In all probability the only way to understand the theoretical possibilities and limitations of magnetic analysis is the use of a trial-and-error method. To demonstrate this, a virgin field of rigorous mathematical foundations of a three-dimensional (3D) equilibrium problem is briefly presented. In the first part of the paper we clarify the problem of plasma profile determination. We previously have established the limitations following from a direct 3D plasma equilibrium problem on the possibility of the moderate current density profile identification. Here we demonstrate the limitations on the pressure profile determination under zero net current regime of operation. Realistic experimental conditions that significantly complicate the use of magnetic analysis for equilibrium identification are outlined. The second part of the paper deals with the peculiarities of diamagnetic measurements in stellarators. The influence of the 3D plasma induced magnetic fields is briefly sketched. We will also treat in detail an attractive, although questionable, possibility for the estimation of the electron cyclotron resonance heating absorbed power from the jump in the time derivative of the diamagnetic signal. It is shown that the limitations of such a method are completely determined by the accuracy of the experimental system set-up, but do not depend on the mathematical properties of the equations considered, as was previously expected. [References: 33]
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