Plasma Confinement by Direct‐Current Magnetic Fields Assisted by an Arbitrary External Force

The equations for confinement of an isotropic plasma are formulated to include an arbitrary external force, which can be assumed to be provided by radio‐frequency fields. A restriction is found which relates the allowable forms of the magnetic field and external force. Two specific results are as follows: (1) A dc magnetic field in the absence of other forces cannot support a pressure gradient transverse to its radius of curvature; (2) If the arbitrary external force is conservative, equilibrium can only be achieved when the external force just compensates the particle drift due to inhomogeneous magnetic fields at those points where the direct current is along the radius of curvature of the magnetic field. Stability problems are not considered although the time dependent equation, from which they may be studied, is presented.