Plasma Density Measurement by Means of Self-Modulation of Long Electron Bunches

We present a new method to determine the electron density of a plasma by measuring the periodicity of modulations introduced to the longitudinal phase space of a relativistic particle bunch by the interaction with the plasma via the self-modulation instability. As the modulation is solely depending on the plasma density and the beam parameters, this method allows to determine the time-resolved density of a plasma at the position of beam passage, which is confirmed in particle-in-cell simulations. Densities in the range of 3.6 × 10$^{12}$ cm$^{−3}$ – 7.2 × 10$^{15}$ cm$^{−3}$ have been measured and the measurement accuracy is confirmed by comparison to spectroscopic plasma density measurements