Centrifugal space-charge force of an electron beam in a focusing element

Abstract

The centrifugal space-charge force of a continuous electron beam, focused in a lens of an accelerator, is numerically calculated. As in the case of an electron beam in a dipole magnetic field, the effect on the transverse motion of the particles from the centrifugal space-charge force in a focusing element tends to cancel the effect from the potential depression of the beam; however, the cancellation is not exact, as it is for the dipole case. The centrifugal space-charge force in the focusing case arises from a nonzero axial derivative of the transverse vector potential due to the beam's space charge, as the beam is transversely accelerated in the focusing element. The transverse equation of motion for particles in the beam is used to quantify the partial cancellation of the nonlinear transverse acceleration from the centrifugal space-charge force and from the beam's potential depression, for focusing both with a magnetic quadrupole lens and a solenoid.