Non-local Transport of Strongly Coupled Plasmas

1. Non-local Transport of Strongly Coupled Plasmas Department of Fundamental Energy Science, Kyoto University Satoshi Hamaguchi, Tomoyasu Saigo, and August Wierling

2. Outline • Introduction • Theory • MD simulation methods • Results • Summary

3. i e Debye screening clouds -Q Fine Particle Yukawa potential ：inverse of Debye length ：Charge of fine particle Introduction dusty plasmas, colloidal suspension, non-neutral plasmas, etc.,

4. strongly coupled system Yukawa System = a system of particlesinteracting through Yukawa potential Screening parameter： ：inter particle spacing Coupling parameter ： ：particle temperature : one component plasma

5. Plasma Crystal Experiments G. E. Morfill: Max-Planck-Institute for Extraterrestrial Physics http://www.mpe.mpg.de/www_th/plasma-crystal/index_e.html

6. Molecular Dynamics Simulation

7. phase diagram of Yukawa systems

8. Motivation Strongly Coupled Systems Ordinary Hydrodynamics: valid only for  want to have fluid equations valid for up to : relaxation time : shear viscosity : bulk viscosity

9. Non-local transport coefficients Generalized Hydrodynamics: non-local effects  i.e., wavenumber and frequency dependent transport coefficients : generalized shear viscosity : generalized bulk viscosity

10. Simple Assumption If we assume Fourier-Laplace transform Linearized equation

11. ka Under the simple assumption For example, transverse wave

12. More generally… Fourier-Laplace transform of Linearized Generalized Hydrodynamics equation in Laplace-Fourier space

13. goals • determine the generalized shear viscosity • in general, the simple assumption mentioned in the previous page does not hold: the wavenumber dependence of τR cannot be ignored. • determine the relaxation time τR asa function of Γ (or system temperature T) and .

14. Microscopic flux (current): Assumption: hydrodynamic j should behave similarly at least if . Theory microscopic analysis ↔ hydrodynamics analysis Consider Transverse Current Autocorrelation Function

15. transverse: current autocorrelation functions longitudinal:

16. q = 0.619 q = 1.24 q =1.75 q =1.96 q =2.23 q =2.48 current correlation functions

17. ka Under the simple assumption For example, transverse wave

18. Transverse Current Autocorrelation Function Under Navier-Stokes Eqn: However microscopically…. Low wave number high wave number

19. Need to extend Memory Function This equation may be viewed as the definition of Memory Function. • hydrodynamic approximation (no memory) Relaxation Time Approximation(RTA)

20. General Properties of Memory Function kinematic shear viscosity

21. Memory Function The memory function usually decays monotonically. The memory function usually decays more rapidly than the Transverse Current Autocorrelation Function (TCAF).

23. Assumption for Memory Function and obtain τ(k) as a function of Γ and  by fitting the function to the MD simulation data.

24. Normalized Memory Functions

25. =2.0 fitting parameters: ka wavenumber dependence of τ

26. Scaling of the relaxation time Einstein frequency melting temperature

27. Summary • Memory functions for Transverse Current Correlation Functions are calculated. • In the strongly coupling regime, non-exponential long time tail was observed in the memory function. • The relaxation time in Generalized Hydrodynamics has been estimated in the wide range of parameters. • The relaxation time takes the minimum value as a function of the system temperature (or Γ).