A MAGNETOSTATIC CALCULATION OF FRINGING FIELD FOR THE ROGOWSKI POLE BOUNDARY WITH FLOATING SNAKE

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1 A MAGNETOSTATIC CALCULATION OF FRINGING FIELD FOR THE ROGOWSKI POLE BOUNDARY WITH FLOATING SNAKE Yan Chen, Fan Ming-Wu To cite this version: Yan Chen, Fan Ming-Wu. A MAGNETOSTATIC CALCULATION OF FRINGING FIELD FOR THE ROGOWSKI POLE BOUNDARY WITH FLOATING SNAKE. Journal de Physique Colloques, 1984, 45 (C1), pp.c1-889-c < /jphyscol: >. <jpa > HAL Id: jpa Submitted on 1 Jan 1984 HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

2 JOURNAL DE PHYSIQUE Colloque C1, suppl6ment au no 1, Tome 45, janvier 1984 page Cl-889 A MAGNETOSTATIC CALCULATION OF FRINGING FIELD FOR THE ROGOWSKI POLE BOUNDARY WITH FLOAT1 NG SNAKE Yan Chen and Fan Ming-wu Institute of Atomic Energy, P.O. Box 275 (25), Peking, China Resume - Une mgthode d1int6grale bornee est utilisge pour calculer la distribution de champ d'un p61e de Rogowski collier flottant pour un spectrographe magnetique QDDD de type MG2. L'EFB est pratiquement reproduit par un calcul BIM. Comme critpre suppl&mentaire, un calcul sur des p8les de Rogowski fix6s sans collier a Bt6 effectu6 et le calcul dlefb prssente un parfait accord avec l'expgrience. En 6valuant quantitativement l'effet des colliers, ce travail prgdit Gqalement les valeurs d'efb pour deux positions diffgrentes des colliers. Abstract - A Boundary Integral Method has been used to calculate the fringing field distribution of Rogowski pole boundary with floating snake for ag2 type of QDDD magnetic spectrograph and the experimental EFB is nearly reproduced from BIM calculation. As a further criteria, a calculation for clamped ~ogowski pole but without snake is also performed and the calculated EFB shows perfect identity with the experiment. For evaluating the effect of snake quantitatively, this work also predicts the EFB values for two different positions of snake. A specific Rogowski pole configuration with floating snake (1) is used at the D2 exit and D3 entrance of QMG2 type charged particle magnetic spectrograph (2) for post-manfacture adjustment of shapes of EFB along the boundary. In the experimental measurements of such fringing field (3), a relative large discrepancy is found between the EFB of manufactured magnet and the original design. Comparing this fact with a series measured data obtained from other types of QDDD spectrographs (4)( A EFGax-& 2.0 mm 1 such large deviation is anomalous, for example AEFB = 12.5 ma for D2 exit as shown in Fig.1. In search of reason why SO large error existed, a Boundary Integral Method (5) was used to calculate the fringing field distribution along the intermediate symmetric plane instead of TRIM code. As the BIM code does not need boundary condition, it is suitable for a large gap - - magnet calculation. The method is based on following formuia,,,-- I A H= %-H~ ; H =- 4v~?xs(+)dnj ; b =-v@ and - A A ~ = & ~ I n m M r ~ ( $ ) d ~,; 8 =p(gs-v@) where H is thz field intengity which is expressed as the Q, sum of the source field H and fleld I&, of induced mwneti~_atioq. is the induced potential 8ue to permeable material and R = I r'- rl is 1 the d istan- ce from the source point?*to the field point i'. If a magnet possesses relatively simple geometry like a common dipole structure with large gap and saturation in yoke is not inhomogeneous very much* BIM method has probably more advantages over other methods for avoiding the necessity of imposing the far field bmndary condition. Article published online by EDP Sciences and available at

3 C1-890 JOURNAL DE PHYSIQUE Obviously QWIG2 magnets satisfy almost all characteristics mentioned above. Because the dipole magnet of QlG2 spectrograph has 3-D configuration, a trick has to be used to convert 3-D problem to 2-D problem. Here we should keep two requirements in mind. First, after changing 3-D to 2-D the magnetic flux should be invariant. Second, the boundary condition remains stationary in the in teresing region and the effect of yoke on pole boundary can be eliminated. As shown in Fig.2, yoke 1 is rotated for a angle in anticlock- wise direction and yoke 2 turns in opposite direction for -. Fig.3 shows the imaging simulation and the first requirement is satisfied. The boundary condition near the interesting side AB has not been changed, so that the second requirement is also satisfied. The calculation also includes different permeabilities and different positions of snake for the practical size of magnet. As a further criteria, a calculation on the clamped Rogowski pole boundary without snake is also compared with measured distribution. In Bm calculation a boundary shape correction facter S must be taken into account while the theoretical result and the measured data are compared,because this method can deal with a 2-D problem only. The results from BlT!4 calculation, of course, describe the distributions of magnets with straight boundaries. The final results from BIN calculations can be summarized as following : 1. For the 02 exit boundary with snake the fringing field distribution from BWI approaches the measured nearly. h EFB (measured-theoretical) = gap, see Fig There is a small displacement of EFB for Rogowski boundary Thth snake for different permeabilities p= 750 and p= 1000 AEFB = gap. 3. The ETB will displace inward magnet for a distance of gap while the snake is moved outward for a half of snake thickness and vice versa. It is found that for a straight boundary the ratlo of EFB displacement to snake displacement is about 1:-9.5* where the minus symbol means opposite direction for each other. 4. For the clamped D2 entrance boundary the BIM distribution reproduces the experimental perfectly, as shown in Fig.5 A EFB (measured-theoretical) = gap. It is obvious that the BIM calculation simulates the actual fringing field distribution successfully. According to the designed construction of dipole magnet, such large inward-displacement of EFB is in the nature of case. It is also necessary to point out that there is no need to use a virtual iron bar connecting snake with yoke for the purpose of determination of magnetic potential and also no need to enclose the problem area with yoke for boundary condition. A simple conclution from above is that the snake is only a floating element and no field enhancement effect exists near it. REFFEREN CE 1. A.G.Drentje, R.J.de Meijer, H*A.Enge and K.B.Kowalski Nucl. ~nctr. and Meth =(I976 ) A.G.Drentje, ti.a.enge and K*B.Kowalski Nuclr Instre and Meth E(l974) Yang Jin-gang lnternal Report for field mapping of WG2 spectrograph magnets 4. M.Goldschmidt et a1 The Fourth International Conference on Magnet Te chnology Brookhaven, 1972

4 Beam Limit 6 V CI 0 Q) a V N q -16. Fig.1 A comparison of D2 exit EFB between the theoretical design and the measured data Fig.2 A simplified section of D2 magnet of 34G2 magnetic spectrograph

5 JOURNAL DE PHYSIQUE - Yoke.-. Coil M M p 4 snake Intermediate Symmetric Plane Fig.3 A structure simulation of D2 magnet Fig.4 The fringing field distribution of D2 exit with floating snake Fig.5 The fringing field distribution of D2 entrance with field clamp