There are three requirements in making a traveling wave accelerator: longitudinal electric field, synchronization, and confinement. We present and analyze a conceptually new kind of charged particle accelerator, making use of a photonic band gap lattice for field confinement near the beam axis, and employing dielectric material to produce a speed of light synchronous longitudinal electric field. An example structure design is presented. We also discuss nonlinear effect and other configurations without higher order dipole modes. Parallel scheme and fabrication are presented.