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Optical Thomson scattering is now a mature diagnostic tool for precisely measuring local plasma density and temperature. These measurements typically take advantage of a simplified analytical model of the scattered spectrum, which is built upon the assumption that each plasma species is in thermal equilibrium. However, this assumption fails for most laboratory plasmas of interest, which are often produced through high field ionization of atoms via ultrashort laser pulses and vulnerable to several kinetic instabilities. While it is possible to analytically model the Thomson scattered spectrum for some non-Maxwellian distribution functions, it is often not practical to do so for laboratory plasmas with highly complex and unstable distribution functions. We present a new method for predicting the Thomson scattered spectrum from any plasma directly from fully kinetic particle-in-cell simulations. This approach allows us to model the contributions of kinetic instabilities to the Thomson spectrum that aren’t taken into account in Maxwellian theory. We demonstrate this method’s capability to capture nonthermal features in the Thomson spectrum by simulating a simple bumpon- tail plasma as well as a more complex laser-ionized plasma. The versatility of this approach makes it an effective aid in the experimental design of Thomson diagnostics to directly characterize kinetic instabilities in laboratory plasmas. Index Terms—plasma measurement, low-temperature plasmas, plasma diagnostics, plasma simulation, plasma stability, plasma density, plasma temperature
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Computing the generalized plasma dispersion function for non-Maxwellian plasmas, with applications to Thomson scattering
Kinetic plasma studies often require computing integrals of the velocity distribution over a complex-valued pole. The standard method is to solve the integral in the complex plane using the Plemelj theorem, resulting in the standard plasma dispersion function for Maxwellian plasmas. For non-Maxwellian plasmas, the Plemelj theorem does not generalize to an analytic form, and computational methods must be used. In this paper, a new computational method is developed to accurately integrate a non-Maxwellian velocity distribution over an arbitrary set of complex valued poles. This method works by keeping the integration contour on the real line, and applying a trapezoid rule-like integration scheme over all discretized intervals. In intervals containing a pole, the velocity distribution is linearly interpolated, and the analytic result for the integral over a linear function is used. The integration scheme is validated by comparing its results to the analytic plasma dispersion function for Maxwellian distributions. We then show the utility of this method by computing the Thomson scattering spectra for several non-Maxwellian distributions: the kappa, super-Gaussian, and toroidal distributions. Thomson scattering is a valuable plasma diagnostic tool for both laboratory and space plasmas, but the technique relies on fitting measured wave spectra to a forward model, which typically assumes Maxwellian plasmas. Therefore, this integration method can expand the capabilities of Thomson scatter diagnostics to regimes where the plasma is non-Maxwellian, including high energy density plasmas, frictionally heated plasmas in the ionosphere, and plasmas with a substantial suprathermal electron tail.
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- Award ID(s):
- 2330254
- PAR ID:
- 10586258
- Publisher / Repository:
- American Institute of Physics
- Date Published:
- Journal Name:
- Physics of Plasmas
- Volume:
- 32
- Issue:
- 4
- ISSN:
- 1070-664X
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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