Beam Injection Using a Nonlinear Kicker for the HLS-II Storage Ring

The single nonlinear kicker (NLK) injection has been adopted by several synchrotron radiation light source facilities or their upgrades. The injected beam receives a kick from an NLK and goes into the acceptance of the storage ring while the stored beam passes through the center of the NLK where the magnetic field is almost zero. Compared with the local-bump injection, NLK injection requires less space for kickers and causes less disturbance to the stored beam during injection. Currently, a conventional local bump injection including four pulsed dipole kicker magnets is adopted in the HLS-II storage ring. In this paper, we propose an NLK injection scheme by only replacing one kicker with a pulsed NLK for HLS-II. The simulation result is also presented.


INTRODUCTION
Hefei Light Source II (HLS-II) is a dedicated electron synchrotron light source with a beam energy of 800MeV, which consists of a full energy linac injector and a 66.1m storage ring.The off-axis injection with four dipole kickers and one pulsed septum is adopted, which forms a closed local orbit bump in the injection region to bring the injected beam closer to the stored beam.The layout of the injection system is shown in figure 1.
The injection system using a nonlinear kicker (NLK) which the injected off-axis beam passes through and receives a kick to achieve the injection.The nonlinear kicker should be designed to bring the injected beam to the acceptance of the storage ring without considerable disturbance to the stored beam.The nonlinear kicker injection is developed by using pulsed multipole magnets (PMMs), such as pulsed quadrupoles and sextupoles [1,2], and recently NLK magnets are usually specially designed sextupole or octupole magnets.The NLK injection is a simple, compact and transparent method which has been adopted or proposed by several facilities, including BESSY, ALS-U, SLS, MAX-IV, UVSOR-III and HALF projects [3][4][5][6][7][8][9].
In order to simplify the injection system, we plan an NLK injection scheme to replace the current local bump injection system by changing one dipole kicker to an NLK kicker while the original septum is kept in use.

LOCAL BUMP INJECTION SYSTEM
Currently, a local bump injection system is used for beam injection.This injection system consists of four kicker magnets and one septum.The four kickers are used to form a local bump.The septum located at the end of the platform of the local bump is used to provide a horizontal SEPTUM (remained) K4 (repalced with an NLK) Figure 1.The layout of the current injection system in the HLS-II storage ring.The new injection scheme will replace the downstream kicker with a non-linear kicker and remains the pulsed septum.The other 3 dipole kickers could be removed.deflection angle to the injected beam with no effect on the stored beam.The parameters of the septum magnet are given in table 1.

NLK INJECTION SCHEME
In the development of the NLK injection system, the original septum is kept.An NLK is applied to replace the dipole kicker K4 and the other three dipole kickers are turned off or removed.The HLS-II storage ring has large dynamic acceptance, therefore the requirement of the characteristic of the NLK is not strict.A pulsed sextupole magnet is selected as the NLK.To avoid additional kick from the NLK after the first turn, the excitation pulse length of the NLK needs to be less than the revolution time.
To ensure a sufficient injection efficiency, we should calculate the acceptance phase space in the horizontal plane at the NLK and try to ensure that all the injected beam goes into the acceptance.The theoretical acceptance at the middle of NLK is an ellipse related to the Twiss parameters of the storage ring.The electron beam passes through NLK and receives a kick angle which varies with its displacement from the axis.
The theoretical formula for the normalized magnetic field error can be written as where B 0 ρ 0 is the magnetic rigidity and B(s) is the magnetic field at s position, dk is the differential kick angle, ds is the differential distance travelled by a particle in a magnetic field and θ(s) is the normalized magnetic field error.x (mm) be calculated from dipole components in the feed-down of sextupole magnets.The horizontal and vertical components B x , B y can be written as follows where x 0 , y 0 represent the horizontal and vertical distances between the bunch center and the center of the sextupole magnet, x, y are the horizontal and vertical displacements between the particle and the bunch center, b 2 is the normalized strength of sextupole magnets in m −3 .We only consider the dipole component of the vertical magnet field B y and ignore the multipole magnetic field.In a uniform magnetic field that does not vary with s, the approximation formula between the kick angle θ and x 0 can be expressed as where L is the length of the magnet field.In our NLK injection scheme, the L is taken to be 30cm.According to the required kick angle, the normalized magnetic field strength b 2 is calculated to be −280m −3 .The horizontal kick angle of NLK is drawn as a quadratic curve which is shown in figure 2. The acceptance with the NLK kick is the combination of the original theoretical ring acceptance ellipse and the NLK kick curve, which is shown in figure 2.

SIMULATION OF THE NLK INJECTION
This work aims to replace the 4-kicker bump system with an NLK magnet in the case of minimum changes to the existing conditions.Therefore, Twiss parameters of the injected beam, the deflecting angle of the septum and the strength of the NLK are used to obtain better match to the injection.The Accelerator Toolbox (AT) is used for the particle tracking simulation [10,11].By slightly modifying the strength of the septum, the injected beam is brought to a position closest to the original theoretical ring acceptance in the phase space at the NLK.The deflection angle adjustment from 105mrad to 108.4mrad is within the acceptance range of the original septum magnet design strength.The NLK strength is confirmed according to the injected beam position in the phase space which is shown in figure 2. With this NLK strength, the characteristics of the ring acceptance with the NLK kick are used to generate the optimum matching position for the injected beam.The Twiss parameters of the injected beam at the NLK position can be derived from the optimum matching.These parameters can be backtracked from the NLK to the septum to obtain the Twiss parameters and the injection displacement of the injected beam at the septum.The main parameters of the injected bunch at the septum are listed in table 2. x (mm) In the particle tracking simulation, a bunch with 1,000 injected particles is used for tracking.Figure 3 shows the distribution of the injected bunch at the middle of the NLK after matching with and without injection error.In the simulation, the injected bunch can survive from the first turn to 3 damping times (27,000 turns).The attached random error of the injected beam obeys the normal distribution with truncation at three standard deviation.The injection efficiency in the tracking simulation can reach 100% when errors of the injected beam are considered.It is also found that by introducing an energy spread of 0.5% to the injected beam, the injection efficiency remains unchanged.The results of simulation shows the NLK injection scheme can satisfy the requirement of the HLS-II operations.That is, the NLK injection can be a replacement to the conventional local bump injection in the HLS-II storage ring.And the new injection system uses the original septum and only needs one pulsed NLK kicker.

SUMMARY
In this paper, we report the plan of replacing the conventional local bump injection with an NLK injection system in the HLS-II storage ring.This replacement method is an easy way to only replace the last kicker with the NLK while the septum remains.The simulation results show the injection efficiency of NLK injection can meet the requirements of HLS-II operations.For future work, more study will be carried out based on a real NLK, including the NLK field characteristics and errors.

Figure 2 .
Figure2.The horizontal phase space of acceptance at the middle of the NLK.The blue ellipse is the theoretical acceptance.The black closed curve is the acceptance with the NLK kick which is the combination of the original theoretical acceptance ellipse and the NLK kick curve.The green quadratic curve represents the horizontal kick angle of NLK.The small red ellipse is the optimum matching location for the injected bunch.The schematic representation of the optimum injection position is also shown in this figure.

Figure 3 .
Figure 3. Distribution and the ring acceptance on the horizontal phase diagram of the injected bunch.(a) Bunch distribution at the middle of the NLK after matching without injection error.(b) Tracking result with injection error.Bunch distribution for the injected beam, the first turns, 2 and 3 damping times in the horizontal plane (one horizontal radiation damping time of this lattice is approximately 90,000 turns).

Table 1 .
Main parameters of the pulsed septum.
The magnetic field strength of the sextupole can

Table 2 .
Main parameters of the injected bunch.