The mean magnetic field equation describes the process of generating a magnetic field on a large scale as a result the EMF arising on a small scale. We consider the case where the large-scale magnetic field is also random and determine the density function of magnetic helicity. This function is invariant under gauge transformations of the magnetic vector potential. We study the equation for the magnetic helicity flux of a large-scale field and introduce a correction term related to the quadratic magnetic helicity invariant.

中文翻译：

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平均磁场方程的磁螺旋通量

平均磁场方程描述了在大规模产生磁场的过程，结果是在小范围内产生 EMF。我们考虑大尺度磁场也是随机的情况，并确定磁螺旋度的密度函数。该函数在磁矢量势的规范变换下是不变的。我们研究了大尺度场的磁螺旋通量方程，并引入了与二次磁螺旋不变量相关的校正项。