An Equation of the Quasilinear Theory with Wide Resonance Region

  • Ya. I. Kolesnichenko Institute for Nuclear Research, Nat. Acad. Sci. of Ukraine
  • V. V. Lutsenko Institute for Nuclear Research, Nat. Acad. Sci. of Ukraine
  • T. S. Rudenko Institute for Nuclear Research, Nat. Acad. Sci. of Ukraine

Abstract

An equation of the quasilinear theory is derived. It is based on the same assumptions as the well-known equation in [1]. However, it has another form of the quasilinear operator, which does not contain the longitudinal wavenumber. Due to this, characteristics of the derived equation determine the routes of a quasilinear evolution of the particle distribution function, even when the resonance region determined by the spectrum of longitudinal wavenumbers is wide. It is demonstrated that during the ion acceleration by the ion cyclotron resonant heating, (i) the change of the longitudinal ion energy can be considerable and (ii) the increase of the particle energy may well exceed the increase described by characteristics of the Kennel–Engelmann equation (which are shown, in particular, in [10]), because these characteristics represent the ways of the quasilinear diffusion only when the resonance region is narrow.

References


  1. C.F. Kennel, F. Engelmann. Velocity space diffusion from weak plasma turbulence in a magnetic field. Phys. Fluids 9, 2377 (1966).
    https://doi.org/10.1063/1.1761629

  2. A.N. Kaufman. Quasilinear diffusion of an axisymmetric toroidal plasma. Phys. Fluids 15, 1063 (1972).
    https://doi.org/10.1063/1.1694031

  3. V.S. Belikov, Ya.I. Kolesnichenko. Derivation of the quasilinear theory equations for the axisymmetric toroidal systems. Plasma Phys. 24, 61 (1982).
    https://doi.org/10.1088/0032-1028/24/1/006

  4. V.S. Belikov, Ya.I. Kolesnichenko. Quasilinear theory for a tokamak plasma in the presence of cyclotron resonance. Plasma Phys. Control. Fusion 36, 1703 (1994).
    https://doi.org/10.1088/0741-3335/36/11/001

  5. L.-G. Eriksson, P. Helander. Monte Carlo operators for orbit-averaged Fokker–Planck equations. Phys. Plasmas 1, 308 (1994).
    https://doi.org/10.1063/1.870832

  6. L.-G. Eriksson, M.J. Mantsinen, T. Hellsten, J. Carlsson. On the orbit-averaged Monte Carlo operator describing ion cyclotron resonance frequency wave–particle interaction in a tokamak. Phys. Plasmas 6, 513 (1999).
    https://doi.org/10.1063/1.873195

  7. P.J. Catto, J. Lee, A.K. Ram. A quasilinear operator retaining magnetic drift effects in tokamak geometry. J. Plasma Phys. 83, 905830611 (2017).
    https://doi.org/10.1017/S0022377817000903

  8. A. B` ecoulet, D.J. Gambier, A. Samain. Hamiltonian theory of the ion cyclotron minority heating dynamics in tokamak plasmas. Phys. Fluids B 3, No. 1, 137 (1991).
    https://doi.org/10.1063/1.859951

  9. T.H. Stix. Fast-wave heating of a two-component plasma. Nucl. Fusion 15, 737 (1975).
    https://doi.org/10.1088/0029-5515/15/5/003

  10. T.H. Stix. Waves in Plasmas (Springer, 1992).

  11. M.J. Mantsinen et al. Alpha-tail production with ion-cyclotron-resonance heating of 4He-beam ions in JET plasmas. Phys. Rev. Lett. 88, 105002 (2002).
    https://doi.org/10.1103/PhysRevLett.88.105002

  12. A.A Galeev, R.Z. Sagdeev. Nonlinear plasma theory. In: Reviews of Plasma Physics, Vol. 7, edited by M.A. Leontovich (Consultants Bureau, 1979).

  13. Ya.I. Kolesnichenko, V.V Lutsenko, T.S. Rudenko, H. Helander. Ways to improve the confinement of fast ions in stellarators by RF waves: General analysis and application to Wendelstein 7-X. Nucl. Fusion 57, 66004 (2017).
    https://doi.org/10.1088/1741-4326/aa6871

  14. Ya.I. Kolesnichenko, R.B. White, Yu.V. Yakovenko. Mechanisms of stochastic diffusion of energetic ions in spherical tori. Phys. Plasmas 9, 2639 (2002).
    https://doi.org/10.1063/1.1475685

  15. A.I. Akhiezer, I.A. Akhiezer, R.V. Polovin, A.G. Sitenko, K.N. Stepanov. Plasma Electrodynamics, Vol. 2 (Pergamon Press, 1975).
Published
2018-04-20
How to Cite
Kolesnichenko, Y., Lutsenko, V., & Rudenko, T. (2018). An Equation of the Quasilinear Theory with Wide Resonance Region. Ukrainian Journal of Physics, 63(3), 232. https://doi.org/10.15407/ujpe63.3.232
Section
Plasma physics