# CalculateSelfInducedMagneticField

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#### CalculateSelfInducedMagneticField

Section Hamiltonian
Type logical
Default no

The existence of an electronic current implies the creation of a self-induced magnetic field, which may in turn back-react on the system. Of course, a fully consistent treatment of this kind of effect should be done in QED theory, but we will attempt a first approximation to the problem by considering the lowest-order relativistic terms plugged into the normal Hamiltonian equations (spin-other-orbit coupling terms, etc.). For the moment being, none of this is done, but a first step is taken by calculating the induced magnetic field of a system that has a current, by considering the magnetostatic approximation and Biot-Savart law:

$\nabla^2 \vec{A} + 4\pi\alpha \vec{J} = 0$

$\vec{B} = \vec{\nabla} \times \vec{A}$

If CalculateSelfInducedMagneticField is set to yes, this B field is calculated at the end of a gs calculation (nothing is done – yet – in the tdcase) and printed out, if the Output variable contains the potential keyword (the prefix of the output files is Bind).

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