Sensitivity of detachment extent to magnetic configuration and external parameters

Abstract

Divertor detachment may be essential to reduce heat loads to magnetic fusion tokamak reactor divertor surfaces. Yet in experiments it is difficult to control the extent of the detached, low pressure, plasma region. At maximum extent the front edge of the detached region reaches the X-point and can lead to degradation of core plasma properties. We define the ‘detachment window’ in a given position control variable C (for example, the upstream plasma density) as the range in C within which the front location can be stably held at any position from the target to the X-point; increased detachment window corresponds to better control. We extend a 1D analytic model [] to determine the detachment window for the following control variables: the upstream plasma density, the impurity concentration and the power entering the scrape-off layer (SOL). We find that variations in magnetic configuration can have strong effects; increasing the ratio of the total magnetic field at the X-point to that at the target, , (total flux expansion, as in the super-x divertor configuration) strongly increases the detachment window for all control variables studied, thus strongly improving detachment front control and the capability of the divertor plasma to passively accommodate transients while still staying detached. Increasing flux tube length and thus volume in the divertor, through poloidal flux expansion (as in the snowflake or x-divertor configurations) or length of the divertor, also increases the detachment window, but less than the total flux expansion does. The sensitivity of the detachment front location, zh, to each control variable, C, defined as , depends on the magnetic configuration. The size of the radiating volume and the total divertor radiation increase and , respectively, but not by increasing divertor poloidal flux expansion or field line length. We believe this model is applicable more generally to any thermal fronts in flux tubes with varying magnetic field, and similar sources and sinks, such as detachment fronts in stellarator divertors and solar prominences in coronal loops.

Using SOLPS to confirm the importance of total flux expansion in Super-X divertors

“…(Petrie et al 2013) predicted that in the attached, conduction-limited phase, the target electron density and temperature scale approximately with f 2 R and 1/f 2 R , respectively. (Lipschultz et al 2016), using a model based on energy balance, predicted that the upstream density required for detachment onset scales with 1/f R , while the upstream density required for the thermal front to reach the X-point is independent of f R (i.e. the detachment 'window' increases with f R , making detachment control easier).…”

“…§ This quantity has been previously referred to as 'total flux expansion', e.g. (Lipschultz et al 2016, Theiler et al 2016. Here we choose the nomenclature 'parallel area expansion', since it is the parallel area that is chaging while the magnetic flux is conserved.…”

E×B Flux Driven Detachment Bifurcation in the DIII-D Tokamak

“…The key parameter to be controlled when operating with detached divertor legs is the extent at which the upper end of the cold plasma region below T e ∼ 5 eV, i.e., the detachment front, is located in the divertor leg between the target and the X-point [7,8] (Fig. 1).…”

Overview of new MAST physics in anticipation of first results from MAST Upgrade

“…MAST-U will have unprecedented flexibility to tailor the magnetic geometry within up-down symmetric, tightly baffled divertor chambers and excellent diagnostics to improve our understanding of detachment onset and control with a radiating zone in the leg away from the X-point in conventional and alternative divertor configurations, such as the Super-X [1]. The sensitivity of detachment to external control was studied using an analytic 1D model along the magnetic field [25] including heat conduction and impurity concentration to estimate the 'detachment window', i.e. the variation of the upstream density, power crossing the separatrix (PSOL) and radiation from impurities that leads to the detachment front moving from the divertor target to the X-point.…”