1. Nano-sized electromagnetic source on the principles of Free Electron Lasers K.G.Batrakov, P.P.Kuzhir S.A.Maksimenko

2. The main principle of Free Electron Laser (FEL) operation The work produced by electromagnetic wave on the electron: Electron trajectory Electromagnetic field

3. Cherenkov synchronism condition : Slowing down systems (TWT, BWO, Cherenkov Lasers: resonators and waveguides change electromagnetic wave properties and decrease it phase velocity, Destructive interference diminishes A. So, bunching of electron beam is necessary. Structure factor:

4. Pump wave : Trajectory perturbation by pump wave Induced by the pump wave perturbation of velocity

5. CARBON NANOTUBE – quasi-one-dimensional carbon macromolecula Graphene crystalline lattice SWCNT (m,n) R c =ma 1 +na 2 (m,0) for zigzag CNT (m,m) for armchair CNT

6. Unrolled circumferential vectors c for a (4,4) armchair nanotube (black arrow), a (4,0) zigzag nanotube (blue arrow) and a chiral (4,2) nanotube (red arrow) are shown on a graphene plane. a1 and a2 are the unit cell vectors of graphene. The chiral angle and the translational periodicity vector ` of the (4,2) nanotube (green arrow) are also shown. Dashed lines indicate the area spanned by c and ` which corresponds to the unrolled unit cell of the (4,2) nanotube.

7. Structural parameters and isogonal point group of nanotubes. d is the tube diameter, n is the greatest common divisor of (n1,n2), and q is the number of carbonhexagons (2 C atoms) per unit cell. a0 is the in-plane lattice constant of graphite.

8. (8,0), (8,2), (8,4), and (8,8) nanotubes with 32, 56, 112, and 32 atoms in the unit cell (indicated in black), respectively.

9. Some exceptional properties of nanotubes and conventional materials for comparison.(P. G. Collins and P. Avouris, \Nanotubes for electronics", Sci. Am. 283, 62 (2000))

10. Nanoelectromagnetics Complex-valued slow-wave coefficient  for a polar-symmetric surface wave 1 THz 100 THz b=0.142 nm is the C-C bond length |Im(  )| << Re(  ) Dispersionless surface wave nanowaveguide in the IR range

11. Light emission in CNTs ELECTRIC-FIELD-INDUCED HEATING OF THE ELECTRON GAS O. Kibis, M. Portnoi, Carbon nanotubes: A new type of emitter in the terahertz range, Technical Physics Letters. V.31. p. 671 (2005)Technical Physics Letters IMPACT IONIZATION J. Chen, V. Perebeinos, M. Freitag, J. Tsang, Q. Fu, Jie Liu, Ph. Avouris, Bright Infrared Emission from Electrically Induced Excitons in Carbon Nanotubes, Science 2005, Vol. 310. no. 5751, pp. 1171 - 1174 CHERENKOV RADIATION MECHANISM K. Batrakov, P. Kuzhir, S. Maksimenko, Radiative instability of electron beams in carbon nanotubes, Proceedings of SPIE, V. 6328 “Nanomodeling II”, p. 63280Z (2006)

12. Interaction between electron beam and produced electromagnetic wave leads to electron beam modulation. This process can be described by self-consistent system for electromagnetic field: and for electrons : Properties of nanotubes useful for generation by electron beam 1)Large length of electrons ballistic transport (~1 – 10 micron); 2) Large current density (to 10 10 A/cm 2 ) [ M. Radosavljevi´c, J. Lefebvre, and A. T. Johnson, “High-field electrical transport and breakdown in bundles of single-wall carbon nanotubes”, Phys. Rev. B 64, 241 307® (2001), S.-B. Lee, K. B. K. Teo, L. A. W. Robinson, A. S. Teh, M. Chhowalla, et al., J. Vac. Sci. Technol. B 20, 2773 (2002)].

13. Dispersion equation Emission term Absorption term electron group velocity in nanotube

14. If width of emission line exceeds the magnitude of quantum recoil, then traditional form of second-order Cherenkov resonance is realized : Otherwise, quantum recoil contributes to resonance condition.

15. Gain is extremely large as compared with the gain per unit length for macro- devices Boundary conditions on nanotube tips and dispersion equations give threshold condition and instability increment Threshold current and instability increment of generation

16. Radiation generation is already possible at the current stage of nanotechnologies development.

17. Method for the instability control  The points of maximum group velocity and respectively low excitation energy can be advantageous for lasing.  In the point of group velocity extremum the negative influence of the beam energy spread is smaller, and therefore more electrons interact with the wave: the radiation effectiveness can be increased.  It is also possible to intensify the effect of radiation instability in nanotube due to the generation in the region of small effective mass of quasiparticle.

18. Compensation of electron beam spread Extremum of group velocity Dispersion equation Then, expansion near this point gives So, negative influence of beam spread can be reduced.

19. CONCLUSION: What has been done to the moment? Thus, the generation of the stimulated radiation by electron beams in nanotubes is predicted. The dispersion equations of the electron beam instability and threshold conditions for stimulated radiation are derived and studied. The analysis of the threshold conditions shows realizability of the CNT-based molecular TWT at the current CNT technology development

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21. TU/e Eindhoven J.Havercort Usikov Institute For Radiophysics And Electronics Ukraine,Kharkov A.Lakhtakia J. Herrmann, I.Hertel A.Hoffmann, D.Bimberg O.Yevtushenko N Ledentsov I Krestnikov Universitaires Notre-Dame de la Paix NAMUR, BELGIUM Ph. Lambin Boreskov Institute of Catalysis SB RAS Novosibirsk Ecole Polytechnique Federale de Lausanne Switzerland L. Forro Chalmers University of Technology, Sweden, E. Campbell V Kuznetsov LABORATOIRE DE PHYSIQUE DE LA MATIERE CONDENSEE G. BOSSIS Laboratory National des Champs Magnetiques Pulses J. Galibert Collaboration of the Institute of Nuclear Problems of Belarusian State University in the field of NANOSCIENCE etceteras