Magnetized plasma-wall transition layer with cold ions

Abstract

The magnetized plasma-wall transition (MPWT) layer occurring, for example near a tokamak diverter, typically consists of three distinct sublayers: the Debye sheath (DS), the magnetic presheath (MPS) and the collisional presheath (CPS), with characteristic lengths λ D (electron Debye length), ρ i (ion gyroradius) and λ (smallest relevant ion collision length), respectively. For analytical simplicity one usually assumes the ordering λ D Ӷ ρ i Ӷ λ, or, equivalently, ε D m ≡ λ D ρ i → 0 and ε m c ≡ ρ i λ → 0 ('asymptotic three-scale (A3S) limit'), in which the three sublayers are precisely defined. In the present work the equations and length scales governing the transition, or the 'intermediate' regions between neighboring sublayers (DS-MPS, MPS-CPS), in the A3S limit are derived, allowing one to avoid the singularities arising from the ε D m → 0 and ε m c → 0 approximations. The MPS entrance and the related Bohm-Chodura condition is defined in a natural way. It is found that in the hydrodynamic T i = 0 approximation the intermediate scales and equations have a universal form and a similar structure not only for the MPS-DS and CPS-MPS transitions but also for the DS-CPS transition in the non-magnetized case.

Comprehensive kinetic analysis of the plasma-wall transition layer in a strongly tilted magnetic field

“…We expect (and following calculations confirm) that (i) the width of the MPS sub-layer is of the order of q i ; This is quite commonly accepted assumption. 4,5,19,20 Below we show that in fact moving towards the MPS edge, the ions cover the distance Շ q i . fulfilled.…”

“…Using smallness of the parameter ðq e =' en Þ ( 1 (q e is the electron gyro-radius and ' en in the electron-neutral collations mean-free path) the electron distribution function we can represent in the form of the expansion (20) and reduce the corresponding kinetic equation to the form analogous to Eq. (25).…”

“…Comparison of expressions (45) and (77) shows that for connection of the potential shapes from both sides of the MPS and the CPS interface, we can as usually 11,20 introduce a characteristic scale-length l m and the renormalized variables…”

Debye-sheath properties in the Tonks–Langmuir discharge with warm neutrals

“…From the sheath side (on the sheath scale z/λ D ) the sheath edge is shifted to infinity, where the electric field goes to zero. Hence, the solutions corresponding to PS and DS cannot be matched smoothly without accounting for transition region on an intermediate scale (Riemann 2003;Tskhakaya et al 2010). It is obvious that for realizing such a smooth coupling, one has to find correct and comprehensive solutions and their asymptotic behaviour in the vicinity of the PS edge.…”

Pulsating fireballs with high-frequency sheath–plasma instabilities

“…The research on sheaths in plasmas has a long history [1]. It has been concerned with steady-state sheath and presheath properties in unmagnetized [2] and magnetized plasmas [3][4][5], transient phenomena [6][7][8], sheaths in rf plasmas [9], sheath instabilities [10][11][12] and sheaths with ionization phenomena [13][14][15][16][17][18][19][20]. The last is the topic of this work.…”