Theoretical study of pre-ionization by inductive field in tokamaks

Abstract

A one-dimensional fluid model is developed for a numerical study of pre-ionization in a tokamak device under a given external inductive field. The calculation space is a magnetic field line connecting the bottom and the top limiters, and the spatial profiles of ion and electron densities and their time evolutions are calculated, assuming density growth by the Townsend avalanche. It was found that at a low initial density, electrons are evacuated and exponential growth can be stopped (i.e. stagnation phase), and at a high density, formation of an ambipolar diffusion state may suppress further avalanche by compensating the external inductive field. The numerical study revealed that these two obstacles for pre-ionization can be avoided or mitigated under a certain condition. A high ion impact secondary electron emission efficiency at the limiter, a long field line length and a large Townsend’s coefficient are preferable to avoid the stagnation phase or to resume growth from the stagnation phase. The ambipolar diffusion state can be mitigated or avoided using the following four mechanisms: drift induced diffusion, and curvature drifts, a high ion impact secondary electron emission efficiency and AC inductive field. Among them, only the first is practically useful in weak inductive field large devices. Various analytical expressions describing these behaviors and the conditions for a successful pre-ionization are obtained.

Modelling of ohmic startup and runaway electron formation in support of JT-60SA initial operation

“…When the self-shielding field in equation (A.4) increases with the electron density, the mechanism can significantly retard the breakdown time. Although the effect of the self-shielding field requires self-consistent description of the potential formation [87,91,92] including the magnetic drift, the E × B drift, and the secondary electron emission from the wall, we here apply an ad hoc model considered by Battaglia et al [52], assuming that the applied electric field is shielded by up to 75% when E self in equation (A.4) exceeds E. We set the other parameter of equation (A.4) as γ ≈ 0.2-0.3 and T e = 1 eV in the simulation of this work. Another mechanism that breaks the assumption underlying the Townsend avalanche must be considered at low pressure.…”

Kinetic Analysis of the Characteristics of Electron Cyclotron Heating Assisted Ohmic Start-Up in the Trapped Particle Configuration of a Tokamak

“…It has been observed that reliable Ohmic breakdown requires E t B t /B p ≳ 10 3 V/m (E t is the toroidal electric field strength, B t is the toroidal magnetic field strength and B p is the poloidal magnetic field strength) that puts an upper limit on the tolerable "stray" poloidal field strength for successful start-up [1]. This is understood to be because the author's e-mail: tsujii@k.u-tokyo.ac.jp Ohmic breakdown is a Townsend avalanche process along the magnetic field lines that requires the connection length to be sufficiently long to minimize the electron loss [7]. Such minimization of the poloidal field, i.e., the field-null configuration, is not necessary when ECH is used for preionization since ECH accelerates electrons in the direction perpendicular to the magnetic field.…”

Understanding the electromagnetic topology during the ohmic breakdown in tokamaks considering self-generated electric fields

“…As the self-generated electric field has been getting more attention after our researches, some recent studies investigated its effect based on simplified geometry and model, such as 1D particle simulation in a periodic slab geometry [25][26][27], 1D fluid model along a straight poloidal magnetic field line [28], and 3D particle simulation without any magnetic field [29]. However, the simplified geometries and models may mislead the underlying mechanisms of the ohmic breakdown.…”