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Title: Error studies of Halbach Magnets

Abstract

These error studies were done on the Halbach magnets for the CBETA “First Girder” as described in note [CBETA001]. The CBETA magnets have since changed slightly to the lattice in [CBETA009]. However, this is not a large enough change to significantly affect the results here. The QF and BD arc FFAG magnets are considered. For each assumed set of error distributions and each ideal magnet, 100 random magnets with errors are generated. These are then run through an automated version of the iron wire multipole cancellation algorithm. The maximum wire diameter allowed is 0.063” as in the proof-of-principle magnets. Initially, 32 wires (2 per Halbach wedge) are tried, then if this does not achieve 1e-­4 level accuracy in the simulation, 48 and then 64 wires. By “1e-4 accuracy”, it is meant the FOM defined by √(Σ n≥sextupole a n 2+b n 2) is less than 1 unit, where the multipoles are taken at the maximum nominal beam radius, R=23mm for these magnets. The algorithm initially uses 20 convergence interations. If 64 wires does not achieve 1e-­4 accuracy, this is increased to 50 iterations to check for slow converging cases. There are also classifications for magnets that do not achieve 1e-4more » but do achieve 1e-3 (FOM ≤ 10 units). This is technically within the spec discussed in the Jan 30, 2017 review; however, there will be errors in practical shimming not dealt with in the simulation, so it is preferable to do much better than the spec in the simulation.« less

Authors:
 [1]
  1. Brookhaven National Lab. (BNL), Upton, NY (United States)
Publication Date:
Research Org.:
Brookhaven National Laboratory (BNL), Upton, NY (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26)
OSTI Identifier:
1412719
Report Number(s):
BNL-114543-2017-IR
DOE Contract Number:
SC0012704
Resource Type:
Technical Report
Country of Publication:
United States
Language:
English
Subject:
43 PARTICLE ACCELERATORS

Citation Formats

Brooks, S. Error studies of Halbach Magnets. United States: N. p., 2017. Web. doi:10.2172/1412719.
Brooks, S. Error studies of Halbach Magnets. United States. doi:10.2172/1412719.
Brooks, S. Thu . "Error studies of Halbach Magnets". United States. doi:10.2172/1412719. https://www.osti.gov/servlets/purl/1412719.
@article{osti_1412719,
title = {Error studies of Halbach Magnets},
author = {Brooks, S.},
abstractNote = {These error studies were done on the Halbach magnets for the CBETA “First Girder” as described in note [CBETA001]. The CBETA magnets have since changed slightly to the lattice in [CBETA009]. However, this is not a large enough change to significantly affect the results here. The QF and BD arc FFAG magnets are considered. For each assumed set of error distributions and each ideal magnet, 100 random magnets with errors are generated. These are then run through an automated version of the iron wire multipole cancellation algorithm. The maximum wire diameter allowed is 0.063” as in the proof-of-principle magnets. Initially, 32 wires (2 per Halbach wedge) are tried, then if this does not achieve 1e-­4 level accuracy in the simulation, 48 and then 64 wires. By “1e-4 accuracy”, it is meant the FOM defined by √(Σn≥sextupole an 2+bn 2) is less than 1 unit, where the multipoles are taken at the maximum nominal beam radius, R=23mm for these magnets. The algorithm initially uses 20 convergence interations. If 64 wires does not achieve 1e-­4 accuracy, this is increased to 50 iterations to check for slow converging cases. There are also classifications for magnets that do not achieve 1e-4 but do achieve 1e-3 (FOM ≤ 10 units). This is technically within the spec discussed in the Jan 30, 2017 review; however, there will be errors in practical shimming not dealt with in the simulation, so it is preferable to do much better than the spec in the simulation.},
doi = {10.2172/1412719},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Thu Mar 02 00:00:00 EST 2017},
month = {Thu Mar 02 00:00:00 EST 2017}
}

Technical Report:

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  • A principle of the non-scaling Fixed Field Alternating Gradient (NS-FFAG) is that different energy beam has orbit oscillations Δx around the central circular orbit in both positive and negative direction within a small radial aperture as: Δx=D x*δp/p. For the central circular orbit Δx=0, or for the combined function magnets the field is equal to Bo (B (x) = B o + G* x). The smallest orbit offsets Δx are obtained when the defocusing magnet provides most of the bending for the central energy, while the focusing magnet could be even the regular quadrupole with the central orbit in themore » middle. Stable orbits for a very large energy range [in the case of CBETA this is 4 times in energy], is obtained using opposite polarity magnets producing linear magnetic fields, small dispersion, and very strong focusing.« less
  • The CBETA magnets will be marked by the manufacturer with two sides called “A” and “B”, as well as which part of the magnet is the “top” vertically. The significances of these sides are given in the table below.
  • A principle of the non-scaling Fixed Field Alternating Gradient (NS-FFAG) is that different energy beam has orbit oscillations Δx around the central circular orbit in both positive and negative direction within a small radial aperture as: Δx=D x *δp/p. For the central circular orbit Δx=0, or for the combined function magnets the field is equal to B o (B (x) = B o + G*x). The smallest orbit offsets Δx are obtained when the defocusing magnet provides most of the bending for the central energy, while the focusing magnet could be even the regular quadrupole with the central orbit inmore » the middle. Stable orbits for a very large energy range [in the case of CBETA this is 4 times in energy], is obtained using opposite polarity magnets producing linear magnetic fields, small dispersion, and very strong focusing.« less