# Lifetime and universal distribution of seed runaway electrons

## Abstract

The lifetime of pre-existing runaway electrons determines how likely the runaways will undergo avalanche multiplication. We estimate the lifetime of runaway electrons via kinetic analysis. We show that the rate of runaway decay depends on the combination of parameters α≡(Z+1)/$$\sqrt{{\bar{τ}}_{rad}}$$ (where $$τ_{rad}$$ is the synchrotron timescale normalized to the collisional timescale and Z is the ion charge) compared to the electric field. We identify two cases where the decay rate is slow enough to enable a quasi-steady shape of the runaway distribution function. This distribution and its lifetime represent the eigenfunction and the lowest eigenvalue of the kinetic equation. In one case, α$$\ll$$1: the field required to sustain the pre-existing runaways is barely larger than the Connor-Hastie critical value. In the same manner as by Aleynikov and Breizman [Phys. Rev. Lett. 114, 155001 (2015)], we solve the kinetic equation perturbatively but extend the work to demonstrate that the lifetime grows exponentially with the field at a rate that depends on α. Finally, in the second case, α$$\gg$$1: the sustainment field is much greater than the Connor-Hastie value, and the largeness of the field in this case enables us to universalize the kinetic equation via the re-scaling procedure.

- Authors:

- Univ. of Texas, Austin, TX (United States). Inst. for Fusion Studies

- Publication Date:

- Research Org.:
- Univ. of Texas, Austin, TX (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC)

- OSTI Identifier:
- 1540126

- Alternate Identifier(s):
- OSTI ID: 1420640

- Grant/Contract Number:
- FG02-04ER54742; SC0016283

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Physics of Plasmas

- Additional Journal Information:
- Journal Volume: 24; Journal Issue: 11; Journal ID: ISSN 1070-664X

- Publisher:
- American Institute of Physics (AIP)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- Physics

### Citation Formats

```
Fontanilla, Adrian K., and Breizman, Boris N. Lifetime and universal distribution of seed runaway electrons. United States: N. p., 2017.
Web. doi:10.1063/1.5001931.
```

```
Fontanilla, Adrian K., & Breizman, Boris N. Lifetime and universal distribution of seed runaway electrons. United States. doi:10.1063/1.5001931.
```

```
Fontanilla, Adrian K., and Breizman, Boris N. Tue .
"Lifetime and universal distribution of seed runaway electrons". United States. doi:10.1063/1.5001931. https://www.osti.gov/servlets/purl/1540126.
```

```
@article{osti_1540126,
```

title = {Lifetime and universal distribution of seed runaway electrons},

author = {Fontanilla, Adrian K. and Breizman, Boris N.},

abstractNote = {The lifetime of pre-existing runaway electrons determines how likely the runaways will undergo avalanche multiplication. We estimate the lifetime of runaway electrons via kinetic analysis. We show that the rate of runaway decay depends on the combination of parameters α≡(Z+1)/$\sqrt{{\bar{τ}}_{rad}}$ (where $τ_{rad}$ is the synchrotron timescale normalized to the collisional timescale and Z is the ion charge) compared to the electric field. We identify two cases where the decay rate is slow enough to enable a quasi-steady shape of the runaway distribution function. This distribution and its lifetime represent the eigenfunction and the lowest eigenvalue of the kinetic equation. In one case, α$\ll$1: the field required to sustain the pre-existing runaways is barely larger than the Connor-Hastie critical value. In the same manner as by Aleynikov and Breizman [Phys. Rev. Lett. 114, 155001 (2015)], we solve the kinetic equation perturbatively but extend the work to demonstrate that the lifetime grows exponentially with the field at a rate that depends on α. Finally, in the second case, α$\gg$1: the sustainment field is much greater than the Connor-Hastie value, and the largeness of the field in this case enables us to universalize the kinetic equation via the re-scaling procedure.},

doi = {10.1063/1.5001931},

journal = {Physics of Plasmas},

number = 11,

volume = 24,

place = {United States},

year = {2017},

month = {11}

}

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