Skip to main content
Log in

A description on plasma background effect in growth rate of THz waves in a metallic cylindrical waveguide, including a dielectric tube and two current sources

  • Original Paper
  • Published:
Indian Journal of Physics Aims and scope Submit manuscript

Abstract

The propagation of slow waves in a dielectric tube surrounded by a long cylindrical metallic waveguide is investigated. The dielectric tube located in a background region of plasma under two different states A and B. In the A-state the dielectric tube hollow filled with the plasma and in the B-state the outer surface of dielectric tube has been covered by the plasma layer. There are two relativistic electron beams with opposite velocities injected in the waveguide as the energy sources. Using the fluid theory for the plasmas, the Cherenkov instability in the mentioned waveguide will be analyzed. The dispersion relations of E-mode waves for the states AB have been obtained. The time growth rate of surface waves are compared with each other for two cases A and B. The effect of plasma region on time growth rate of the waves, will be investigated. In all cases it will be shown, while an electron beam is responsible for instability, another electron beam plays a stabilizing role.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  1. V O Girka and S Yu Puzyrkov Plasma Phys. Rep. 28 351 (2002)

    Article  ADS  Google Scholar 

  2. B Jazi, M Nejati and A Salehi Int. J. Infrared Millim. Waves 27 1469 (2006)

    Article  ADS  Google Scholar 

  3. A V Gaponov-Grekhov and V L Granatstein Artech House, Boston (1994)

  4. B Jazi, and H Mehdiyan Plasma Phys. Control. Fusion 43 (2001)

  5. B Shokri and B Jazi Phys. Lett. A 336 47789 (2005)

    Article  Google Scholar 

  6. M V Kuzelev and A A Rukhadze Fiz. Plazmy 26 231 (2000)

    Google Scholar 

  7. M V Kuzelev and A A Rukhadze Plasma Phys. Rep. 26 231 (2000)

    Article  ADS  Google Scholar 

  8. Z Hajijamali-Arani and B Jazi Eur. Phys. J. Plus 132 474 (2017)

    Article  Google Scholar 

  9. P S Strelkov and D K Ul’yanov Fiz. Plazmy 26 329 (2000)

    Google Scholar 

  10. P S Strelkov and D K Ul’yanov Plasma Phys. Rep. 26 303 (2000)

    Article  ADS  Google Scholar 

  11. I L Bogdankevich, D M Grishin, A V Gunin, I E Ivanov, S D Korovin, O T Loza, G A Mesyats, D A Pavlov, V V Rostov, P S Strelkov, and D K Ul’yanov Plasma Phys. Rep. 34 10 (2008)

    Article  Google Scholar 

  12. H Saito and J S Wurtele Phys. Fluids 30 2209 (1987)

    Article  ADS  Google Scholar 

  13. I H Kho, A I Lin, and L Chen Phys. Fluids 31 3120 (1988)

    Article  ADS  Google Scholar 

  14. R C Davidson and K T Tsang Laser Part. Beams 6 661 (1988)

    Article  ADS  Google Scholar 

  15. Y Y Lau, in Proceedings of the Symposium on Non-Neutral Plasma Physics Washington p 210 (1988)

  16. M V Kuzelev and A A Rukhadze Electrodynamics of Dense Electron Beams in Plasma Russian Nauka, Moscow, (1990)

  17. B Jazi, B Shokri, H Arbab Plasma phys. and controlled fusion 48 1105 (2006)

    Article  ADS  Google Scholar 

  18. A S Shlapakovski and M Yu Krasnitskiy Plasma Phys. Rep. 34 1 (2008)

    Article  ADS  Google Scholar 

  19. B Shokri, B Jazi Phys. Plasmas 12 033104 (2005)

    Article  ADS  Google Scholar 

  20. Z Rahmani, B Jazi and E Heidari-Semiromi Phys. Plasmas 21 092122 (2014)

    Article  ADS  Google Scholar 

  21. K Felch Ph.D. disseration (Plasma Laboratory Department of Physics and Astronomy Dartmouth College, Hanover, NH) (1980)

  22. J Zheng, C X Yu, Z J Zheng and K A Tanaka Phys. Plasmas 12 093105 (2005)

    Article  ADS  Google Scholar 

  23. D Kamiyama, M Takano, T Nagashima, D Barada, Y J Gu, X F Li, Q Kong, P X Wang and S Kawata J. Phys.: Conf. Ser. 717 012065 (2016)

    Google Scholar 

  24. Sh M Khalil, N M Mousa Theoretical and Applied Physics 8 111 (2014)

    Article  Google Scholar 

  25. B Maraghechi and B Maraghechi Plasma Fusion Res. 8 1534 (2009)

  26. Y Carmel, K Minami, W Lou, R A Kehs, W W Destler, V L Granat- stein, D K Abe, and J Rodgers IEEE Trans. Plasma Sci. 18 497 (1990)

    Article  ADS  Google Scholar 

  27. J Q Wu Phys. Plasmas 11 4 (1997)

    Google Scholar 

  28. M V KuzelevO, T Loza, A A Rukhadze, P S Strelkov, A G Shkvarunets Fiz. Plazmy 27 710 (2001)

    Google Scholar 

  29. M V KuzelevO, T Loza, A A Rukhadze, P S Strelkov, A G Shkvarunets Plasma Phys. Rep. 27 669 (2001)

    Article  ADS  Google Scholar 

  30. B Jazi, A Abdoli-Arani, Z Rahmani, M Monemzadeh, R Ramezani-Arani Waves in Random and Complex Media (2010)

  31. H K Malik Phys. Let. A 379 2826 (2015)

    Article  ADS  Google Scholar 

  32. D Singh and H K Malik Plasma Sources Sci. Technol. 24 045001 (2015)

    Article  ADS  Google Scholar 

  33. D Singh and H K Malik Phys. Plasmas 21 083105 (2014)

    Article  ADS  Google Scholar 

  34. A K Malik and H K Malik IEEE J. Quantum Electronics 49 232 (2013)

    Article  ADS  Google Scholar 

  35. H K Malik and A K Malik Europhysics Let. 100 45001 (2012)

    Article  ADS  Google Scholar 

  36. H K Malik and A K Malik Appl. Phys. Lett. 99 251101 (2011)

    Article  ADS  Google Scholar 

  37. A K Malik, H K Malik, and U Stroth Appl. Phys. Lett. 99 071107 (2011)

    Article  ADS  Google Scholar 

  38. A K Malik, H K Malik, and S J. Appl. Phys. 107 113105 (2010)

    Article  ADS  Google Scholar 

  39. A K Malik, H K Malik, and U Stroth Phys. Rev. E 85 016401 (2012)

    Article  ADS  Google Scholar 

  40. H K Malik Europhysics Letters 106 55002 (2014)

    Article  ADS  Google Scholar 

  41. A F Alexandrov, L S Bogdankevich, A A Rukhadze Principles of Plasma Electrodynamics. Springer, Heidelberg (1984)

    Book  Google Scholar 

  42. L D Landau and E M Lifshitz Theoretical Physics: Electro- dynamics of Continuous Media Pergamon Press, Oxford (1960)

    Google Scholar 

  43. S R Rengarajan and J E Lewis Microwave Theory Tech. 28 1089 (1980)

    Article  Google Scholar 

  44. R C Davidson An Introduction to the Nonneutral Plasmas Addison- Wesley, Reading, MA, (1990)

    Google Scholar 

  45. N A Krall and A W Trivelpiece Principles of Plasma Physics McGraw-Hill New York (1973)

    Google Scholar 

  46. H P Freund and T M Abu-Elfadl IEEE Trans. Plasma Sci. 32 1015-1027 (2004)

    Article  Google Scholar 

  47. F F Chen Introduction to Plasma Physics and Controlled Fusion Springer US (1984)

    Book  Google Scholar 

  48. B Jazi, M Nejati and A Salehi Int. J. Infrared Millim. Waves 27 146995 (2006)

    Google Scholar 

  49. J E Walsh, T C Marshall, and S P Schlesinger Phys. Fluids 20 709 (1977)

    Article  ADS  Google Scholar 

  50. M Nejati, C Javaherian, B Shokri and B Jazi Phys. of Plasmas 16 022108 (2009)

    Article  ADS  Google Scholar 

  51. A Abdoli-Arani and B Jazi Waves Random Complex Media 23 2 (2013)

    Article  Google Scholar 

  52. Y Ahmadizadeh, B Jazi, and A Abdoli-Arani IEEE Trans. Plasma Sci. 42 7 (2014)

    Article  Google Scholar 

  53. X Tang, Z Yu, X Tu, J Chen, A Argyros, B T Kuhlmey, and Y Shi Opt. Express 23 22587 (2015)

    Article  ADS  Google Scholar 

  54. B Jazi, M Nejati, and B Shokri Phys. Lett. A 370 319 (2007)

  55. A S Shlapakovski and E Schamiloglu Plasma Electronics 30 7 (2004)

    Google Scholar 

  56. W Jianqiang Int. J. of Infrared and Millimeter Waves 24 12 (2003)

    Article  Google Scholar 

  57. Z Hajijamali-Arani and B Jazi Eur. Phys. J. Plus 132 151 (2017)

    Article  Google Scholar 

  58. K L Felch, K O Busby, R W Layman, D Kapilow, and J E Wallsh Appl. Phys. Lett. 38 601 (1981)

    Article  ADS  Google Scholar 

  59. B Shokri, H Ghomi, and H Latifi Phys. Plasmas 7 2671 (2000)

    Article  ADS  Google Scholar 

  60. M Birau, M A Krasilnikov, M V Kuzelev, and A A Rukhadze Phys. Usp. 40 975 (1997)

    Article  ADS  Google Scholar 

  61. A F Aleksandrov, M V Kuzelev, and A N Khalilov Zh. Eksp. Teor. Fiz. 93 1714 (1987)

    ADS  Google Scholar 

  62. J Zheng, C X Yu, Z J Zheng, and K A Tanaka Phys. Plasmas 12 093105 (2005)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Z. Hajijamali-Arani.

Appendix

Appendix

1.1 Derivation of the perturbed relativistic equation of the motion, and the continuity equation for the beam electrons presented in Sect. 2

The equations to describe the system are the equation of motion and the continuity equation

$$\begin{aligned} \frac{d (\gamma _{0} \overrightarrow{V})}{dt}= & {} \frac{-e}{ m_{0}}\left[ (I-\beta _{0}^{2}\hat{{z}}\hat{{z}})\overrightarrow{E} + \frac{\overrightarrow{V}}{c}\times \overrightarrow{B}\right] \end{aligned}$$
(24)
$$\begin{aligned} \frac{\partial n}{\partial t}+\overrightarrow{\nabla }\cdot (n\overrightarrow{V})=\, & {} 0 \end{aligned}$$
(25)

where n and V are the density and the velocity of particles (electrons of plasma and beam), and all other terms have their usual meaning. The interaction of the electromagnetic waves with the plasma will disturb the equilibrium density and velocity of the particles and electromagnetic fields. These disturbtions will be analyzed by considering the perturbation variables n, V, E and B. We can define them as follows:

$$\begin{aligned} n=n_{0}+\delta n,\quad \overrightarrow{V}=\overrightarrow{V}_{0}+\overrightarrow{\delta V},\quad \overrightarrow{E}=\overrightarrow{E}_{0}+\overrightarrow{\delta E},\quad \overrightarrow{B}=\overrightarrow{B}_{0}+\overrightarrow{\delta B} \end{aligned}$$
(26)

where in the system of equations, the small deviations from the equilibrium state is considered as (\(\delta n\ll n_{0}\), \(\mid \overrightarrow{\delta V}\mid \ll \mid \overrightarrow{ V}_{0} \mid\), \(\mid \overrightarrow{\delta E}\mid \ll \mid \overrightarrow{ E}_{0} \mid\), \(\mid \overrightarrow{\delta B}\mid \ll \mid \overrightarrow{ B}_{0} \mid\)). Also, all of the perturbations are described as \(\delta \psi = \delta \psi _{0}e^{-i(\omega t-\beta z)}\). Using (24)-(26), we can derive the expressions for Eqs. (1) and (2). Form Eqs.(1) and (2), the perturbed density and velocity of electron beam and plasma layer will have the form:

$$\begin{aligned} {\delta V}_{z\pm }= \frac{-ie}{m_{0}\gamma _{0}^{3}(\omega \mp \beta V_{0})^2}\delta E_{z}, \quad \delta n_{\pm }= \frac{-ie\beta n_{0\pm }}{m_{0}\gamma _{0}^{3}(\omega \mp \beta V_{0})^2}\delta E_{z} \end{aligned}$$
(27)
$$\begin{aligned} {\delta V}_{zp}= \frac{-ie}{m_{0}\gamma _{0}^{3}\omega ^2}\delta E_{z}, \quad \delta n_{p}= \frac{-ie\beta n_{0p}}{m_{0}\gamma _{0}^{3}\omega ^2}\delta E_{z} \end{aligned}$$
(28)

Now, we can derive the expressions for the charge and current density. The charge and current density \(J,\rho\) are defined through the electron plasma and beam quantities as:

$$\begin{aligned} \overrightarrow{J}= -en\overrightarrow{V}, \quad \rho = -en \end{aligned}$$
(29)

Eqs. (26)–(29) give us Eqs. (3) and (4).

1.2 Derivation of the solutions to the wave equations presented in Sect. 2

Using Eqs. (3)–(8), the solutions of the wave equation for all of the regions of given cylinder waveguide can be presented. For example, the wave equation in the core region with plasma column in the model A is

$$\begin{aligned} \left( \frac{1}{r}\frac{\partial }{\partial r}r\frac{\partial }{\partial r}+\frac{\partial ^{2}}{\partial z^{2}}\right) \delta E_{z} -4\pi \frac{\partial }{\partial z}(\delta \rho _{p}+\delta \rho _{b+}) +\frac{\omega ^{2}}{c^{2}}\delta E_{z} =-\frac{4\pi i\omega }{c^{2}}(\delta J_{zp}+\delta J_{zb+}). \end{aligned}$$
(30)

Substituting Eqs. (3)-(4) and using linear approximation of monochromatic plane waves for all of the perturbed quantities, one can derive

$$\begin{aligned} \frac{1}{r}\frac{\partial }{\partial r}r\frac{\partial }{\partial r}\delta E_{z} +(\frac{\omega ^{2}}{c^{2}}-\beta ^{2})\delta E_{z} +\left( \frac{\omega _{b_{+}}^{2}}{\gamma _{0}^2(\omega -\beta V_{0})^2}+\frac{\omega _{p}^{2}}{\omega ^2}\right) \left( \beta ^2-\frac{\omega ^2}{c^2}\right) \delta E_{z} =0. \end{aligned}$$
(31)

By introducing the parameter \(\Gamma ^{2}_{b+}(1,\omega _{b_{+}},\omega _{p})\) (like Eq. (8)), the z-component of the perturbed electric field \(\delta E_{z}\) is obtained as Eq. (8). It is obvious that the solutions of Eq. (8) are the modified Bessel functions of the first and second kinds. Regarding the modified Bessel function of the second kind has a singularity at the origin \((r = 0)\), the modified Bessel function of the first kind is acceptable for this region as Eq. (10). The solving method in other regions is the same.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hajijamali-Arani, Z., Jazi, B. A description on plasma background effect in growth rate of THz waves in a metallic cylindrical waveguide, including a dielectric tube and two current sources. Indian J Phys 92, 1307–1318 (2018). https://doi.org/10.1007/s12648-018-1198-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12648-018-1198-0

Keywords

PACS Nos.

Navigation