延长Tokamak运转时间的机理

The Mechainism of Tokamak Operation Elongating

首先建立超环体内等离子体稳定时的三维正交向量磁场B、电流密度J和压子梯度Δp的力平衡方程,再取超环曲面坐标系和对激励的基准磁场的处理,使三维向量方程问题化为常微分方程问题,并求出其解析解。从数理方程的存在性引入正算子和正定算子定义,再结合力场做功构成变分学中的泛函。从论证数理方程和泛函数中确认Tokamak解的存在性、唯一性和稳定性问题,得到正定算子的门限是使Tokamak稳定运转的保证。电阻率为零的理想等离子体是稳定的,但电阻率不为零的非理想情况的时变电流会逐渐消蚀正定算子的门限使算子成为非正算子,从而系统不稳定。保证正定算子的门限不随时间增长而渐趋消蚀是延长Tokamak运转时间的关键。其处方是构造一个克隆样本来克隆整个Tokamak的运转规律。并采用数字处理方法,使所有样本值相等,则该样本理想化。再用这个方法延拓到Tokamak整体,使整体也趋向理想化。

First, the toroidal plasma＇ s force balance equations of three-dimensional orthogonal vector mag- netic field B,current density J and pressure gradient▽p are established in the stable state,then taking the toroidal surface coordinate system and processing the incentives of the basic magnetic field, the prob- lem of three-dimensional vector equation is changed into an ordinary differential equation problem, and then we find its analytical solution. From the existence of mathematical equation we can get the definition of positive operator and positive definite operator, combined with work of force field we develop functional form in variational learning. From the proof of mathematical equation and pan function, we confirm the ex- istence of solutions Tokamak, uniqueness and stability problems, get positive definite operator threshold, and ensure stable operation of the Tokamak. The ideal plasma with zero resistivity is stable, but non-zero resistivity with non-ideal time-varying current will gradually erode the threshold of positive definite opera- tor, then its operator will become non-positive making the system unstable. The key to extend the running time of Tokamak is to keep the threshold of positive definite operator constant. The prescription is building a digital ＂clone＂ to clone the whole Tokamak. By using digital processing all sample＇s values are made equal, then the whole Tokamak, will tend to be idealized.