Differential rotation and angular momentum

Differential rotation not only occurs in astrophysical plasmas like accretion disks, it is also measured in laboratory plasmas as manifested in the toroidal rotation of tokamak plasmas. A re-examination of the Lagrangian of the system shows that the inclusion of the angular momentum’s radial variation in the derivation of the equations of motion produces a force term that couples the angular velocity gradient with the angular momentum. This force term is a property of the angular velocity field, so that the results are valid wherever differential rotation is present.