# 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 »

- Authors:

- 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}

}