Tokamak小型化的猜想

Conjecture of Tokamak Minimizafion

超环体磁场对Z轴对称,设想在Z轴置一个均匀长永磁体来产生向四周辐射磁场,其幅度和离Z轴距离成反比。这个磁场产生场强的梯度变化,牵引离子向容器冲击造成不稳。仿星器是在四周构造仿照Z轴永磁体的反射磁场,用它来弥补传输磁场单调下降的部分,但不能完全弥补。Tokamak磁场问题是三维波动方程柯西方程的一个范例。如把柯西问题用傅里叶变换变化为常微分方程问题,其解的一部分传输过程的时间空间变化为柯西问题的动态解,即反映Tokamak磁场问题,另一部分解反映场理论的初始分布。再利用椭圆型方程的基本解以及δ函数的概念直接求得柯西问题的解。最后,引用非齐次方程柯西问题结合Tokamak磁场问题,设计一个外加的振动函数,以消去Tokamak的与距离成反比的磁场,使场强成为常数B0,取消仿星器达到Tokamak小型化。

Toroidal magnetic field is symmetrical on the Z-axis.We suppose that a uniform length permanent magnet is set in the Z-axis to generate magnetic field to the surrounding,the amplitude and the distance from the Z-axis is inversal proportional to the distance.The gradient of the field strength,pulls ions to impact the container causing instability.Stellarator is constructed around the Z-axis along the reflection lines of the permanent magnetic field,use it to make up for the monotonously decrease part of the transfer magnetic field,but it can not complete.Tokamak problem is an example of three-dimensional wave Cauchy equation.If the Cauchy problem changes into ordinary differential equation with Fourrier transform,the time and space changes of the part of the solution is the dynamic solution for the Cauchy problem,that reflects the Tokamak problem,another part of the solution reflects the initial distribution of field.By means of basic solution and conception of partial differential equation,we get the solution of Cauchy problem directly.Finally,references nonhomogeneous Cauchy problem in connection with the Tokamak problem,an applied vibration function is offered to eliminate the Tokamak＇s magnetic field which is inversal proportional to the distance.So that the field strength is a constant,cancel stellarator to obtain Tokamak minimization.