EDDY CURRENTS INDUCED IN A MUON STORAGE RING VACUUM CHAMBER DUE TO A FAST KICKER*
神木二郎山W.Q.Feng,Physics Department,Nanjing University,Nanjing,China
E.B.Forsyth,AGS Department,Brookhaven National Laboratory,Upton,New York11973USA
Abstract
The goal of AGS E821is a precision measurement of the muon magnetic moment(g-2)value to0.35ppm.A problem with muon injection is the effect of the residual magnetic field during the measurement period due to the eddy currents in the vacuum chamber induced by the kicker pul.The paper prents a mainly analytical look at the nature of the eddy currents as an equivalent RL circuit and describes a method to solve2D Maxwell’s operations under pul excitation with some quantitative estimates of the decay time constants. Analysis of the results show that the field due to eddy currents is dependent on the chamber dimensions,type of material,and duration of pul ri,flattop and fall.The field created by the rising edge of the waveform is largely cancel-led by the falling edge,providing the pul is short compared to the diffusion time of the eddy current.The simulation results agree with the theoretical analysis and confirm the residual integral field at the start of the measurement period is acc
eptable.
I.INTRODUCTION
A new experiment is being built at Brookhaven National Laboratory to measure the g-2value of the muon to a precision of0.35:an improvement of a factor of20over the best available data.The ultrahigh precision aimed for at BNL prents unusual challenges in physics and in technology. Muon injection plays an important role in achieving the precision of0.35ppm,becau direct muon injection into the storage ring is more efficient in producing stored muons,and the hadronic background associated with many pions interact-ing with storage ring material is abnt.Direct muon injec-tion into the storage ring is accomplished by giving the muon beam a10milliradian kick at a quarter of a betatron wave-length from the inflector.The disadvantage of direct muon injection is that one has to deal with the effect of the residual magnetic field of the fast kicker due to eddy currents in the vacuum chamber.
The method of attack is to derive LR circuits for the eddy currents and to solve2D Maxwell’s equation with pul excitation,thus obtaining a group of solutions of the eddy current magnetic field,eddy currents and decay time
*Work performed under the auspices of the U.S.Department stants[1].Some computer simulations are given of eddy currents induced by a fast kicker.The simulation results agree with the theoretical analysis and confirm the residual integral field at the start of the measurement period is acceptable.今天的足球比赛
II.SOLUTION OF THE DIFFUSION EQUATION
In Fig.1,if l>>w and h>>d,then the two-dimensional kicker magnetic field in the chamber wall,parallel to the wall can be
considered.
Fig.1.Vacuum chamber with two-plate kicker.
In this situation,and Maxwell’s equations
are:
(1a),
(1b) where is the magnetic permeability,and is
the electrical Applying boundary conditions we obtain the diffusion equations for the special situation:
(2a),
(2b) An form of been examined[2], assuming the fast kicker produces a exponential step pul. In th
e beginning of the iteration,the magnetic field H o(t)is uniform over the cross ction of the chamber wall;this field is perturbed by the eddy currents.The decay times
Table 1
Time Constant L
/R
骨盆前倾最有用的6个动作have been calculated,reprent in Fig.2by L n (t)/R n (t),quantitative results are given in Table 1.
快充对电池有伤害吗
作文礼物
Typical time constant for the decay in aluminum is ~500µs.In practice the excitation waveform of the kicker has both a rising and falling edge with a width that is much less than L 1/R 1.The net effect due to the difference between positive and negative eddy currents will produce residual magnetic field which could affect the accuracy in determining the overall field integral around the storage ring.Calculation shows the next field decays much more quickly than for a unidirectional pul due to the cancellation effect:a short pul is required relative to the diffusion times.The ri and fall times can be optimized to keep the eddy current field to
a minimum.
IIIPUTER SIMULATION
Fig.2.Eddy current equivalent circuits.
The required high precision implies the integrated residual field
should become less than 1part in 107of the
integrated main dipole magnetic field
on the mid-plane at the start of the measurement (~10µs),where B e is the eddy current field,B o is main dipole field,θis the angle subtended to the center of the ring,θl is the angle occupied by the fast kicker,and R is the radius of the storage ring.
For the magnetic kicker,using an underdamped sine waveform the eddy current field/main field is <1x 10-7if t r <100ns.The eddy current field at beam centerline using the program PE2D with a waveform assumed to have 60ns The vacuum chamber material is 2020aluminum.Table 2lists the eddy current contribution to
附近的景点as a function of time
after injection for a stripline &H field deflection).The time dependent diffusion of eddy currents is clearly en:there is a rapid change immediately after the end of the kicker excitation pul which slows as time increas.
IV.CONCLUSIONS
The analysis has rved to emphasize the following important points:
(1)The field due to eddy currents is dependent on the chamber dimensions,type of material and times of ri,flat-top and fall of the excitation pul.
(2)The eddy current field has a fast transient component and a steady state component.
(3)The cancellation of the field produced by the rising edge of the excitation wave form is largely produced by the falling edge,providing the flat-top portion is brief.
(4)Numerical computations indicate the residual integral field due eddy currents to eddy currents at the start of the measurement period will be <1part in 107of the main bending force for a fast kicker with an optimized excitation waveform.有形资产
Table2
Ratio of Kicker Field正方形是特殊的平行四边形吗
Deflection to Main Field Deflection
ACKNOWLEDGEMENT
The authors would like to thank W.Meng and S.Kahn for their support and helpful discussions.
REFERENCES
[1]W.Feng and E.B.Forsyth,private communication.
[2]Jiri Lammeraner and Miles Stafl,"Eddy Currents"CRC Press,1966.
