An Equation of the Quasilinear Theory with Wide Resonance Region
DOI:
https://doi.org/10.15407/ujpe63.3.232Abstract
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
<li>C.F. Kennel, F. Engelmann. Velocity space diffusion from weak plasma turbulence in a magnetic field. Phys. Fluids 9, 2377 (1966).
<a href="https://doi.org/10.1063/1.1761629">https://doi.org/10.1063/1.1761629</a>
</li>
<li>A.N. Kaufman. Quasilinear diffusion of an axisymmetric toroidal plasma. Phys. Fluids 15, 1063 (1972).
<a href="https://doi.org/10.1063/1.1694031">https://doi.org/10.1063/1.1694031</a>
</li>
<li>V.S. Belikov, Ya.I. Kolesnichenko. Derivation of the quasilinear theory equations for the axisymmetric toroidal systems. Plasma Phys. 24, 61 (1982).
<a href="https://doi.org/10.1088/0032-1028/24/1/006">https://doi.org/10.1088/0032-1028/24/1/006</a>
</li>
<li>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).
<a href="https://doi.org/10.1088/0741-3335/36/11/001">https://doi.org/10.1088/0741-3335/36/11/001</a>
</li>
<li>L.-G. Eriksson, P. Helander. Monte Carlo operators for orbit-averaged Fokker–Planck equations. Phys. Plasmas 1, 308 (1994).
<a href="https://doi.org/10.1063/1.870832">https://doi.org/10.1063/1.870832</a>
</li>
<li>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).
<a href="https://doi.org/10.1063/1.873195">https://doi.org/10.1063/1.873195</a>
</li>
<li>P.J. Catto, J. Lee, A.K. Ram. A quasilinear operator retaining magnetic drift effects in tokamak geometry. J. Plasma Phys. 83, 905830611 (2017).
<a href="https://doi.org/10.1017/S0022377817000903">https://doi.org/10.1017/S0022377817000903</a>
</li>
<li>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).
<a href="https://doi.org/10.1063/1.859951">https://doi.org/10.1063/1.859951</a>
</li>
<li>T.H. Stix. Fast-wave heating of a two-component plasma. Nucl. Fusion 15, 737 (1975).
<a href="https://doi.org/10.1088/0029-5515/15/5/003">https://doi.org/10.1088/0029-5515/15/5/003</a>
</li>
<li> T.H. Stix. Waves in Plasmas (Springer, 1992).
</li>
<li> 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).
<a href="https://doi.org/10.1103/PhysRevLett.88.105002">https://doi.org/10.1103/PhysRevLett.88.105002</a>
</li>
<li> A.A Galeev, R.Z. Sagdeev. Nonlinear plasma theory. In: Reviews of Plasma Physics, Vol. 7, edited by M.A. Leontovich (Consultants Bureau, 1979).
</li>
<li> 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).
<a href="https://doi.org/10.1088/1741-4326/aa6871">https://doi.org/10.1088/1741-4326/aa6871</a>
</li>
<li> Ya.I. Kolesnichenko, R.B. White, Yu.V. Yakovenko. Mechanisms of stochastic diffusion of energetic ions in spherical tori. Phys. Plasmas 9, 2639 (2002).
<a href="https://doi.org/10.1063/1.1475685">https://doi.org/10.1063/1.1475685</a>
</li>
<li> A.I. Akhiezer, I.A. Akhiezer, R.V. Polovin, A.G. Sitenko, K.N. Stepanov. Plasma Electrodynamics, Vol. 2 (Pergamon Press, 1975).
</li></ol>
Downloads
Published
How to Cite
Issue
Section
License
Copyright Agreement
License to Publish the Paper
Kyiv, Ukraine
The corresponding author and the co-authors (hereon referred to as the Author(s)) of the paper being submitted to the Ukrainian Journal of Physics (hereon referred to as the Paper) from one side and the Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, represented by its Director (hereon referred to as the Publisher) from the other side have come to the following Agreement:
1. Subject of the Agreement.
The Author(s) grant(s) the Publisher the free non-exclusive right to use the Paper (of scientific, technical, or any other content) according to the terms and conditions defined by this Agreement.
2. The ways of using the Paper.
2.1. The Author(s) grant(s) the Publisher the right to use the Paper as follows.
2.1.1. To publish the Paper in the Ukrainian Journal of Physics (hereon referred to as the Journal) in original language and translated into English (the copy of the Paper approved by the Author(s) and the Publisher and accepted for publication is a constitutive part of this License Agreement).
2.1.2. To edit, adapt, and correct the Paper by approval of the Author(s).
2.1.3. To translate the Paper in the case when the Paper is written in a language different from that adopted in the Journal.
2.2. If the Author(s) has(ve) an intent to use the Paper in any other way, e.g., to publish the translated version of the Paper (except for the case defined by Section 2.1.3 of this Agreement), to post the full Paper or any its part on the web, to publish the Paper in any other editions, to include the Paper or any its part in other collections, anthologies, encyclopaedias, etc., the Author(s) should get a written permission from the Publisher.
3. License territory.
The Author(s) grant(s) the Publisher the right to use the Paper as regulated by sections 2.1.1–2.1.3 of this Agreement on the territory of Ukraine and to distribute the Paper as indispensable part of the Journal on the territory of Ukraine and other countries by means of subscription, sales, and free transfer to a third party.
4. Duration.
4.1. This Agreement is valid starting from the date of signature and acts for the entire period of the existence of the Journal.
5. Loyalty.
5.1. The Author(s) warrant(s) the Publisher that:
– he/she is the true author (co-author) of the Paper;
– copyright on the Paper was not transferred to any other party;
– the Paper has never been published before and will not be published in any other media before it is published by the Publisher (see also section 2.2);
– the Author(s) do(es) not violate any intellectual property right of other parties. If the Paper includes some materials of other parties, except for citations whose length is regulated by the scientific, informational, or critical character of the Paper, the use of such materials is in compliance with the regulations of the international law and the law of Ukraine.
6. Requisites and signatures of the Parties.
Publisher: Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine.
Address: Ukraine, Kyiv, Metrolohichna Str. 14-b.
Author: Electronic signature on behalf and with endorsement of all co-authors.
.png){kind=small}
