Regenerative multibunch beam breakup instabilities and countermeasures for a high-intensity electron accelerator and the superconducting Darmstadt linear electron accelerator

Regenerative multibunch beam breakup instabilities are a well-known phenomenon in recirculating linacs where particle bunches pass multiple times through the same superconducting rf cavities with extremely high quality factor. This is in particular true for energy recovery linacs. Parasitic electromagnetic modes excited in the cavities can affect bunch dynamics in such a way, that on its subsequent passes it excites the modes further and a positive feedback loop is formed. Direct bunch tracking and a stability analysis technique can be used to study the instability. Usually only dipole modes are considered. In the present work, similar approaches are applied to monopole and quadrupole modes and illustrated with simulation results for the S-DALINAC and MESA facilities. An approximated stability analysis technique with better performance for the case of multiple recirculations is proposed. Countermeasures including betatron phase advance adjustment and additional betatron coupling are considered and a universal criterion for assessment of their effectiveness is proposed. A simple model of a damped oscillator with feedback is proposed as a universal example illustrating the phenomenon in general.

Figure 1

The MESA facility scheme (ER mode) used in this study.

Figure 2

The S-DALINAC facility scheme (twice recirculating ERL mode) used in this study.

Figure 3

Interaction loops between accelerating modules in ER operating mode of MESA.

Figure 4

Mode separation compared to mode width for the lowest two dipole passbands in MESA cavity.

Figure 5

Measured mode detuning distribution for the lowest two dipole passbands in MESA cavity compared to Gaussian distribution.

Figure 6

Measured and simulated quality factor ratio distribution for the lowest two dipole passbands in MESA cavity compared to Gamma-distribution.

Figure 7

Complex current plot for one of the mode configurations in MESA (only one pair of dipole modes is active). The threshold current value is marked with a red point.

Figure 8

Dipole mode voltages time dependence for a current 10% below the threshold. Mode configuration is the same as in Fig. 7.

Figure 9

Dipole mode voltages time dependence for a current 10% above the threshold. Mode configuration is the same as in Fig. 7.

Figure 10

Minimal threshold current for different modes in MESA. Five of the most dangerous dipole mode pairs are enclosed in a green box.

Figure 11

Minimal threshold current for different modes in S-DALINAC. Four of the most dangerous quadrupole mode pairs are enclosed in a green box.

Figure 12

Examples of 2D phase trombone scans for different configurations of MESA ($Q_{x,y}={\varphi }_{x,y}/2\pi$).

Figure 13

Examples of 1D beam rotator scans for different configurations of MESA ($Q_c={\varphi }_c/2\pi$).

Figure 14

Minimal and maximal threshold current values achievable with different BBU mitigation techniques for 10 randomized configurations of MESA.

Figure 15

Minimal and maximal threshold current values achievable with different BBU mitigation techniques for 10 randomized configurations of S-DALINAC.

Figure 16

$K(\phi )$ dependency at $B=0.1$.

Figure 17

$K(\phi )$ dependency at $B=0.001$.