## The importance of electrothermal terms in Ohm's law for magnetized spherical implosions

## Abstract

The magnetohydrodynamics (MHD) of magnetic-field compression in laser-driven spherical targets is considered. Magnetic-field evolution is cast in terms of an effective fluid velocity, a convective term resulting from resistivity gradients, a resistive diffusion term, and a source term. Effective velocity is the sum of fluid velocity, drift velocity, and heat-flux velocity, given by electron heat flux divided by electron enthalpy density, which has two components: the perpendicular or Nernst velocity and the cross-field velocity. The Nernst velocity compresses the magnetic field as a heat front moves into the gas. The cross-field velocity leads to dynamo generation of an azimuthal magnetic field. It is proposed that the heat-flux velocity should be flux limited using a “Nernst” flux limiter independent of the thermal flux limiter but should not exceed it. The addition of MHD routines to the 1-D, Lagrangian hydrocode LILAC and the Eulerian version of the 2-D hydrocode DRACO is described, and the codes are used to model a magnetized spherical compression on the OMEGA laser. Thermal flux limiting at a shock front is found to cause unphysical electron temperature gradients that lead to large, unphysical magnetic fields caused by the resistivity gradient, so thermal flux limiting in the gas ismore »

- Authors:

- Univ. of Rochester, Rochester, NY (United States)

- Publication Date:

- Research Org.:
- Univ. of Rochester, Rochester, NY (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1228366

- Alternate Identifier(s):
- OSTI ID: 1225401

- Grant/Contract Number:
- NA0001944; FC02-04ER54789; FG02-04ER54786

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Physics of Plasmas

- Additional Journal Information:
- Journal Volume: 22; Journal Issue: 11; 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; magnetic fields; limiters; electrical resistivity; shock waves; thermal conductivity

### Citation Formats

```
Davies, J. R., Betti, R., Chang, P. -Y., and Fiksel, G. The importance of electrothermal terms in Ohm's law for magnetized spherical implosions. United States: N. p., 2015.
Web. doi:10.1063/1.4935286.
```

```
Davies, J. R., Betti, R., Chang, P. -Y., & Fiksel, G. The importance of electrothermal terms in Ohm's law for magnetized spherical implosions. United States. doi:10.1063/1.4935286.
```

```
Davies, J. R., Betti, R., Chang, P. -Y., and Fiksel, G. Fri .
"The importance of electrothermal terms in Ohm's law for magnetized spherical implosions". United States. doi:10.1063/1.4935286. https://www.osti.gov/servlets/purl/1228366.
```

```
@article{osti_1228366,
```

title = {The importance of electrothermal terms in Ohm's law for magnetized spherical implosions},

author = {Davies, J. R. and Betti, R. and Chang, P. -Y. and Fiksel, G.},

abstractNote = {The magnetohydrodynamics (MHD) of magnetic-field compression in laser-driven spherical targets is considered. Magnetic-field evolution is cast in terms of an effective fluid velocity, a convective term resulting from resistivity gradients, a resistive diffusion term, and a source term. Effective velocity is the sum of fluid velocity, drift velocity, and heat-flux velocity, given by electron heat flux divided by electron enthalpy density, which has two components: the perpendicular or Nernst velocity and the cross-field velocity. The Nernst velocity compresses the magnetic field as a heat front moves into the gas. The cross-field velocity leads to dynamo generation of an azimuthal magnetic field. It is proposed that the heat-flux velocity should be flux limited using a “Nernst” flux limiter independent of the thermal flux limiter but should not exceed it. The addition of MHD routines to the 1-D, Lagrangian hydrocode LILAC and the Eulerian version of the 2-D hydrocode DRACO is described, and the codes are used to model a magnetized spherical compression on the OMEGA laser. Thermal flux limiting at a shock front is found to cause unphysical electron temperature gradients that lead to large, unphysical magnetic fields caused by the resistivity gradient, so thermal flux limiting in the gas is removed. The Nernst term reduces the benefits of magnetization in inertial fusion. In addition, a Nernst flux limiter ≤ 0.12 is required in the gas in order to agree with measured neutron yield and increases in the neutron-averaged ion temperature caused by magnetization. This corresponds to maintaining the Nernst velocity below the shock velocity, which prevents significant decoupling of the magnetic field and gas compression.},

doi = {10.1063/1.4935286},

journal = {Physics of Plasmas},

number = 11,

volume = 22,

place = {United States},

year = {2015},

month = {11}

}

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