Propagation of an Intense Ion Beam Transverse to a Magnetic Field

It has been verified experimentally that an intense, space-charge-neutralized ion beam having a dielectric constant $\epsilon \gg 1$ will cross a transverse magnetic field undeflected. A polarization electric field $\overrightarrow{\mathrm{E}}$ is measured within the beam channel such that $\overrightarrow{\mathrm{E}}+\left(\frac{\overrightarrow{\mathrm{v}}}{c}\right)\times \overrightarrow{\mathrm{B}}=0\mathrm{}$, where $\overrightarrow{\mathrm{v}}$ is the beam velocity and $\overrightarrow{\mathrm{B}}$ is the applied field. It is shown theoretically that $\epsilon \gg {\left(\frac{m_i}{m_e}\right)}^{\frac{1}{2}}$ is required for the beam to enter the transverse field from a region with no field, where $m_i$ and $m_e$ are the ion and electron masses.