Plasma and Fusion Research

Volume 10, 3401024 (2015)

Regular Articles

Density Peaking by Parallel Flow Shear Driven Instability
Yusuke KOSUGA1,2), Sanae-I. ITOH2,3) and Kimitaka ITOH3,4)
Institute for Advanced Study, Kyushu University, Fukuoka 812-8581, Japan
Research Institute for Applied Mechanics, Kyushu University, Fukuoka 816-8580, Japan
Research Center for Plasma Turbulence, Kyushu University, Fukuoka 816-8580, Japan
National Institute for Fusion Science, Toki 509-5202, Japan
(Received 25 November 2014 / Accepted 16 February 2015 / Published 19 March 2015)


A theory to describe coupled dynamics of drift waves and D'Angelo modes is presented. The coupled dynamics is formulated by calculating fluctuation energy evolution. When drift waves dominate, turbulence production is due to release of free energy in density profile. Drift waves in turn exert Reynolds stress to drive secondary axial flows. When parallel flow shear is strong, D'Angelo modes dominate. Turbulent production occurs from release of free energy in parallel flow shear. D'Angelo modes can generate a secondary structure in density profile and can peak density profile. It is shown that when D'Angelo modes are unstable, they necessarily contribute to an inward particle flux, that compete against an outward, down-gradient flux. Net inward, up-gradient particle flux can result for strong flow shear, which can lead to density peaking in plasmas. Application to laboratory and astrophysical plasmas is discussed.


drift wave, D'Angelo mode, transport, up-gradient transport, residual stress

DOI: 10.1585/pfr.10.3401024


  • [1] B.B. Kadomtsev, Tokamak Plasma: A Complex Physical System (IoP publishing, Bristol and Philadelphia, 1992).
  • [2] K. Itoh, S.-I. Itoh and A. Fukuyama, Transport and Structural Formation in Plasmas (IoP publishing, Bristol and Philadelphia, 1999).
  • [3] P.H. Diamond, S.-I. Itoh, K. Itoh and T.S. Hahm, Plasma Phys. Control. Fusion 47, R35 (2005).
  • [4] B.B. Kadomtsev, Plasma Turbulence (Academic, New York, 1965).
  • [5] K. Ida and J.E. Rice Nucl. Fusion 54, 045001 (2014).
  • [6] P.H. Diamond, Y. Kosuga, Ö.D. Gürcan, C.J. McDevitt, T.S. Hahm, N. Fedorczak, J.E. Rice, W.X. Wang, S. Ku, J.M. Kwon, G. Dif-Pradalier, J. Abiteboul, L. Wang, W.H. Ko, Y.J. Shi, K. Ida, W. Solomon, H. Jhang, S.S. Kim, S. Yi, S.H. Ko, Y. Sarazin, R. Singh and C.S. Chang, Nucl. Fusion 53, 104019 (2013).
  • [7] W.E. Amatucci, J. Geophys. Res. 104, 14481 (1999).
  • [8] B. Albertazzi, A. Ciardi, M. Nakatsutsumi, T. Vinci, J. Beard, R. Bonito, J. Billette, M. Borghesi, Z. Burkley, S.N. Chen, T.E. Cowan, T. Herrmannsdörfer, D.P. Higginson, F. Kroll, S.A. Pikuz, K. Naughton, L. Romagnani, C. Riconda, G. Revet, R. Riquier, H.-P. Schlenvoigt, I.Yu. Skobelev, A.Ya. Faenov, A. Soloviev, M. Huarte-Espinosa, A. Frank, O. Portugall and H. Pepin, J. Fuchs, Science 346, 325 (2014).
  • [9] V.V. Garvrishchaka, S.B. Ganguli and G.I. Ganguli, Phys. Rev. Lett. 80, 728 (1998).
  • [10] E. Agrimson, N. D'Angelo and R.L. Merlino, Phys. Rev. Lett. 86, 5282 (2001).
  • [11] C. Teodorescu, E.W. Reynolds and M.E. Koepke, Phys. Rev. Lett. 88, 185003 (2002).
  • [12] T. Kaneko, H. Tsunoyama and R. Hatakeyama, Phys. Rev. Lett. 90, 125001 (2003).
  • [13] T. Kobayashi, “Parallel flow structure formation by turbulent momentum transport in linear magnetized plasmas,” The 4th Asia Pacific Transport Working Group International Conference, BO2 (2014).
  • [14] N. D'Angelo, Phys. Fluids 8, 1748 (1965).
  • [15] P.J. Cattor, M.N. Rosenbluth and C.S. Liu, Phys. Fluids 16, 1719 (1973).
  • [16] L. Bai, A. Fukuyama and M. Uchida, Phys. Plasmas 5, 989 (1998).
  • [17] L. Bai, A. Fukuyama and M. Uchida, Plasma Phys. Control. Fusion 40, 785 (1998).
  • [18] M. Uchida, S. Sen, A.Fukuyama and D.R. McCarthy, Phys. Plasmas 10, 4758 (2003).
  • [19] N. Mattor and P.H. Diamond, Phys. Fluids 31, 1180 (1988).
  • [20] M. Wakatani and A. Hasegawa, Phys. Fluids 27, 611 (1984).
  • [21] D.R. McCarthy, A.E. Booth, J.F. Drake and P.N. Guzdar, Phys. Plasmas 4, 300 (1997).
  • [22] Y. Kosuga, P.D. Diamond and Ö.D. Gürcan, Phys. Plasmas 17, 102313 (2010).
  • [23] J.G. Charney and P.G. Drazin, J. Geophys. Res. 66, 83 (1961).
  • [24] P.H. Diamond, Ö.D. Gürcan, T.S. Hahm, K. Miki, Y. Kosuga and X. Garbet, Plasma Phys. Control. Fusion 50, 124018 (2008).
  • [25] L. Wang, P.H. Diamond and T.S. Hahm, Plasma Phys. Control. Fusion 54, 095015 (2012).
  • [26] S. Inagaki, T. Tokuzawa, N. Tamura, S.-I. Itoh, T. Kobayashi, K. Ida, T. Shimozuma, S. Kubo, K. Tanaka, T. Ido, A. Shimizu, H. Tsuchiya, N. Kasuya, Y. Nagayama, K. Kawahata, S. Sudo, H. Yamada, A. Fujisawa, K. Itoh, and the LHD Experiment Group, Nucl. Fusion 53, 113006 (2013).
  • [27] S.-I. Itoh and K. Itoh, Sci. Rep. 2, 860 (2012).
  • [28] M. Lesur, P.H. Diamond and Y. Kosuga, Plasma Phys. Control. Fusion 56, 075005 (2014).
  • [29] T.H. Dupree, Phys. Rev. Lett. 25, 789 (1970).
  • [30] Y. Kosuga, P.H. Diamond, L. Wang, Ö.D. Gürcan and T.S. Hahm, Nucl. Fusion 53, 043008 (2013).
  • [31] Y. Kosuga, S.-I. Itoh, P.H. Diamond and K. Itoh, Plasma Phys. Control. Fusion 55, 125001 (2013).

This paper may be cited as follows:

Yusuke KOSUGA, Sanae-I. ITOH and Kimitaka ITOH, Plasma Fusion Res. 10, 3401024 (2015).