the variation of turbulence spreading speed and heat transport speed as heat flux increases, intensity pulse propagation with a constant front speed and penetration through a transport barrier, some important conditions required to prevent inward intensity pulse penetration, and fast transients of "cold pulse" induced opposite polarity and "heat pulse" induced profile resilience.First of all, transient nonlocal transport is reviewed in Chapter 1, such as the observations in "cold pulse" and "heat pulse" experiments, the discussions of two nonlocal transport mechanisms, some important factors of influencing heat transport and the research progresses of transient nonlocal transport in simulations. According to nonlinear mode coupling mechanism, a model of turbulence intensity spreading with self-consistent nonlinear noise is derived via triad mode nonlinear coupling processes in Chapter 2 of this thesis. The range of any nonlinear mode interactions of the background with a test mode is restricted to within a mode scale width from the test mode rational surface during the derivation. It is found that all the nonlinear terms (such as noise, dissipation and diffusion) derived from nonlinear mode coupling can be written in the form of▽·J. The nonlinear noise and the dissipation terms indeed cancel each other upon the summation over all modes, thus it satisfies energy conservation. Both the nonlinear noise term and the dissipation term are necessary. The dynamics of turbulence spreading can be completely expressed only if both the nonlinear noise and the dissipation terms are included. During the nonlinear mode coupling processes, the characteristic length scale of free energy transport is defined by the balance of turbulence growth rate and dissipation rate. The local free energy of fluctuation is scattered in two steps. First, the excitation and dissipation of free energy balances with each other at the correlation length. Second, this correlation length defines a nonlinear diffusion coefficient for turbulence intensity, which transfers the free energy from source to sink continually and makes turbulence transport nonlocally at last.Based on the model built in Chapter 2, a residual i.e., the local non-zero difference of nonlinear noise and dissipation terms is calculated, and the influence of the residual on the local front speed of turbulence spreading is also calculated in Chapter 3. It is found that the residual is on the correlation length scale, depending on the square of the ratio of mode correlation length to mode width, and no net residual survives summation of the residuals of all the modes. Without the residual, the turbulence spreading speed is a constant at the Fisher front speed. If the residual is included, a small correction to the Fisher front speed, is found at low order rational surfaces, depending on the mode number k. Note that the Fisher front speed is generic to reaction (growth)-diffusion models, and thus gives a generic answer to the question of how one extracts non-diffusive dynamics from a seemingly diffusive model.After the discussions of the turbulence spreading dynamics in Chapters 2 and 3, another simple model consisting of coupled equations for both turbulence spreading and heat transport is proposed in Chapter 4 to further investigate the implications of turbulence spreading models on nonlocal heat transport. Supression of self-consistent E×B shear feedback on turbulence intensity growth and transport and critical temperature gradient effect are also included in the model. The variations of heat flux-driven turbulence spreading speed and heat transport speed as heat flux increases are elucidated in envelop theory. It is found that the dynamics of heat transport is dominated by turbulent heat transport at low heat flux (low-Q), but by neoclassical heat transport at high heat flux Q (high-Q). Even more noteworthy is that as heat flux increases the propagation speed of a turbulence intensity pulse first increases as Q1/2 at low-Q and then decreases as 1/Q at high-Q to zero, without saturation.The influence of internal transport barrier (ITB) on intensity pulse propagation is studied in Chapter 5. It suggests that the ITB inhibits both the inward turbulence propagation and the outward heat transport. It is found that, in a case of uniform turbulence propagation, the edge excited intensity pulse propagates inwards with a nearly constant front speed. However, in a case of non-uniform turbulence propagation (i.e., a finite extent region with no local turbulence excitation), the intensity pulse can tunnel through the gap in some cases. But, the tunneling process can be prevented in some other cases of increasing total heat flux, a wider gap, a stable gap with a local damping rate, and stronger E×B shear feedback. This shows that local stability alone does not exclusively control the local turbulence intensity sometimes, since it is also influenced by turbulence growth in nearby unstable regions and other conditions. Of course, the mean temperature profile can be influenced by ITB. Within the ITB, turbulence intensity will be suppressed, thus, the local turbulent thermal diffusivity is reduced and the local mean temperature profile is steepened. Therefore, the local mean temperature profile is changed.Finally, both "cold pulse" and "heat pulse" induced transient nonlocal transports, opposite polarity and profile resilience which are different but much related, are reproduced and compared by the turbulence spreading model proposed in Chapter 4. These transient nonlocal transports are always investigated seperately and have not been explained together by previous theoretical models. It is found that these transient nonlocal transports have the same characteristic time scale, which is about the time scale of turbulence spreading, although they are seemly different with one and the other. It is found that the fast propagation of intensity pulses induced by both "cold pulse" and "heat pulse" is the crucial factor to explain the opposite polarity and profile resilience. In a sense, the turbulence fast nonlocal propagation provides the element of'non-locality'for the transient nonlocal responses between edge and core. Thus, mean temperature profile evolution with and without the turbulence intensity propagation can be very different.