### Analytic saddlepoint approximation for ionization energy loss distributions

Here, we present a saddlepoint approximation for ionization energy loss distributions, valid for arbitrary relativistic velocities of the incident particle 0 < v/c < 1, provided that ionizing collisions are still the dominant energy loss mechanism. We derive a closed form solution closely related to Moyal’s distribution. This distribution is intended for use in simulations with relatively low computational overhead. The approximation generally reproduces the Vavilov most probable energy loss and full width at half maximum to better than 1% and 10%, respectively, with significantly better agreement as Vavilov’s κ approaches 1.

- Publication Date:

- Report Number(s):
- LA-UR-17-21075

Journal ID: ISSN 0168-583X; TRN: US1800663

- Grant/Contract Number:
- AC52-06NA25396

- Type:
- Accepted Manuscript

- Journal Name:
- Nuclear Instruments and Methods in Physics Research. Section B, Beam Interactions with Materials and Atoms

- Additional Journal Information:
- Journal Volume: 407; Journal Issue: C; Journal ID: ISSN 0168-583X

- Publisher:
- Elsevier

- Research Org:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Sponsoring Org:
- USDOE

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Accelerator Design, Technology, and Operations; Atomic and Nuclear Physics; energy straggling; ionization energy loss; Vavilov distribution; Landau distribution

- OSTI Identifier:
- 1414139

```
Sjue, Sky K. L., George, Jr., Richard Neal, and Mathews, David Gregory.
```*Analytic saddlepoint approximation for ionization energy loss distributions*. United States: N. p.,
Web. doi:10.1016/j.nimb.2017.06.013.

```
Sjue, Sky K. L., George, Jr., Richard Neal, & Mathews, David Gregory.
```*Analytic saddlepoint approximation for ionization energy loss distributions*. United States. doi:10.1016/j.nimb.2017.06.013.

```
Sjue, Sky K. L., George, Jr., Richard Neal, and Mathews, David Gregory. 2017.
"Analytic saddlepoint approximation for ionization energy loss distributions". United States.
doi:10.1016/j.nimb.2017.06.013. https://www.osti.gov/servlets/purl/1414139.
```

```
@article{osti_1414139,
```

title = {Analytic saddlepoint approximation for ionization energy loss distributions},

author = {Sjue, Sky K. L. and George, Jr., Richard Neal and Mathews, David Gregory},

abstractNote = {Here, we present a saddlepoint approximation for ionization energy loss distributions, valid for arbitrary relativistic velocities of the incident particle 0 < v/c < 1, provided that ionizing collisions are still the dominant energy loss mechanism. We derive a closed form solution closely related to Moyal’s distribution. This distribution is intended for use in simulations with relatively low computational overhead. The approximation generally reproduces the Vavilov most probable energy loss and full width at half maximum to better than 1% and 10%, respectively, with significantly better agreement as Vavilov’s κ approaches 1.},

doi = {10.1016/j.nimb.2017.06.013},

journal = {Nuclear Instruments and Methods in Physics Research. Section B, Beam Interactions with Materials and Atoms},

number = C,

volume = 407,

place = {United States},

year = {2017},

month = {7}

}