  In the present work a simple analytical approach is presented in order to
clarify the physics behind the edge current density behaviour of a hot plasma
entering in contact with a resistive conductor. When a plasma enters in contact
with a highly resistive wall, large current densities appear at the edge of the
plasma. The model shows that this edge current originates from the plasma
response, which attempts to conserve the poloidal magnetic flux ($\Psi$) when
the outer current is being lost. The loss of outer current is caused by the
high resistance of the outer current path compared to the plasma core
resistance. The resistance of the outer path may be given by plasma contact
with a very resistive structure or by a sudden decrease of the outer plasma
temperature (e.g. due to a partial thermal quench or due to a cold front
penetration caused by massive gas injection). For general plasma geometries and
current density profiles the model shows that given a small change of minor
radius ($\delta a$) the plasma current is conserved to first order ($\delta I_p
= 0 + \mathcal{O}(\delta a^2)$). This conservation comes from the fact that
total inductance remains constant ($\delta L = 0$) due to an exact compensation
of the change of external inductance with the change of internal inductance
($\delta L_\text{ext}+\delta L_\text{int} = 0$). As the total current is
conserved and the plasma volume is reduced, the edge safety factor drops
according to $q_a \propto a^2/I_p$. Finally the consistency of the resulting
analytical predictions is checked with the help of free-boundary MHD
simulations.
