Tungsten erosion by impurities and redeposition: focus on the magnetised sheath

Abstract

The effect of the magnetised sheath on the gross erosion and redeposition of tungsten is examined with an insight on impurity impact energy and angle. A complete treatment of the impact energy is performed leading to a scaling that differs from the usual 2k B T i +3Zk B T e formula. It is found that even if the energy distribution at the sheath entrance strongly differs from this approximation, the discrepancy remains under 20% for the impact energy. The average impact angle of a set of impurities is calculated. The difference between models with and without sheath electric field depends strongly on the charge state and mass of the impurity considered. This can lead, for example in the case of gross sputtering due to impinging W 12+ , to an underestimation of 3-4 times at T e = 25 eV for very grazing angles. Scalings for high (n e > 10 20 m −3 ) and low (n e < 10 15 m −3 ) density cases are deduced and provide a good estimation of the average impact angle of all impurities. Finally the magnetised sheath is shown to have an effect on the redeposition through two contributions: it increases the prompt redeposition contribution to the total redeposition and constitutes a potential barrier for the ions leaving the surface. A discussion is provided about the optimal width of the simulation domain to capture these effects.

ERO modeling and sensitivity analysis of locally enhanced beryllium erosion by magnetically connected antennas

“…The magnetic field geometry and sheath structure are known to modify these impact distributions, and the angle and energy of the impacts greatly affects the probability for consequent sputtering (see Refs. [22,33,34] and references therein).…”

Recent DIII-D progress toward validating models of tungsten erosion, re-deposition, and migration for application to next-step fusion devices

“…The effect of the sheath electric field on the subsequent trajectories can be characterized by the potential energy of tungsten impurities normalized to their kinetic energy [24]. This ratio can be considered as an effective sheath electric field, , ´-~), as discussed in [12]. As a consequence, the sheath electric field impacts the trajectories of heavy impurities like tungsten more dramatically than lighter impurities (figure 1(b)).…”

“…As a result of the large width of the sheath near divertor targets, a vast majority of tungsten impurities sputtered from divertor PFMs are ionized multiple times within the sheath and accelerated back toward the divertor surfaces by the sheath electric field over a distance comparable to the Larmor radius, a process known as prompt re-deposition [6][7][8]. The complexity of predictive models for tungsten prompt re-deposition and net erosion in divertors has been noted [9][10][11][12][13][14][15]. Experimental measurements of tungsten net erosion in divertors of various devices, such as JET [16], DIII-D [17][18][19], ASDEX-Upgrade [20] or WEST [21], are generally well-reproduced by numerical models, e.g., ERO [22].…”

Determination of the characteristic magnetic pre-sheath length at divertor surfaces using micro-engineered targets on DiMES at DIII-D

“…The ion trajectory in the sheath has been modeled with equation-of-motion (EOM) [16,25], ERO Monte Carlo [12,26,27], kinetic particle-in-cell (PIC) [28], and large gyro-orbit model [9] calculations. A calculation reported that the ion angle distribution (IAD) in the sheath varies drastically by changing the sheath length [25].…”