Improved Kelbg Potentials Achieve Accurate Carbon Plasma Internal Energy Calculations

Scientists are continually refining models to accurately describe the behaviour of matter under extreme conditions, and a new study details significant improvements to the Kelbg potential , a crucial tool for simulating warm dense matter and high energy density plasmas. Heather D. Whitley, Michael S. Murillo, and John I. Castor, alongside colleagues from Lawrence Livermore National Laboratory, Michigan State University, and San Jose State University, present a generalised form of the electron-ion potential, extending the Kelbg potential’s accuracy to higher atomic numbers. Their research, which applies this improved potential to carbon plasmas using classical molecular dynamics, validates its performance against established equation of state models derived from path integral Monte Carlo and density functional theory , offering a computationally efficient alternative for exploring these challenging states of matter and potentially unlocking new insights into astrophysical phenomena and inertial confinement fusion.

This breakthrough enables more accurate modelling of hot, dense plasmas, crucial for understanding phenomena in inertial confinement fusion and high energy density physics. The research team applied classical molecular dynamics, utilizing this improved Kelbg potential alongside various Pauli potential forms, to compute internal energies and pressures under extreme conditions, those found in hot, dense plasmas. Researchers achieved this by numerically fitting an updated Padé approximant to the improved Kelbg potential, extending its applicability beyond hydrogen to encompass a wider range of fully ionized species. This advancement is significant because it provides a more versatile tool for equation of state studies in warm dense matter and high energy density plasmas, areas where accurate modelling is notoriously challenging. The core premise involves mapping a quantum many-body system onto a classical particle system through controlled approximations, allowing for computationally efficient simulations. By applying the pair density approximation, the scientists computed the exact pair density matrix for electron-ion pairs ranging from hydrogen (Z = 1) to xenon (Z = 54), significantly expanding the scope of previous studies. This detailed analysis allows for a more comprehensive understanding of electron-ion interactions and their impact on plasma behaviour under extreme conditions.

The research establishes a robust framework for assessing the validity of quantum statistical potentials, specifically by comparing simulated internal energies and pressures with a previously published equation of state table based on quantum density functional theory and path integral Monte Carlo simulations. Furthermore, the team examined the validity of the potentials for carbon by relating the simulations to the average occupation of the K-shell, as calculated by the Purgatorio code. This work fits the potential to an improved Kelbg model, extending its applicability to atomic numbers up to 54, encompassing a wide range of elements, from hydrogen to xenon, and enabling more accurate simulations of complex plasmas. Researchers applied classical molecular dynamics (MD) using this improved Kelbg potential, specifically for carbon, employing various forms of the Pauli potential to meticulously compute internal energies and pressures under hot, dense plasma conditions. Experiments employed the Purgatorio code to assess the validity of the quantum statistical potentials (QSPs) for carbon, examining the average occupation of the K-shell and comparing simulated internal energies and pressures with the established EOS table published previously. This method achieves a balance between accuracy and computational cost, enabling the study of thermodynamic properties in regimes where approximations remain valid, specifically, for systems with low electron density, avoiding the need for complex three-body or higher-order quantum correlations. Starting from the definition of the partition function and the density matrix, the study demonstrates how a quantum many-body system can be effectively mapped onto a classical system, facilitating the calculation of expectation values through configuration space integrals. The approach enables a detailed examination of the interplay between quantum effects and classical dynamics in extreme plasma conditions, offering valuable insights for advancing our understanding of warm dense matter and high energy density physics.

Kelbg Potential Accurately Models Carbon Plasma Behaviour

Scientists have developed a general form for the electron-ion diffractive potential, derived from the pair density matrix and fitted to the improved Kelbg potential for atomic numbers up to Z = 54. The research team applied classical molecular dynamics using this improved Kelbg potential to carbon, employing various forms of the Pauli potential, to compute internal energies and pressures under hot, dense plasma conditions. Experiments revealed that the derived potentials accurately model the behaviour of carbon plasmas, demonstrating a significant advancement in warm dense matter and high energy density plasma studies. Results demonstrate a strong correlation between the improved Kelbg potential and established equation of state models based on path integral Monte Carlo and density functional theory simulations.

The team meticulously compared simulated internal energies and pressures with those predicted by the equation of state model, confirming the validity of the approach for carbon plasmas. Measurements confirm that the regions of validity for carbon align generally with previously established findings for hydrogen, particularly when pressure ionization effects are considered, indicating a broad applicability of the developed potentials. Data shows the successful extension of the improved Kelbg potential beyond hydrogen, achieving a robust fit for fully ionized species up to an atomic number of 54. Tests prove that the quantum statistical potentials effectively mimic quantum behaviour, preventing the “Coulomb catastrophe” at small electron-ion distances and accurately accounting for Fermi statistics in electron-electron collisions. Measurements confirm the applicability of the derived potentials to equation of state studies in warm dense matter and high energy density plasmas, offering a computationally efficient alternative to fully quantum simulations. Furthermore,. This work builds upon earlier studies of hydrogen plasmas, extending the applicability of quantum statistical potentials to heavier elements and paving the way for more accurate modelling of complex plasma environments.

Kelbg Potential Validates Carbon Plasma EOS

Scientists have developed a generalized functional form for the fitting parameter within the improved Kelbg potential, extending its applicability to atomic numbers greater than one. Researchers then assessed the viability of using this improved Kelbg potential within classical molecular dynamics simulations to calculate the equation of state (EOS) for carbon. Furthermore, this method offers unique capabilities for investigating finite-size effects in quantum simulations, modelling mixtures with low concentrations of species, and examining many-body dynamics in dilute plasmas. However, the authors acknowledge the method’s limitations, noting its applicability is restricted to scenarios where the thermal de Bröglie wavelength is significantly smaller than interparticle distances, implying a classical treatment is sufficient for thermodynamic properties. Future work could focus on implementing this improved Kelbg potential into standard simulation codes, facilitating broader use within the scientific community.