Instability of Electron Bernstein Mode in Presence of Drift Wave Turbulence Associated with Density and Temperature Grad
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ORIGINAL RESEARCH
Instability of Electron Bernstein Mode in Presence of Drift Wave Turbulence Associated with Density and Temperature Gradients P. Senapati1 • P. N. Deka2 Accepted: 8 November 2020 Ó Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract The instability of electron Bernstein mode has been investigated in presence of drifts due to density and temperature gradient. Nonlinear resonant interaction of drift mode is considered for the investigation of the instability. We have considered a uniform force field F which is the cause of F B drift due to temperature perpendicular to the magnetic field B in the system. Using Vlasov-Poissons system of equations and Maxwellian type distribution function of particles that involve the effect of F associated with density and temperature gradient. We have derived a nonlinear dispersion relation for electron Bernstein mode and then estimated its growth rate. We have analyzed various aspects of the growth rate of electron Bernstein mode associated with the variation of the gradients of the density and temperature by using experimental data in tokamak plasmas. Keywords Electron Bernstein mode Density and temperature gradients Wave–particle interaction Particle drift velocity
Introduction Bernstein mode [1] waves are frequently observed in various regions of the earth’s magnetosphere and laboratory plasmas. Bernstein mode waves are electrostatics waves in magnetized plasma which propagate perpendicularly to the confining magnetic field [2–4]. Stix [2] identified that there existed two kinds of Bernstein waves, one was electron mode and the other was ion mode with characteristics frequencies to the electron cyclotron and ion cyclotron frequencies respectively and with their corresponding harmonics. The electron Bernstein modes were observed by spacecraft in the earth’s magnetosphere earlier by Kurth et al. [3] and followed by Stix [2]. Recently, electron Bernstein modes are observed in the earth’s
& P. Senapati [email protected] P. N. Deka [email protected] 1
Department of Mathematics, Nowgong College, Nagaon, Assam 782001, India
2
Department of Mathematics, Dibrugarh University, Dibrugarh, Assam 786004, India
magnetospheric by Lee et al. [4]. Electron Bernstein waves are also found in Jupiter’s magnetosphere [5]. Very recently, electron Bernstein waves are detected in experimental tokamak plasmas [6]. Experimentally, electron Bernstein wave has been studied in tokamak plasma, especially in the spherical tokamak. Current research concerning electron cyclotron wave heating and current drive in the magnetically confined thermonuclear fusion [7] seems to be focused on conventional aspect ratio tokamak, particularly International Thermonuclear Experimental Reactor(ITER). However, in the spherical tokamak with aspect ratio A ¼ R0 =a close to unity (R0 and a being the major and minor radii, respectively) and weaker external magnetic field, the usual electron cyclotron mode transverse O- and X-m
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