Turbulence and transport by electron temperature gradient driven instability in large volume plasma device

Abstract We present a topical review of the detailed experimental investigations of the Electron Temperature Gradient (ETG) instability-induced turbulence and associated transport that have been carried out in the Large Volume Plasma Device (LVPD) at the Institute for Plasma Research. These results pertaining to a high beta plasma are supported by theoretical modeling and their significance with relation to earlier ETG investigations are discussed. The removal of non-thermal electrons and control of electron temperature gradient, $$\nabla {T}_{e}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>∇</mml:mi> <mml:msub> <mml:mi>T</mml:mi> <mml:mi>e</mml:mi> </mml:msub> </mml:mrow> </mml:math> are achieved in a finite beta plasma ( β ∼ 0 . 6) by making use of an Electron Energy Filter (EEF). It divides the plasma into source, EEF and target regions. In the core region ( $$x\le 50$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>x</mml:mi> <mml:mo>≤</mml:mo> <mml:mn>50</mml:mn> </mml:mrow> </mml:math> cm) of target plasma, the observed electromagnetic instability exhibits fluctuations in the lower hybrid range of frequencies ( $$f=1-80 kHz$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> <mml:mo>-</mml:mo> <mml:mn>80</mml:mn> <mml:mi>k</mml:mi> <mml:mi>H</mml:mi> <mml:mi>z</mml:mi> </mml:mrow> </mml:math> ), with a broad band spectra having its peak power at wave number, $${k}_{\perp }=\left(0.1-0.2\right)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>k</mml:mi> <mml:mo>⊥</mml:mo> </mml:msub> <mml:mo>=</mml:mo> <mml:mfenced> <mml:mn>0.1</mml:mn> <mml:mo>-</mml:mo> <mml:mn>0.2</mml:mn> </mml:mfenced> </mml:mrow> </mml:math> cm −1 and frequency, f ~ 10 kHz satisfying condition $${k}_{\perp }{\rho }_{e}\le 1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>k</mml:mi> <mml:mo>⊥</mml:mo> </mml:msub> <mml:msub> <mml:mi>ρ</mml:mi> <mml:mi>e</mml:mi> </mml:msub> <mml:mo>≤</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> and $${k}_{\parallel }/{k}_{\perp }&lt;$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>k</mml:mi> <mml:mo>‖</mml:mo> </mml:msub> <mml:mo>/</mml:mo> <mml:msub> <mml:mi>k</mml:mi> <mml:mo>⊥</mml:mo> </mml:msub> <mml:mo>&lt;</mml:mo> </mml:mrow> </mml:math> 1, where $${\rho }_{e}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>ρ</mml:mi> <mml:mi>e</mml:mi> </mml:msub> </mml:math> is the electron Larmor radius and $${k}_{\perp }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>k</mml:mi> <mml:mo>⊥</mml:mo> </mml:msub> </mml:math> and $${k}_{\parallel }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>k</mml:mi> <mml:mo>‖</mml:mo> </mml:msub> </mml:math> are the perpendicular and parallel wave numbers, respectively. It was demonstrated successfully that when $$\nabla {T}_{e}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>∇</mml:mi> <mml:msub> <mml:mi>T</mml:mi> <mml:mi>e</mml:mi> </mml:msub> </mml:mrow> </mml:math> is made significant such that $${\eta }_{e}\approx {L}_{n}/{L}_{Te}&gt;2/3$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>η</mml:mi> <mml:mi>e</mml:mi> </mml:msub> <mml:mo>≈</mml:mo> <mml:msub> <mml:mi>L</mml:mi> <mml:mi>n</mml:mi> </mml:msub> <mml:mo>/</mml:mo> <mml:msub> <mml:mi>L</mml:mi> <mml:mrow> <mml:mi>Te</mml:mi> </mml:mrow> </mml:msub> <mml:mo>&gt;</mml:mo> <mml:mn>2</mml:mn> <mml:mo>/</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:math> , where $${L}_{n}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>L</mml:mi> <mml:mi>n</mml:mi> </mml:msub> </mml:math> is density scale length and $${L}_{Te}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>L</mml:mi> <mml:mrow> <mml:mi>Te</mml:mi> </mml:mrow> </mml:msub> </mml:math> is electron temperature scale length, the ETG scale turbulence gets excited in the presence of pre-excited Whistler mode. A linear theory of coupled Whistler-Electron Temperature Gradient (W-ETG) mode is developed using a two-fluid model applicable for the LVPD plasma. A comparison of the experimental and numerical results is found to be in good agreement. Upon identification of the ETG turbulence, the electrostatic and electromagnetic particle fluxes and energy flux induced by it in the target region of LVPD were investigated. We observed an inward directed radial particle flux, but total heat flux remained radially outward. The particle and thermal fluxes are compared with the numerically obtained values and are found to be in good agreement in the core plasma of LVPD.