Particle dynamics in multistage wakefield collider

Abstract

The dynamics of particles in laser pulse-driven wakefields over multistages in a collider is studied. A map of phase space dynamics over a stage of wakefield acceleration induced by a laser pulse (or electron beam) is derived. The entire system of a collider is generated with a product of multiple maps of wakefields, drifts, magnets, etc. This systems map may include offsets of various elements of the accelerator, representing noise and errors arising from the operation of such a complex device. We find that an unmitigated strong focusing of the wakefield coupled with the alignment errors of the position (or laser beam aiming) of each wakefield stage and the unavoidable dispersion in individual particle betatron frequencies leads to a phase space mixing and causes a transverse emittance degradation. The rate of the emittance increase is proportional to the number of stages, the energy of the particles, the betatron frequency, the square of the misalignment amplitude, and the square of the betatron phase shift over a single stage. The accelerator with a weakened focus in a channel can, therefore, largely suppress the emittance degradation due to errors.

Emittance control in Laser Wakefield Accelerator

“…Computer simulation indicates that when the acceleration phase is approximately fixed (the phase slip is small) there is an inverse power behavior (for a fixed final energy of the particles), in particular, the emittance degradation decreases like l/N T , where NT is the total number of acceleration units. This confirms the theoretical expectation of CTHY deduced from a statistical theory [5]. The inverse power law suggested that through the use of small acceleration intervals one may be able to achieve high resilience against jitters.…”

“…To study such an accelerator system we introduced a map approach described in [3][4][5]. The longitudinal phase space transformations (for the differential phase 5W and the differential Lorenz factor $7 , respectively) stage by stage are described by the longitudinal map: <J* n+ i = **n (1) <$7 n+ i = 2 7 |$ 0 (cos(W s + A) -cos *,)<**" + 5 7n ,…”

“…However, the high energy is not the only requirement, such a collider demands an extremely small beam emittance and thus extremely precise beam handling. To identify the crucial physical and technological problems associated with this, a systems approach through a dynamical map has been introduced [3][4][5]. There was also an earlier study on a 5 TeV laserwakefield collider [6].…”

“…A drawback is that due to the finite density gradient near the wall of the cavity, there is a local plasma frequency which would match the wakefield frequency and lead to resonance absorption [9]. In [5], numerical models with beam acceleration over a full quarter-wave-region were considered. These models are for both without involving the plasma channel and with the plasma channel ignoring the resonance absorption effect.…”

“…In [5], the study of emittance degradation in the presence of jitters, associated with stochastic misalignment between the beam and the wakefields was carried out where the plasma medium is uniform and the beam is accelerated over a full quarter-wave region. One finds that the system is sensitive to transverse offsets due to the wakefield averaging over the entire accelerating phase and thus typically providing a very strong focusing.…”