Plasma lenses for focusing particle beams

The focusing of particles by a thin plasma lens is analyzed with physical, linearized fluid and particle-in-cell computational models. For parameters similar to next-generation linear colliders, the plasma lens strength can exceed 100 MG/cm, and the luminosity can be enhanced by an order of magnitude by passing each beam through an appropriate plasma slab. The plasma electrons affect the focusing by shifting so as to (partially or completely) charge neutralize the beam. Both overdense and underdense plasma lenses are described (plasma density ${\mathit{n}}_0$ greater or less than beam density ${\mathit{n}}_{\mathit{b}}$). The former case applies equally well to ${\mathit{e}}^{+}$ and ${\mathit{e}}^{\mathrm{-}}$ beams, while the latter has distinct advantages for ${\mathit{e}}^{\mathrm{-}}$ beams (including smaller aberrations and background). The effects of spherical and longitudinal aberrations, emittance, plasma boundaries, and non-linear-plasma dynamics on the final spot size are discussed.