“…In addition, x-ray lasing [9] and soft x-ray high-harmonic generation [10] have benefited from guiding in pre-formed channels. More recently, discharged plasma structures have been applied to focus relativistic electron beams, exploiting the advantages of radial symmetry, tunability, and strong multi kilo-Tesla/meter focusing gradients [11]. Knowledge of the on-axis plasma density is of critical importance to accelerator applications since the density dominates the plasma response time, self-injection threshold, accelerating field strength, electron beam dephasing length [6], and beam-driven wakefield effects [12].…”