1. Workshop on Fundamental Physics
RAL, 3rd – 5th May 2006
An hypothesis for the collective scattering of
gravitational radiation by massive particles
Brian McNeil
Department of Physics, University of Strathclyde

2. Outline Collective radiation/matter interactions
Free Electron Lasers (relativistic scattering)
System of 2-level atoms
Classical dielectric particles
Free carrier plasma in semiconductor
Collective gravitational wave scattering?

3. The FEL interaction (Collective Thompson Scattering)

4. Undulator or ‘Wiggler’
Nu periods

5. Resonant emission - constructive interference

6. The electron-radiation interaction
The Lorentz force (electron dynamics)
Maxwell wave equation (radiation evolution
– no space charge or dielectrics)
Both equations must be solved together simultaneously
(self-consistently) to fully describe the FEL interaction

7. How the electron is effected by the resonant radiation
The Lorentz Force Equation:
Can calculate
Hendrick Antoon Lorentz
The rate of change of electron energy

8. Resonant emission – electron energy change
is +ve
is +ve
is +ve
Energy of electron changes ‘slowly’ when interacting with a resonant radiation field. e- e- e- u

9. Resonant emission – electron energy change
Rate of electron energy change is ‘slow’ but changes periodically with respect to the radiation phase
For an electron with a different phase with respect to radiation field:
is +ve e-
is -ve e- u

10. r is +ve Resonant emission – electron bunching
Electrons bunch at resonant radiation wavelength – coherent process
Gain energy
Lose energy
is +ve
Axial electron velocity r

11. Bunched electrons exchange energy coherently with radiation

12. Basic FEL mechanism Radiation field bunches electrons
Bunched electrons drive radiation

13. F 1) e- begin to bunch about θ=3π/2
1) e- begin to bunch about θ=3π/2
2) Radiation phase driven and shifts
3) Radiation amplitude is driven

15. Collective Atomic Recoil Laser

16. Collective Atomic Recoil Laser
Pump radiation
System of 2-level atoms
Scattered radiation

17. Collective Atomic Recoil Laser
Radiation pressure term
In absence of radiation pressure - formally identical to FEL equations

18. Collective scattering in a BEC
Individual Particle equations of motion replaced by Schrödinger equation
See talk be Gordon Robb on Friday: “Collective recoil-induced instabilities”

19. Collective Rayleigh Scattering

20. Collective Rayleigh scatteringx
- Force per unit particle volume

21. Collective Rayleigh scattering
These are the FEL equations when radn. pressure Γ = 0

22. Collective Rayleigh scattering
Experimental evidence of classical collective scattering

23. Collective Free Carrier Scattering

24. Collective free carrier scattering

25. Collective electromagnetic scattering
Requires
Only one transverse wave of wavelength λ
System of ‘un-prepared’ particles of size d<<λ
Particle-radiation transverse coupling ( j, ∂P/ ∂t )
Results in
Exponential instability with…
Bunching of particles on λ-scale
Coherent back-scattering of incident field
Depletion of the incident field for EM pumps

26. Collective gravitational wave scattering?

27. Collective gravitational wave scattering?
Ellipsoid - tidal forces

28. Collective gravitational wave scattering?
Gravitational wave induces transverse quadrupole ‘current’ in a particle

29. Collective gravitational wave scattering?
Naïve first thoughts:
1) Strong pump drives quadrupole moments in particles => ∂P/ ∂t
2) Interaction of pump induced quadrupole mass ‘currents’ with weak counter-propagating wave sets up a ponderomotive potential
3) Particles begin to bunch in ponderomotive potential driving the phase and amplitude of counter-propagating wave

30. Collective gravitational wave scattering?
How to model?
Wave equation – Einstein equations in weak field
Continuum
Solution if motion of matter is known – note quadrupole nature of source
If the massive particles are treated as point particles then get another result. We want intermediate case: individual particles each acting as an independent quadrupole source.
See:
Peter Szekeres, Annals of Physics, 64, 599 (1971)
G Montani, R Ruffini, R Zalaletdinov, arXiv:gr-qc/ v1 (2003)

31. Collective gravitational wave scattering?
Gravitoelectromagnetism [1,2]:
[1] S J Clark and R W Tucker, Class. Quantum Grav. 17 (2000) 4125
[2] Bahram Mashhoon, arXiv:gr-qc/ v1 8 Nov 2003

32. Collective gravitational wave scattering?
Other interesting factors
Scattering from particles’ Newtonian gravitational potential Φ [1]
Wave-wave interaction: self-phase modulation and multiple-wave non-linear interactions [2]
[1] PC Peters, Phys Rev D, 9, 2207 (1974)
[2] JT Mendonça, V Cardoso, Phys Rev D, 66, (2002)