Study on XiPAF-Upgrading Synchrotron Beam Loss

Xi’an 200MeV proton application Facility (XiPAF) is upgrading its proton synchrotron to a multi-ion synchrotron, which replaces H- stripping injection with multiturn injection scheme. New synchrotron’s vertical tune has been changed from 1.70 to 2.26, beam dynamics of new lattice is much different from the original proton lattice. Simulations has been performed with PyORBIT for beam loss study, with or without space charge effect. The main beam loss is caused by 3-order incoherent resonance νx + 2νy = 6, which is a structure resonance. Space charge and longitudinal synchrotron motion speed up the beam loss process.


Introduction
Xi'an 200 MeV Proton Application Facility (XiPAF) has been operational since 2020 and has conducted several rounds of machine studies and experiments for different users, which can accumulate 2 × 10 11 protons after injection and 1 × 10 11 protons after acceleration [1,2,3].
With the demand of wider range of ions for space radiation experiments, XiPAF is upgrading its proton synchrotron to a multi-ion synchrotron, reusing dipoles, quadrupoles and sextupoles and keeping "missing dipole" lattice structure and 6 periods.The circumference has been extended to 39.96 m, and the vertical tune has been changed from 1.70 to 2.26.Different tunes come with different beam dynamics, especially with space charge.Vacuum equipment in dipole gap reduce vertical acceptance from 77 mm • mrad to 40 mm • mrad, while the transverse emittance after injection painting is about 200 mm • mrad.Transverse coupling is critical in beam loss, which has been confirmed in simulation, most particles are lost at dipole vertical aperture.
In this paper, the beam loss of XiPAF-Upgrading synchrotron has been studied, with or without space charge.Possible resonance is analysed by resonance lines in (  ,   ) space, resonance stopband scan and single particle motion analysis are performed to understand the mechanism of beam loss, with and without space charge.

Resonance Line Analysis
Resonance line analysis is very important for critical resonance prediction.Resonance lines up to 5 order are shown in Fig. 2, red lines are structure resonance and blue lines are nonstructure resonance but excited by normal high order field.Critical structure resonance may be   + 2  = 6, and non-structure resonance may be −  + 2  = 3,   +   = 4, 4  = 7 in our interested tune region.
Frequency map analysis (FMA) is a powerful tool to detect possible resonance or chaos, based on Fourier techniques [4,5,6].FMA without space charge have been performed and shown in Figure 2 to compare with resonance lines, tune (1.73, 2.11), (1.73, 2.26), (1.73, 2.30), (1.73, 2.33), (1.73, 2.36), (1.73, 2.40) are investigated and their results are plotted together.According to KAM-theorem, regular particle motion is restricted to a two-torus in two-dimensional case, and particle tune is const [7].When particle tune touches some resonance lines, its motion becomes non-regular and tune will change to other value.According to the resonance order and tune change magnitude, the most dangerous resonance line is   + 2  = 6, which is a structure resonance and colored red.The second dangerous resonance line may be −  + 2  = 3, which can be excited by normal sextupole field.Other resonance may not be so important as they are in higher order, according to FMA results.

Resonance Stopband Scan
Space charge plays an important role in high beam intensity synchrotron.Space charge tune shift in y dimension is ∼0.14, which makes tune footprint overlaps multiple resonance lines and causes beam loss.
Static resonance stopband scan is used to study space charge effect on nonlinear resonance [8].Horizontal tune is set to 1.72, and vertical tune is varied from 1.90 to 2.40 with different beam intensity.Initial matched beam distribution is Gaussian with  ,rms =20 mm • mrad and  ,rms =2 mm • mrad, there will be no envelope mismatch oscillations, only resonance induced by lattice nonlinearities and space charge.In Fig. 3, a stopband at   = 2.14 is identified both in x and y dimensions, which is the structure resonance   + 2  = 6.Space charge has modified the stopband and shifted it to a higher   , the stronger the space charge, the larger the shift.Also,   = 2 resonance is discovered, the position and shape of the peak at   = 2 remain unchanged with the increase of bean intensity, shown that this resonance mainly comes from lattice nonlinearity rather than space charge.
2D stopband scan has also been performed with or without space charge, and compared in Fig. 4. Without space charge, beam loss occurs only when its tune close to resonance   + 2  = 6, which is caused by lattice nonlinearities.With the beam intensity of 10 mA, space charge modified this resonance stopband as in 1D scan case, resonance stopband is above   + 2  = 6 because of space charge tune shift.
x y _6HSGNTS_ _2O@BD_"G@QFD x _6HSG_ _2O@BD_"G@QFD !D@L_+NRR___ln(1 Besides, there are other resonances that appear in the space charge case, such as −  + 2  = 3, 4  = 9, and   = 2. Additionally, the colored stopbands are above the black resonance lines.This means that space charge can induce or enhance these resonances and modify their stopband structure.

Particle Motion Analysis
As discovered above,   + 2  = 6 is the strongest resonance in XiPAF-Upgrading synchrotron.Simulation starts with multiturn injection painted coasting beam, RF voltage is set to zero to remove capture process, and machine bare tune is set to (1.72, 2.14) to study the beam loss process in a more realistic situation.Coasting beam is tracked 100 ms while beam loss occurs in the first 2 ms, beam loss after 2 ms is almost zero and the current curve is flat for weak space charge case.Stronger space charge causes slow beam loss after 2 ms.
As shown in Fig. 5, with stronger space charge, beam loss increases initially and then decreases.This can be explained by the lost particle distribution.The particle tune   can be written as   =  bare + Δ chrom + Δ sc , where  bare is machine bare tune, which is a fixed value, Δ chrom is chromaticity induced tune shift, which is correlated with particle coordinate Δ, and Δ sc is space charge induced tune shift, which is always negative for all Δ, and correlated with beam intensity.Considering the negative chromaticity, when the space charge effect gets stronger, Δ sc becomes more negative, so particles with negative Δ lie on the resonance line and be lost.Due to dispersion mismatch in multiturn injection, the beam energy distribution after injection is asymmetric with regard to the reference energy, shown by the yellow curves in Fig. 6.With increasing beam intensity, particles with more negative Δ lie on the resonance line, resulting in an increase of beam loss.If the space charge gets strong enough, all particle tunes will move away from the resonance line, resulting in a decrease of beam loss.
The particles lost at different moments are located in different regions of phase space, as shown in Fig. 7.In the first 0.2 ms, particles with initial large   lose via transverse coupling    resonance, After 0.2 ms, particles with initial small   move to the edge of phase space then are lost in the same way.

Effect of Synchrotron Motion
The effect of synchrotron motion on beam loss is studied.Simulations are performed with RF capture process instead of keeping the coasting beam after injection.The difference in beam current curves is displayed in Fig. 8.As mentioned above, the current curve is flat for coast beam, after the first several milliseconds.For the bunch beam, the beam loss follows the same pattern in the first 0.2 ms, then synchrotron motion changes particle energy, particle tune crosses the resonance line periodically.Synchrotron motion induced tune modulation brings more particles to the resonance line, speeds up the loss process, and enlarges the unstable region in the tune diagram, so there is a continuous beam loss after the first 0.2 ms.7LPH>PV@ 3DUWLFOH1XPEHU>×10 10 @ &RDVW %XQFK Space charge plays the same role with synchrotron motion.Unlike synchrotron motion induced modulation particle energy, space charge induced tune modulation is based on longitudinal position in the bunch.Space charge effect is relative to beam density, nonuniform longitudinal distribution, caused by the synchrotron motion, introduces another tune modulation and speeds up the beam loss process.IOP Publishing doi:10.1088/1742-6596/2687/6/0620087 6.CONCLUSION Beam loss of XiPAF-Upgrading synchrotron mainly comes from transverse couple resonance   + 2  = 6, which arises from lattice nonlinearity and space charge.Details of beam loss process have been studied by simulation, synchrotron motion and space charge induced resonance crossing speeds up the beam loss process.

Figure 5 :
Figure 5: Beam loss compared with space charge.

Figure 8 :
Figure 8: Beam loss compared between coast beam and bunch beam.