线性瞬态涡流场定解问题中的法向边界条件与解的唯一性

电磁场初边值问题包括场的约束方程和定解条件。目前，许多文献使用含有磁感应强度法向分量边界条件的初边值问题来求解线性瞬态涡流场。对于涡流场的求解而言，这种初边值问题是否有唯一解，是一个基本的理论问题。该文使用反证法，利用非涡流区中的标量位函数，构造了功率积分表达式和能量积分表达式，引入了一个在整个场域有连续一阶偏导数的新函数，在此基础上，证明了含有磁感应强度法向分量边界条件的涡流场初边值问题有唯一解。作为应用，该文针对通有单脉冲电流的单匝圆环线圈平行放置在半无限大导体上方的瞬态涡流问题，用拉普拉斯变换的方法求出了导体中涡流密度向量的解析表达式。

THE NORMAL INTERFACE CONDITION AND THE UNIQUENESS OF SOLUTION TO THE LINEAR TRANSIENT EDDY CURRENT DEFINITE-SOLUTION PROBLEM

The electromagnetic field initial-boundary value problem consists of constraint equations and conditions for determining solution. At present, the initial-boundary value problem that includes the interface condition on the normal component of the magnetic flux density is used to solve the linear transient eddy current electromagnetic field in many papers. Whether the initial-boundary value problem has unique solution is a fundamental theoretical problem. In this paper, to prove the uniqueness of the solution to the eddy current initial-boundary value problem that includes the interface condition on normal component of the magnetic flux density, reduction to absurdity is used, a scalar potential function is employed in the non-eddy current region, a power integral formula and a energy integral formula are defined and another scalar function whose first order partial derivative is continuous over all the field regions is introduced. An example of engineering application is given. The example is a transient eddy current problem that a single-turn coil is driven by solitary pulse current and is in parallel with the plane of the half-space conductor. By using the method of Laplace transform, the analytical solution of the example is obtained.