Studies Of BBU Effects In Dielectric Wakefield Accelerators

One of the advanced acceleration concepts is the dielectric wakefield accelerator, in which a relativistic charged bunch excites wakefields（Cherenkov radiation） in a dielectric-loaded slow-wave waveguide. The wakefields are then to accelerate a second bunch to high energy. One advantage of the dielectric wakefield accelerator is the high acceleration gradient, thus it has the potential to enable future accelerator such as linear collider and X-ray free electron laser light source.In the dielectric-loaded structures, only the eigen modes of Cherenkov radiation can be excited. The fundamental mode is TM01 mode and mainly provide the longitudinal wakefields. However, large longitudinal wakefields are accompanied by large transverse wakefields of the dipole modes（HEM1n modes） if the drive bunch is misaligned in the structure. The deflection of the transverse wakefields can cause serious single bunch beam breakup（BBU） instability of the drive bunch. The transport of a high current drive bunch in the dielectric wakefield structure becomes critical to the dielectric wakefield acceleration concept.The BBU effects in the conventional linear accelerators can be successfully controlled by BNS damping. Using the similar method of BNS damping, the BBU effects in the dielectric wakefield accelerators can be controlled by applying alternating quadrupole magnets to perform incoherent betatron oscillations for the head and tail of the bunch. Unlike the conventional linear accelerator, a wakefield accelerator gives a large energy spread to the drive bunch by the self-wake deceleration. Also, the transverse wakefields in a dielectric wakefield accelerator are much stronger than those in a conventional linear accelerator. Thus the controlling the BBU in a dielectric wakefield accelerator is a big challenge.In order to better understand the beam dynamics and BBU instability in a dielectric wakefield accelerator, we developed a simple two-particle model to represent analytic particle trajectories. A multi-particle tracking code was also developed to do the numerical simulations for a Gaussian bunch, which shows good agreements with the two-particle results. Through the analytic and numerical results, we found stronger focusing in the FODO lattice allows for improved BBU control. Since the achievable focusing is limited by the attainable magnetic field at the tip of the magnetic pole, the beam stability condition in a dielectric wakefield accelerator is given. Furthermore, the BBU instability imposes a significant limit on the highest acceleration gradient. Our study shows the maximum accelerating gradient increases with structure radius ～a^1/2, which has the opposite trend of what would be expected by using the simple scaling law E_z ^Q/a².Transformer ratio is a key parameter in the collinear acceleration regime of the wakefield acceleration. It can significantly increase the transformer ratio by using a drive bunch with a double-triangular shape. However, it’s more difficult to control the BBU of a double-triangular bunch. Our study finds it can be only controlled by introducing a large energy chirp（>15%） to perform strong BNS damping.