How much laser power can propagate through fusion plasma?

1. How much laser power can propagate through fusion plasma? Pavel Lushnikov1,2,3 and Harvey A. Rose3 1Landau Institute for Theoretical Physics 2Department of Mathematics, University of Notre Dame 3Theoretical Division, Los Alamos National Laboratory

2. Thermonuclear burn D+T=4He (3.5 Mev)+n (14.1 Mev) Required temperature:10 KeV D+ 3He =4He (3.7 Mev)+p (14.7 Mev) Required temperature:100 KeV 3He + 3He =2p+4He (12.9 MeV)

3. Indirect Drive Approach to Fusion Thermonuclear target

4. National Ignition Facility

5. National Ignition Facility Target Chamber

6. Target

7. 192 laser beams Laser pulse duration: 20 ns Total laser energy: 1.8 MJ Laser Power: 500 TW

9. Goal: propagation of laser light in plasma with minimal distortion to produce x-rays in exactly desired positions Difficulty : self-focusing of light

10. Singularity point - Nonlinear Schrödinger Eq. - amplitude of light Self-focusing of laser beam Nonlinear medium Laser beam z

11. Strong beam spray No spray Laser propagation in plasma

12. Experiments (Niemann, et al, 2005) at the Omega laser facility (Laboratory for Laser Energetics, Rochester) Beam spray No beam spray Cross section of laser beam intensity after propagation through plasma Dashed circles correspond to beam width for propagation in vacuum.

13. Plasma parameters at Rochester experiment Electron temperature Intensity threshold for beam spray Plasma Density Plasma composition: plastic

14. Comparison of theoretical prediction with experiment • dimensionless laser • intensity - Landau damping - optic f-number -effective plasma ionization number - number density for I-th ion species - ionization number for I-th ion species

15. National Ignition Facility for He-H plasma Thermal effects are negligible in contrast with Rochester experiments

16. Laser-plasma interactions - amplitude of light - low frequency plasma density fluctuation - Landau damping - speed of sound

17. Thermal fluctuations - thermal conductivity - electron oscillation speed - electron-ion mean free path -electron-ion collision rate

18. Thermal transport controls beam sprayas plasma ionization increases Non-local thermal transport model first verified* at Trident (Los Alamos)

19. Large correlation time limit - Nonlinear Schrödinger Eq. Small correlation time limit - light intensity is constant

20. Laser power and critical power • Power of each NIF’s 48 beams: P=8x1012 Watts • Critical power for self-focusing: Pcr=1.6x109 Watts • P/ Pcr =5000

21. Laser beam Plasma Lens Random phase plate - optic

22. Spatial and temporal incoherence of laser beam “Top hat” model of NIF optics: - optic

23. Idea of spatial and temporal incoherence of laser beam is to suppress self-focusing Intensity fluctuations fluctuate, in vacuum, on time scale Tc Laser propagation direction, z = intensity

24. 3D picture of intensity fluctuations

25. Fraction of power in speckles with intensity above critical per unit length For NIF: • amount of power lost for collapses per 1 cm • of plasma

26. Temporal incoherence of laser beam “Top hat” model of NIF optics: - optic

27. Duration of collapse event - acoustic transit time across speckle Condition for collapse to develop: • probability of collapse • decreases with

28. Existing experiments can not be explained based on collapses. Collective effects dominate. Beam spray No beam spray Cross section of laser beam intensity after propagation through plasma Dashed circles correspond to beam width for propagation in vacuum.

29. Unexpected analytical result: Collective Brillouin instability Even for very small correlation time, , there is forward stimulated Brillouin instability - light - ion acoustic wave

30. Numerical confirmation: Intensity fluctuations power spectrum1 k / km w / kmcs - acoustic resonance 1P. M. Lushnikov, and H.A. Rose, Phys. Rev. Lett. 92, p. 255003 (2004).

31. Instability for Random phase plate: Wigner distribution function:

32. Eq: in terms of Wigner distribution function: Boundary conditions:

33. Equation for density: Fourier transform: -closed Eq. for Wigner distribution function

34. Linearization: Dispersion relation: Top hat:

35. Instability growth rate:

36. Maximum of instability growth rate: - close to resonance

37. and depend only on :

38. Absolute versus convective instability: is real : convective instability only. There is no exponential growth of perturbations in time – only with z.

39. Density response function: - self energy Pole of corresponds to dispersion relation above. As

40. Collective stimulated Brillouin instability Versus instability of coherent beam: - coherent beam instability - incoherent beam instability

41. Instability criteria for collective Brillouin scattering

42. -convective growth rate perturbations ~

43. Instability is controlled by the single parameter: • dimensionless laser • intensity - Landau damping - optic f-number

44. Comparison of theoretical prediction with experiment Solid black curve – instability threshold -effective plasma ionization number - number density for I-th ion species - ionization number for I-th ion species

45. Second theoretical prediction: Threshold for laser intensity propagation does not depend on correlation time for

46. National Ignition Facility for He-H plasma Thermal effects are negligible in contrast with Rochester experiments NIF: By accident(?) the parameters of the original NIF design correspond to the instability threshold

47. Theoretical prediction for newly (2005) proposed NIF design of hohlraum with SiO2 foam: He is added to a background SiO2 plasma, in order to increase the value of nand hence the beam spray onset intensity.

48. Fluctuations are almost Gaussian below threshold:

49. And they have non-Gaussian tails well above FSBS instability threshold:

50. Below threshold a quasi-equilibrium is attained: