Steady-state radiative cooling rates for low-density, high-temperature plasmas

Post, D.; Jensen, Roderick V.; Tarter, C. Bruce; Grasberger, W.H.; Lokke, W.A.

doi:10.1016/0092-640x(77)90026-2

Cited by 775 publications

(464 citation statements)

References 22 publications

Supporting

Mentioning

455

Contrasting

Order By: Relevance

“…The best agreement has been found for a set of ionization rates, which originate from configuration averaged distorted wave (CADW) calculations [14] and recombination rates which originate from the average ion model [9] but have been adjusted by temperature independent factors to match the experimental observations. These adjustments have been performed ad-hoc without a physics explanation to provide a set of ionization and recombination rates that led to an ionization equilibrium as observed in experiment.…”

Section: Ionization Equilibriummentioning

confidence: 84%

“…For the major part of the electron temperature range under consideration this contribution to the total cooling factor is small. The contribution of Bremstrahlung is calculated using the formula of [9] and the free-free Gaunt factor of [18].…”

Section: Radiation Due To Recombination and Bremstrahlungmentioning

confidence: 99%

“…Still, the radiative cooling by W is a concern and the maximum tolerable W concentration is an important value for ITER and a future fusion reactor. This value, however, is based on calculations of the cooling factor [9,10] using the average ion model, a model which does not calculate quantummechanical wave functions of the levels in each ion, but uses scale formulas based on a hydrogenic orbital model. In this work, the Cowan code [11] is used for level resolved calculations in order to calculate a cooling factor based on more detailed atomic physics.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Calculation and experimental test of the cooling factor of tungsten

Pütterich¹,

Neu²,

Dux³

et al. 2010

Nucl. Fusion

203

196

View full text Add to dashboard Cite

Abstract. The cooling factor of W is evaluated using state of the art data for line radiation and an ionization balance which has been benchmarked with experiment. For the calculation of line radiation, level-resolved calculations were performed with the Cowan code to obtain the electronic structure and excitation cross sections (plane-wave Born approximation). The data were processed by a collisional radiative model to obtain electron density dependent emissions. These data were then combined with the radiative power derived from recombination rates and Bremsstrahlung to obtain the total cooling factor. The effect of uncertainties in the recombination rates on the cooling factor were studied and were identified to be of secondary importance. The new cooling factor is benchmarked, by comparisons of the line radiation to spectral measurements as well as to a direct measurement of the cooling factor. Additionally, a less detailed calculation using a configuration averaged model was performed. It was used to benchmark the level-resolved calculations and to improve the prediction on radiation power from line radiation for ionization stages which are computationally challenging. The obtained values for the cooling factor validate older predictions from literature. Its ingredients and the absolute value are consistent with the existing experimental results regarding the value itself, the spectral distibution of emissions and the ionization equilibrium. A table of the cooling factor versus electron temperature is provided. Finally, the cooling factor is used to investigate the operational window of a fusion reactor with W as intrinsic impurity. The minimum value of ¤ ¦ ¥ § © , for which a thermonuclear burn is possible, is increased by 20% for a W concentration of " !

show abstract

Section: Ionization Equilibriummentioning

confidence: 84%

Section: Radiation Due To Recombination and Bremstrahlungmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Calculation and experimental test of the cooling factor of tungsten

Pütterich¹,

Neu²,

Dux³

et al. 2010

Nucl. Fusion

203

196

View full text Add to dashboard Cite

show abstract

“…For models based on principal quantum numbers, these transitions have previously been handled with averaged transition energies and oscillator strengths, calculated under coronal conditions [32]. This data represents these transitions poorly under more general conditions and cannot easily be extended.…”

Section: Extensions To Atomic Models For Radiation Transportmentioning

confidence: 99%

Advances in NLTE modeling for integrated simulations

Scott

Hansen

2010

High Energy Density Physics

188

View full text Add to dashboard Cite

The last few years have seen significant progress in constructing the atomic models required for non-local thermodynamic equilibrium (NLTE) simulations. Along with this has come an increased understanding of the requirements for accurately modeling the ionization balance, energy content and radiative properties of different elements for a wide range of densities and temperatures. Much of this progress is the result of a series of workshops dedicated to comparing the results from different codes and computational approaches applied to a series of test problems. The results of these workshops emphasized the importance of atomic model completeness, especially in doubly excited states and autoionization transitions, to calculating ionization balance, and the importance of accurate, detailed atomic data to producing reliable spectra.We describe a simple screened-hydrogenic model that calculates NLTE ionization balance with surprising accuracy, at a low enough computational cost for routine use in radiation-hydrodynamics codes. The model incorporates term splitting, n=0 transitions, and approximate UTA widths for spectral calculations, with results comparable to those of much more detailed codes. Simulations done with this model have been increasingly successful at matching experimental data for laser-driven systems and hohlraums.Accurate and efficient atomic models are just one requirement for integrated NLTE simulations. Coupling the atomic kinetics to hydrodynamics and radiation transport constrains both discretizations and algorithms to retain energy conservation, accuracy and stability. In particular, the strong coupling between radiation and populations can require either very short timesteps or significantly modified radiation transport algorithms to account for NLTE material response. Considerations such as these continue to provide challenges for NLTE simulations.

show abstract

“…The simulations use an impurity-radiation model based on oxygen, which previously kept the plasma temperatures comparable to TCHI experiments in NSTX ($10-25 eV). The impurity model uses the calculations by Post et al 22 In the present calculations, the impurity density is taken to be comparable to the electron density in the lower-left corner of the tokamak vessel where the injected current strikes and the electron temperature is low, dropping off away from the corner as a Gaussian with characteristic lengths of 0.45 m (radial) and 1.0 m (vertical). Radiation from oxygen has a strong peak at about 25 eV; the large impurity density needed in Ref.…”

Section: A Injection Mechanism and Impurity Modelingmentioning

confidence: 99%

A current-driven resistive instability and its nonlinear effects in simulations of coaxial helicity injection in a tokamak

Hooper

Sovinec

2016

Physics of Plasmas

View full text Add to dashboard Cite

An instability observed in whole-device, resistive magnetohydrodynamic simulations of the driven phase of coaxial helicity injection in the National Spherical Torus eXperiment is identified as a current-driven resistive mode in an unusual geometry that transiently generates a current sheet. The mode consists of plasma flow velocity and magnetic field eddies in a tube aligned with the magnetic field at the surface of the injected magnetic flux. At low plasma temperatures (∼10–20 eV), the mode is benign, but at high temperatures (∼100 eV) its amplitude undergoes relaxation oscillations, broadening the layer of injected current and flow at the surface of the injected toroidal flux and background plasma. The poloidal-field structure is affected and the magnetic surface closure is generally prevented while the mode undergoes relaxation oscillations during injection. This study describes the mode and uses linearized numerical computations and an analytic slab model to identify the unstable mode.

show abstract

Steady-state radiative cooling rates for low-density, high-temperature plasmas

Cited by 775 publications

References 22 publications

Calculation and experimental test of the cooling factor of tungsten

Calculation and experimental test of the cooling factor of tungsten

Advances in NLTE modeling for integrated simulations

A current-driven resistive instability and its nonlinear effects in simulations of coaxial helicity injection in a tokamak

Contact Info

Product

Resources

About