# |Main and Fringe Field Computations for the Electrostatic Quadrupoles of the Muon g-2 Experiment Storage Ring

## Abstract

We consider semi-infinite electrostatic deflectors with plates of different thickness, including plates with rounded edges, and we calculate their electrostatic potential and field using conformal mappings. To validate the calculations, we compare the fringe fields of these electrostatic deflectors with fringe fields of finite electrostatic capacitors, and we extend the study to fringe fields of adjacent electrostatic deflectors with consideration of electrostatic induction, where field falloffs of semi-infinite electrostatic deflectors are slower than exponential and thus behave differently from most magnetic fringe fields. Building on the success with electrostatic deflectors, we develop a highly accurate and fully Maxwellian conformal mappings method for calculation of main fields of electrostatic particle optical elements. A remarkable advantage of this method is the possibility of rapid recalculations with geometric asymmetries and mispowered plates. We use this conformal mappings method to calculate the multipole terms of the high voltage quadrupole used in the storage ring of the Muon g-2 Experiment (FNALE- 0989). Completing the methodological framework, we present a method for extracting multipole strength falloffs of a particle optical element from a set of Fourier mode falloffs. We calculate the quadrupole strength falloff and its effective field boundary (EFB) for the Muon g-2 quadrupole, whichmore »

- Authors:

- Cockcroft Inst. Accel. Sci. Tech.
- Michigan State U.

- Publication Date:

- Research Org.:
- Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)

- Contributing Org.:
- Muon g-2

- OSTI Identifier:
- 1490840

- Report Number(s):
- FERMILAB-CONF-18-571-PPD

1712340

- DOE Contract Number:
- AC02-07CH11359

- Resource Type:
- Conference

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

### Citation Formats

```
Valetov, Eremey, and Berz, Martin.
```*|Main and Fringe Field Computations for the Electrostatic Quadrupoles of the Muon g-2 Experiment Storage Ring*. United States: N. p., 2018.
Web.

```
Valetov, Eremey, & Berz, Martin.
```*|Main and Fringe Field Computations for the Electrostatic Quadrupoles of the Muon g-2 Experiment Storage Ring*. United States.

```
Valetov, Eremey, and Berz, Martin. Mon .
"|Main and Fringe Field Computations for the Electrostatic Quadrupoles of the Muon g-2 Experiment Storage Ring". United States. https://www.osti.gov/servlets/purl/1490840.
```

```
@article{osti_1490840,
```

title = {|Main and Fringe Field Computations for the Electrostatic Quadrupoles of the Muon g-2 Experiment Storage Ring},

author = {Valetov, Eremey and Berz, Martin},

abstractNote = {We consider semi-infinite electrostatic deflectors with plates of different thickness, including plates with rounded edges, and we calculate their electrostatic potential and field using conformal mappings. To validate the calculations, we compare the fringe fields of these electrostatic deflectors with fringe fields of finite electrostatic capacitors, and we extend the study to fringe fields of adjacent electrostatic deflectors with consideration of electrostatic induction, where field falloffs of semi-infinite electrostatic deflectors are slower than exponential and thus behave differently from most magnetic fringe fields. Building on the success with electrostatic deflectors, we develop a highly accurate and fully Maxwellian conformal mappings method for calculation of main fields of electrostatic particle optical elements. A remarkable advantage of this method is the possibility of rapid recalculations with geometric asymmetries and mispowered plates. We use this conformal mappings method to calculate the multipole terms of the high voltage quadrupole used in the storage ring of the Muon g-2 Experiment (FNALE- 0989). Completing the methodological framework, we present a method for extracting multipole strength falloffs of a particle optical element from a set of Fourier mode falloffs. We calculate the quadrupole strength falloff and its effective field boundary (EFB) for the Muon g-2 quadrupole, which has explained the experimentally measured tunes, while simple estimates based on a linear model exhibited discrepancies up to 2%.},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2018},

month = {10}

}