# Algebraic motion of vertically displacing plasmas

## Abstract

In this paper, the vertical motion of a tokamak plasma is analytically modelled during its non-linear phase by a free-moving current-carrying rod inductively coupled to a set of fixed conducting wires or a cylindrical conducting shell. The solutions capture the leading term in a Taylor expansion of the Green's function for the interaction between the plasma column and the surrounding vacuum vessel. The plasma shape and profiles are assumed not to vary during the vertical drifting phase such that the plasma column behaves as a rigid body. In the limit of perfectly conducting structures, the plasma is prevented to come in contact with the wall due to steep effective potential barriers created by the induced Eddy currents. Resistivity in the wall allows the equilibrium point to drift towards the vessel on the slow timescale of flux penetration. The initial exponential motion of the plasma, understood as a resistive vertical instability, is succeeded by a non-linear “sinking” behaviour shown to be algebraic and decelerating. Finally, the acceleration of the plasma column often observed in experiments is thus concluded to originate from an early sharing of toroidal current between the core, the halo plasma, and the wall or from the thermal quenchmore »

- Authors:

- Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)

- Publication Date:

- Research Org.:
- Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1429048

- Alternate Identifier(s):
- OSTI ID: 1422853

- Grant/Contract Number:
- AC02-09CH11466

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Physics of Plasmas

- Additional Journal Information:
- Journal Volume: 25; Journal Issue: 2; Journal ID: ISSN 1070-664X

- Publisher:
- American Institute of Physics (AIP)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; eddies; electronic circuits; condensed matter properties; electrical properties; plasma confinement; differential equations; classical electromagnetism

### Citation Formats

```
Pfefferle, D., and Bhattacharjee, A. Algebraic motion of vertically displacing plasmas. United States: N. p., 2018.
Web. doi:10.1063/1.5011176.
```

```
Pfefferle, D., & Bhattacharjee, A. Algebraic motion of vertically displacing plasmas. United States. doi:10.1063/1.5011176.
```

```
Pfefferle, D., and Bhattacharjee, A. Tue .
"Algebraic motion of vertically displacing plasmas". United States. doi:10.1063/1.5011176. https://www.osti.gov/servlets/purl/1429048.
```

```
@article{osti_1429048,
```

title = {Algebraic motion of vertically displacing plasmas},

author = {Pfefferle, D. and Bhattacharjee, A.},

abstractNote = {In this paper, the vertical motion of a tokamak plasma is analytically modelled during its non-linear phase by a free-moving current-carrying rod inductively coupled to a set of fixed conducting wires or a cylindrical conducting shell. The solutions capture the leading term in a Taylor expansion of the Green's function for the interaction between the plasma column and the surrounding vacuum vessel. The plasma shape and profiles are assumed not to vary during the vertical drifting phase such that the plasma column behaves as a rigid body. In the limit of perfectly conducting structures, the plasma is prevented to come in contact with the wall due to steep effective potential barriers created by the induced Eddy currents. Resistivity in the wall allows the equilibrium point to drift towards the vessel on the slow timescale of flux penetration. The initial exponential motion of the plasma, understood as a resistive vertical instability, is succeeded by a non-linear “sinking” behaviour shown to be algebraic and decelerating. Finally, the acceleration of the plasma column often observed in experiments is thus concluded to originate from an early sharing of toroidal current between the core, the halo plasma, and the wall or from the thermal quench dynamics precipitating loss of plasma current.},

doi = {10.1063/1.5011176},

journal = {Physics of Plasmas},

number = 2,

volume = 25,

place = {United States},

year = {2018},

month = {2}

}

*Citation information provided by*

Web of Science

Web of Science

#### Figures / Tables:

^{2}= γ

_{DE}/γ

_{LR}(sets of curves with di erent colour, see legend) and h

^{⁻2}ϵ {0, 1/3, 2/3, 1} (bottom to top curves of same colour). The initial exponential behaviourmore »

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*Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.*