# Experimental Runaway Electron Current Estimation in COMPASS Tokamak

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## Abstract

**:**

## 1. Introduction

## 2. Experimental Setup: COMPASS Tokamak

## 3. Experiment: High RE Current Discharge

- Loop voltage measured plasma voltage ${V}_{plasma}$ bellow 1 V, while the typical range is $1.5$–2 V;
- Electron temperature from Thomson Scattering was 1 order of magnitude colder than ordinary tokamak plasma;
- Hard X-ray scintillators observed a significant amount of RE losses;
- Poloidal internal pick-up coils detected inner structure that is moving outwards;
- Vertical field for feedback of horizontal plasma position was increasing during the discharge, even though plasma current was constant;
- EFIT reconstruction of poloidal cross-section depicted plasma shrinkage towards inner side, due to the increasing magnetic pressure coming from the above-mentioned vertical field;
- Plasma pressure in terms of its ratio to the poloidal magnetic field pressure (i.e., poloidal beta ${\beta}_{pol}$), estimated from EFIT showed unrealistic large values.

## 4. Method: RE Current Calculation

#### 4.1. RE Energy Calculation

#### 4.2. RE Distribution Functions

#### 4.3. Pitch Angle

## 5. Result: COMPASS Discharge 7298

## 6. Application: RE Influence on Ramp-Up

## 7. Application: RE Localisation

## 8. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

RE | Runaway Electron |

REDF | Runaway Electron Distribution Function |

HXR | Hard X-ray |

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1 | m is plasma current profile $I\left(\rho \right)$ peaking factor, defined as: $I\left(\rho \right)={I}_{p}(1-{(1-{\rho}^{2})}^{m+1})$. |

**Figure 1.**Poloidal beta ${\beta}_{pol}$ estimated by EFIT (red) and from Thomson Scattering (blue) for discharge #7298.

**Figure 2.**(

**a**) The maximum kinetic energy ${W}_{max}$ of discharge #7298 obtained for the different RE distribution functions: mono-energetic ${f}_{mono}$ (black solid), uniform ${f}_{uni}$ (black dotted), linear ${f}_{lin}$ (black dashed), exponential ${f}_{exp}$ (red), skewed Gaussian ${f}_{sG}$ (green) and Maxwell–Jüttner ${f}_{MJ}$ (blue). (

**b**) Time traces of the plasma current ${I}_{p}$ (blue), Shielded HXR (black) and Standard HXR (red). (

**c**) Estimated RE current ${I}_{RE}$ corresponding to each RE distribution function with the same labeling as on (

**a**).

**Figure 3.**Time traces of total electron density (black) measured with interferometer, RE density from Kruskal–Bernstein theory (green), RE density from NORSE simulation (cyan) and RE densities corresponding to RE currents from Figure 2c (dashed lines).

**Figure 4.**Time traces of the estimated ${n}_{RE}$ for the three typical discharges: #8553 (blue, standard discharge), #8555 (black, intermediate case) and #8559 (red, slide-away regime). (

**a**) Estimates from measurements where for each discharge the two most extreme REDF: the monoenergetic ${f}_{mono}$ (full line) and the exponential ${f}_{exp}$ (dashed line). (

**b**) Estimates from Kruskal–Bernstein theory (solid line) and NORSE simulation (dashed line).

**Figure 5.**Time traces for lower ${\rho}_{min}$ (solid colored lines) and upper ${\rho}_{max}$ (dashed coinciding colored lines) limits of RE major radii for all six REDFs are presented for discharge #7298. For orientation, major radius of plasma geometrical center ${R}_{geom}$ (black dash-dotted line), outer plasma major radius ${R}_{out}$ (black solid line), plasma current barycenter ${R}_{bc}$ (black dashed line) and theoretical bulk plasma barycenter from Shafranov shift ${R}_{sh}$ (black dotted line) are added. Beside all major radii, the Shielded HXR signal (green points) is presented. Figure is plotted for two of current profile factor m values: (

**a**) $m=1$; and (

**b**) $m=2$.

**Table 1.**Comparison of parameters (RE energy w, relativistic $\beta $, the term from Equation (3) $\u2329{\beta}^{2}\gamma \u232a=\u2329{\beta}_{\parallel}^{2}\gamma \u232a+0.5\u2329{\beta}_{\perp}^{2}\gamma \u232a$ and drift term $\eta $ for ${W}_{max}$ estimation) averaged over w for different REDFs.

REDF | $\u2329\mathit{w}\u232a$ [MeV] | $\u2329\mathit{\beta}\u232a$ | $\u2329{\mathit{\beta}}^{2}\mathit{\gamma}\u232a$ | $\u2329\mathit{\eta}\u232a$ | ||
---|---|---|---|---|---|---|

$\mathit{\theta}=\mathbf{0.0}$ | $\mathit{\theta}=\mathbf{0.3}$ | $\mathit{\theta}=\mathbf{0.1}$ | $\mathit{\theta}=\mathbf{0.3}$ | |||

${f}_{mono}$ | 10.00 | 0.9988 | 20.5 | 19.6 | 4.91 | 15.8 |

${f}_{uni}$ | 5.00 | 0.9721 | 10.6 | 10.2 | 9.55 | 30.7 |

${f}_{lin}$ | 3.33 | 0.9497 | 7.30 | 6.98 | 13.9 | 44.7 |

${f}_{exp}$ | 0.86 | 0.8141 | 2.18 | 2.09 | 43.8 | 140 |

${f}_{sG}$ | 8.02 | 0.9980 | 16.6 | 15.9 | 6.05 | 19.4 |

${f}_{MJ}$ | 1.58 | 0.9301 | 3.78 | 3.62 | 26.21 | 84.2 |

**Table 2.**The maxima of ${W}_{max}$ and ${I}_{RE}$ over the time domain of the whole discharge, plotted in Figure 2.

REDF | $max\left({\mathit{W}}_{\mathit{max}}\right)$ [MeV] | $max\left({\mathit{I}}_{\mathit{RE}}\right)$ [kA] |
---|---|---|

${f}_{mono}$ | 25.61 | 3.9 |

${f}_{uni}$ | 24.49 | 7.9 |

${f}_{lin}$ | 23.05 | 11.9 |

${f}_{exp}$ | 13.39 | 50.3 |

${f}_{sG}$ | 25.37 | 5.0 |

${f}_{MJ}$ | 18.54 | 26.5 |

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**MDPI and ACS Style**

Vlainic, M.; Ficker, O.; Mlynar, J.; Macusova, E.; the COMPASS Tokamak Team.
Experimental Runaway Electron Current Estimation in COMPASS Tokamak. *Atoms* **2019**, *7*, 12.
https://doi.org/10.3390/atoms7010012

**AMA Style**

Vlainic M, Ficker O, Mlynar J, Macusova E, the COMPASS Tokamak Team.
Experimental Runaway Electron Current Estimation in COMPASS Tokamak. *Atoms*. 2019; 7(1):12.
https://doi.org/10.3390/atoms7010012

**Chicago/Turabian Style**

Vlainic, Milos, Ondrej Ficker, Jan Mlynar, Eva Macusova, and the COMPASS Tokamak Team.
2019. "Experimental Runaway Electron Current Estimation in COMPASS Tokamak" *Atoms* 7, no. 1: 12.
https://doi.org/10.3390/atoms7010012