The error arising in the description of the magnetic field is evaluated when the constraint is imposed that the external three-dimensional (3D) perturbation \({\mathbf{b}}\) does not penetrate into the tokamak plasma. Such a three-dimensional approach has been used in the plasma equilibrium evolutionary problems solved by the CarMa code [F. Villone, L. Barbato, S. Mastrostefano, and S. Ventre, Plasma Phys. Control. Fusion 55, 095008 (2013)], where the plasma is treated as a two-dimensional (2D) object, while the vacuum vessel wall is three-dimensional (3D). The toroidal surface separating the 2D and 3D regions is called the coupling surface (CS). This surface acts as a virtual casing, but with the additional condition \({\mathbf{b}} = 0\) imposed within the torus CS. Here, attention is attracted to the fact that, in a normal situation, the field \({\mathbf{b}}\) in the plasma-wall gap must depend on the plasma response. However, the prescription \({\mathbf{b}} = 0\) inside the torus CS eliminates this ambiguity. As a consequence, a discontinuity in the tangential component of \({\mathbf{b}}\) inevitably arises at the CS, necessitating the presence of a current on this surface. The magnitude of this fictitious current and its contribution to the magnetic perturbation \({\mathbf{b}}\) are estimated. It is shown that this current significantly influences both the magnitude and the distribution of the field \({\mathbf{b}}\) .
