Plasma wakefield acceleration is a method of accelerating charged particles, allowing to obtain a high accelerating gradient. The plasma, disturbed by the passage of the driver, creates fields that are several orders of magnitude higher than the fields in traditional accelerators. This allows beams of charged particles to be accelerated to high energies with a smaller facility size.
The AWAKE experiment at CERN demonstrates wakefield acceleration with a proton beam from the SPS ring as the driver. In a plasma, the driver self-modulates and then creates a field of constant amplitude. One of the current tasks of this project is external injection of an electron beam to be accelerated, called witness. If injected before self-modulation of the proton beam, the witness loses quality and its emittance increases. One of the options for solving this problem is to divide the plasma section into two parts, with a vacuum gap between them. Thus, in the first plasma section, a long proton beam self-modulates, then an electron bunch is injected, and in the second plasma section its acceleration occurs.
The problem with this solution is the radial expansion of the driver in a vacuum, and, as a consequence, a decrease in the field amplitude in the accelerating section. Therefore, the task arises: to study how the accelerating field changes, as well as the energy gain of the electron witness, depending on the length of the vacuum gap.
There are two limiting cases in this problem, both accessible to operating modes of the AWAKE facility. The expected witness energy gain can be calculated analytically in both modes, allowing its parametrical optimization. The analytical expressions for the witness energy gain coincide with the values obtained by LCODE simulations with good accuracy.
 

plasma wakefield acceleration