Eddy Current And Coupling Impedance Of Ceramic Rings-Loaded Thin-Walled Vacuum Chamber In The HIAF/BRing

In the process of accelerating beam in the Booster Ring(BRing)of High Intensity heavy ion Accelerator Facility(HIAF),the magnetic field with a ramping speed of 12 T/s will generate non-negligible eddy current in the iron core of magnet and the wall of stainless steel vacuum chamber.In order to reduce the eddy current of vacuum cham-ber,HIAF team came up with the idea that the 0.3 mm thick ultra-thin stainless steel vacuum chamber is selected in the dipole and quadrupole magnet section in BRing.At the same time,in order to avoid the large deformation of vacuum chamber caused by atmospheric pressure,ceramic rings are added inside vacuum chamber to support the ultra-thin vacuum chamber.In the ceramic rings-loaded thin-wall vacuum chamber,the ceramic rings generate a large broadband impedance.The broadband impedance which are generated by ceramic rings,bellows and other components,resistive wall impedance,narrowband impedance and space charge equivalent impedance are stud-ied in detail to build the impedance model of BRing.The beam collective instabilities based on impedance model and the impedance reduction techniques of ceramic rings are discussed in detailAccording to the Faraday's law of induction and the Maxwell's equations,the an-alytical formulas of eddy-current magnetic field and eddy current loss are derived.The transient electromagnetic simulation and the thermal analysis of eddy current loss are done by OPERA.For the 0.3 mm thick ultra-thin vacuum chamber,the magnetic field attenuation and hysteresis effect caused by eddy-current magnetic field are 9.69 Gs and 80.706 ?s.There is no 3 mm-thick nanometer insulation layer outside the vacuum chamber,the temperature rise of vacuum chamber caused by eddy current loss is ?T=42.39?.With consideration of eddy-current magnetic field,the uniformity of trans-verse magnetic field(2.354×10-4)and longitudinal integral magnetic field(1.981×10-4)in the good field area of dipole magnet are lower than 3×10-4 and can meet the physical design criteria.The maximum eddy-current Lorentz force is 240.861 N,which is far less than the atmospheric pressure(3.103×104 N)and can be ignored.The transverse tune shift caused by eddy-current-induced quadrupole field and the chromaticity shift caused by eddy-current-induced sextupole field are studied in detailIn the ceramic rings-loaded thin-wall vacuum chamber,the ceramic rings generate a large broadband impedance,which is discussed in detail by analytical calculations,numerical simulation and impedance measurement.At the same time,a prototype of ceramic rings-loaded thin-wall vacuum chamber is manufactured and the impedance measurements are performed.The analytical results are good agreement with numer-ical simulation results for the longitudinal and transverse impedance of ceramic rings There is a small deviation between analytical results and measurement results and the reason of deviation is analyzed briefly.According to the research experience and meth-ods of coupling impedance of ceramic rings,the broadband impedance generated by other components,the space charge equivalent impedance,the resistive wall impedance and the impedance generated by magnetic alloy cavity and kicker magnet are discussed in detail by analytical calculations and numerical simulation.The python code is writ-ten to quickly build the impedance models which is corresponded to the injection and extraction energy of several typical ions in BRingAccording to the impedance models of BRing and the basic parameters of proton beam,the transverse mode-coupling instability of proton beam is discussed by analyti-cal method,verifying the conclusion that there is a transverse mode-coupling instability caused by transverse brodband impedance in BRing.In order to mitigate the transverse mode-coupling instability,the horizontal and vertical broadband impedance need to be reduced separately by more than 67.427%and 69.834%.Compared with other compo-nents,the ceramic rings are the primary source of total transverse broadband impedance and the ration is over 72%.Therefore,the impedance reduction techniques of ceramic rings are discussed in detailFirstly,in order to reduce the impedance of ceramic rings,the ceramic rings are optimized that YSZ is used instead of Al2O3 to make ceramic rings and the thickness of ceramic rings is reduced from 5 mm to 3 mm.Secondly,for the ceramic rings which have been optimized,the 1 ?m-thick Au film is coated on the surface of ceramic rings to reduce the impedance of ceramic rings.Finally,a prototype of gilded ceramic rings-loaded thin-wall vacuum chamber is manufactured and the impedance measurements are performed,which has verified that the ceramic rings coated by 1 ?m Au film can ef-fectively reduce the transverse impedance of ceramic rings.According to the numerical simulation and measurement results,the ceramic rings are optimized and coated by 1?m Au film,the horizontal and vertical broadband impedance are reduced separately by 87.346%and 89.176%.For the impedance model which is corresponded to the extrac-tion energy of proton beam,the total horizontal broadband impedance can be reduced from Z1H(?)=-6.195i×105 ?/m to Z1H(?)=-1.966i×105 ?/m,and the total verti-cal broadband impedance can be reduced from Z1V(?)-=-6.307i×105 ?/m to Z1V(?)=-2.225i×105 Q/m.They are reduced separately by 68.265%and 64.722%.The total hor-izontal broadband impedance can be reduced by less than the threshold impedance,and the total vertical broadband impedance can be reduced to near the threshold impedance.With consideration of the transverse feedback system in BRing,the transverse mode-coupling instability can be effectively mitigated.