【作者】 王占辉；

【导师】 王晓钢； Patrick H. Diamond；

【作者基本信息】 大连理工大学 ， 等离子体物理， 2011， 博士

【摘要】 在层状流调制的托卡马克湍流输运模型中,能量输运(如热扩散)过程遵循回旋玻姆定标律。然而,在一些边缘调制实验中却发现,边界注入的冷脉冲或热脉冲会导致芯部的等离子体温度在很短的时间内做出响应,该响应的时间尺度远小于回旋玻姆定标律下的热扩散时间尺度,即在回旋玻姆标度下可以看成是“瞬时”的输运。实验还发现,尽管这一响应的空间尺度小于系统平均温度剖面的尺度,但是大于波模的相干长度,即在回旋玻姆标度下可以看成是“非局域”的。这表明回旋玻姆定标律在这个过程中已经失效,需要寻找新的“介观”尺度上的定标律,去完善地描述这种“瞬时”、“非局域”输运过程的物理机制。理论上,非线性波模耦合和自组织临界这两种机制可用于解释“介观”尺度上的“瞬时”、“非局域”输运现象。但是,之前的非线性湍流输运理论模型如K-ε模型、福克-普朗克模型以及临界梯度模型等,都忽略了非线性噪音项即三波耦合的非相干部分,以及自洽的电场剪切对湍流输运的抑制作用。本文根据非线性波模耦合机制,考虑三个波模间的直接相互作用,建立了一个含有自洽的非线性噪音项的湍流输运谱方程,分析了三个波模耦合产生的非线性噪音项对湍流输运速度的影响；然后,根据自组织临界机制,考虑自洽的电场剪切对湍流输运的抑制作用,建立了另一个双场临界温度梯度模型；并采用稳恒热通量驱动湍流的计算方法,研究了“瞬时”非局域输运的几个相关方面：湍流及热输运速度随热通量的变化关系,隙垒对湍流输运的影响,边界扰动强度脉冲以稳恒波前速度传播的现象,隧穿隙垒的现象,影响并阻止隧穿过程的一些重要因素,冷脉冲引起的逆极性响应和热脉冲引起的平均温度剖面不变性等。首先,本文在第一章里综述了“瞬时”非局域输运的研究概况,其中包括：冷脉冲和热脉冲注入分别引起的非局域响应及其性质的实验观测、两种非局域输运机制的讨论、影响热输运的一些重要因素、以及数值计算方面的研究进展。本文的第二章基于非线性波模耦合机制,通过考虑三个波模间的直接相互作用,建立了含有自洽非线性噪音项的湍流输运谱方程。在推导过程中,非线性波模之间的直接相互作用被局限在距离有理面附近约一个波模宽度的范围内。研究发现所有的三波非线性作用项(非线性扩散项、非线性噪音项和非线性碰撞项)都可以写成扰动强度通量▽·JQ的形式。在对所有波模求和之后,非线性噪音项和非线性碰撞项就相互抵消,并且满足能量守恒定律。所以,非线性噪音项和非线性碰撞项两者缺一不可,只有当二者同时存在时,才能全面展现湍流输运的动力学特性。在非线性波模耦合过程中,湍流增长率和耗散率之间的相互平衡关系给出自由能输运的相干长度。则局域的扰动自由能的输运可以看作下面的过程：首先,在这个相干长度上自由能的激发和衰减之间相互抵消；其次,这个相干长度定义了一个非线性湍流扩散系数,它不断地把自由能从源点输运到耗散点,从而实现湍流的非局域输运。第三章是在第二章所建立的湍流输运谱方程的基础之上,进一步计算了在有理面附近非线性噪音项和非线性碰撞项之间的差值,即残留项；并研究了这个残留项对湍流波前输运速度的影响。本文发现该残留项存在于相干长度的尺度内,它与相干长度和波模宽度之比的平方成正比,且在对所有波模求和之后,残留项就会消失。在忽略残留项的情况下,湍流会以一个稳恒的Fisher波前速度进行传播。这一特性是所有反应-扩散型输运方程所共有的特性。同时它也说明,为什么一个看似扩散性的输运方程却能够解释非扩散性的输运现象。在考虑残留项的情况下,局域的湍流输运速度相对于不考虑残留项时的Fisher波前速度有所增加,而且在较低波模的有理面附近,Fisher波前速度的增量将会更为明显。在前两章讨论湍流输运的动力学性质的基础上,第四章基于自组织临界机制,建立了一个耦合了湍流输运方程和热输运方程的简单理论模型来进一步研究湍流输运模型对非局域热输运研究的应用。这个模型包含了电场剪切对湍流的增长率和湍流输运的抑制作用,以及临界温度梯度效应。通过对此理论模型的计算求解,研究了包络理论下热通量驱动的湍流输运速度和热输运速度随热通量的变化关系。研究结果表明：在低热通量Q状态,热输运的动力学特性主要由湍性热输运所决定；但在高热通量Q状态,则由新经典热输运所决定。更值得注意的是：湍流输运速度会随着热通量的增加,先以Q1/2进行增长然后以1/Q进行衰减,但并没有达到一个稳恒的饱和值。第五章研究了隙垒对湍流输运的影响,发现隙垒不仅可以阻挡热输运,而且还可以隔绝湍流传输。在均匀湍流激发的区域,外部边界所激发的扰动强度脉冲会以一个几乎稳恒的波前速度向内传播。然而,在非均匀湍流激发的区域,即存在隙垒区(一个湍流增长率为零的区域)时,虽然边界激发的扰动强度脉冲在一定情况下可以隧穿隙垒,但是,这种隧穿过程会受一些条件的限制而终止。这些条件包括：热通量的增加、隙垒的宽度较大、隙垒内湍流的耗散率增强,或者很强的电场剪切对湍流的反馈作用等。所以,局域的稳定性并不能够总是控制局域的扰动强度,它还受到邻近不稳定区域和其它一些条件的影响。此外,隙垒还会引起平均温度剖面的改变：隙垒的存在将导致局域扰动强度不断衰减,随着局域湍性热输运的减少,隙垒内的温度将不断增加,从而改变平均温度剖面。第六章综合对比分析了冷脉冲和热脉冲注入所分别引起的逆极性响应现象和平均温度剖面不变性现象,并且同时再现了这两种看似不同、实则相关的“瞬时”非局域输运现象。而之前人们对冷脉冲和热脉冲所引起的这两种“瞬时”非局域响应现象,大多是分别独立地进行研究,且很少有理论模型能同时解释这两种“瞬时”非局域输运现象。尽管它们看似不同,但是它们却具有相同的特征时间尺度,而且该时间尺度与湍流输运的时间尺度相当,所以它们实质上是相关的。研究发现,冷脉冲或热脉冲注入所引起的扰动强度脉冲快速非局域的输运过程,是导致逆极性响应和平均温度剖面不变性的关键因素。在某种意义上,湍流“瞬时”非局域输运为芯部和边界之间的“瞬时”非局域响应提供了“非局域”这一特性。湍流输运存在和不存在两种情况下平均温度剖面随时间的演化存在着本质的区别。更多还原

【Abstract】 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.更多还原