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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 cm – 7.2×10 cm have been measured and the measurement accuracy is confirmed by comparison to spectroscopic plasma density measurements.

Plasma density measurement by means of self-modulation of long electron bunches