Analytic solution of the two-dimensional Fokker–Planck equation governing stochastic ion heating by a lower-hybrid wave

1982 ◽  
Vol 25 (8) ◽  
pp. 1411 ◽  
Author(s):  
G. Malescio
Keyword(s):  
Analytic Solution ◽  
Planck Equation ◽  
Lower Hybrid ◽  
Two Dimensional ◽  
Hybrid Wave ◽  
Ion Heating ◽  
Lower Hybrid Wave ◽  
Fokker Planck Equation ◽  
Fokker Planck

Semi-analytical inspection of the quasi-linear absorption of lower hybrid wave in presence of -particles in tokamak reactor

2018 ◽  
Vol 84 (5) ◽  
Author(s):  
A. Cardinali ◽  
C. Castaldo ◽  
R. Ricci
Keyword(s):  
Distribution Function ◽  
Planck Equation ◽  
Current Drive ◽  
Dielectric Tensor ◽  
Lower Hybrid ◽  
Linear Diffusion ◽  
Tokamak Reactor ◽  
Slowing Down ◽  
Fokker Planck Equation ◽  
Fokker Planck

In a reactor plasma like demonstration power station (DEMO), when using the radio frequency (RF) for heating or current drive in the lower hybrid (LH) frequency range (Frankeet al.,Fusion Engng Des., vol. 96–97, 2015, p. 46; Cardinaliet al.,Plasma Phys. Control. Fusion, vol. 59, 2017, 074002), a large fraction of the ion population (the continuously born$\unicode[STIX]{x1D6FC}$-particle, and/or the neutral beam injection (NBI) injected ions) is characterized by a non-thermal distribution function. The interaction (propagation and absorption) of the LH wave must be reformulated by considering the quasi-linear approach for each species separately. The collisional slowing down of such an ion population in a background of an electron and ion plasma is balanced by a quasi-linear diffusion in velocity space due to the propagating electromagnetic wave. In this paper, both propagations are considered by including the ion distribution function, solution of the Fokker–Planck equation, which describes the collisional dynamics of the$\unicode[STIX]{x1D6FC}$-particles including the effects of frictional slowing down, energy diffusion and pitch-angle scattering. Analytical solutions of the Fokker–Planck equation for the distribution function of$\unicode[STIX]{x1D6FC}$-particles with a background of ions and electrons at steady state are included in the calculation of the dielectric tensor. In the LH frequency domain, ray tracing (including quasi-linear damping), can be analytically solved by iterating with the Fokker–Planck solution, and the interaction of the LH wave with$\unicode[STIX]{x1D6FC}$-particles, thermal ions and electrons can be accounted self-consistently and the current drive efficiency can be evaluated in this more general scenario.

Ion heating by lower hybrid wave in the HT-7 tokamak

2001 ◽  
Vol 43 (6) ◽  
pp. 805-811 ◽  
Author(s):  
S X Liu ◽  
B N Wan ◽  
G L Kuang ◽  
X Gao ◽  
L Q Hu ◽  
...  
Keyword(s):  
Lower Hybrid ◽  
Hybrid Wave ◽  
Ion Heating ◽  
Lower Hybrid Wave
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