Transformer core radius and number of turns
This answer assumes that &quot;no load current&quot; refers to the magnetization current in the primary of the transformer and that is defined by the magnetization inductance.
If the radius is halved then the inductance falls by 4 times because area is quartered. If the core is a regular shaped core with a decent value of permeability then you can assume that inductance is proportional to the square of turns hence, to restore the inductance, you need to double the turns to increase the inductance 4 times: -

Picture from here.
For a closed magnetic core \$\ell\$ becomes the mean length around the core.