2.3. Effects of roughness on PMI

2. PMI basics

fusion device.

2.1. Ion-surface interactions

effects on the core plasma performance.

2.2. Simulating ion-surface interactions

The basic interaction of a plasma bounded by a material surface is the balance of charged particles that arrive at a given time. In a magnetized plasma, the incident ions gyro-orbit around magnetic field lines that intersect material surfaces at ultra-shallow angles between 1 and 3 with respect to the surface, resulting in the so-called "Chodura sheath" where incident ions arrive with a distribution of incident angles and energies ranging from 20 to 60 with respect to surface normal and energies between 10 and 100 eV, respectively. The incident ions (mostly hydrogen fuel particles) implant at depths between a few nm to hundreds of nm. Sputtering of the wall material will depend on these conditions for both light and heavy mass target materials. The incident hydrogen particles will also reflect or backscatter from the surface and carry a finite amount of energy also resulting in a balance of implanted versus recycled fuel particles in a fusion device. In this section, we briefly discuss some of the most salient sputtering and reflection mechanisms with realistic (e.g., rough) surfaces found in a

50 Plasma Science and Technology - Basic Fundamentals and Modern Applications

Ion-surface interactions are one of the most important effects in fusion research devices. Open field lines terminate at divertor plates or strike walls at very grazing angles. The ion trajectories, which spiral around these field lines, direct energetic ions onto the wall material. Therefore, ion-solid and more recently ion-liquid interactions are the critical reaction at the boundary and therefore the most important to understand. The incident ion could reflect back into the plasma or could become embedded in the surface. Perhaps more importantly, the ion could knock some of the wall material into the plasma, thus leading to sputtering. Since sputtered species are usually electrically neutral, they ignore magnetic field lines and can penetrate a significant distance into the plasma before becoming ionized. Therefore, the energy and angular distribution of sputtered material becomes crucial to predicting edge plasma behavior, and the behavior of the edge plasma is often a controlling factor on the behavior of the core plasma. The interaction of energetic ions with wall materials can also result in not only erosion and re-deposition of post-ionized material wall particles but also could drive composition and morphology changes that over time significantly affect materials' surface properties. Both composition and morphology changes on the surface can result in significant changes both to the plasma-material interactions and consequently to the plasma edge, which can have

The number of variables that could go into a single ion-surface interaction is numerous. Consider the incident ion. What is its mass, its atomic number, its energy? What angle does it strike the surface with respect to the surface normal? Now, consider the target material. What is its composition, and how does that composition vary with depth? What does the surface roughness look like and at what scale lengths? What is the chemical binding energy of the variety of constituents that may be present, and with what energy is each constituent bound to Expanding from the successful TRIM simulation platform, many variances have emerged over many decades and one of them is the incorporation of fractal geometry to mimic realistic surfaces [4].

Figure 1a shows the reflection of 50 eV H from an Ni surface as a function of fractal dimension [5]. Rn is the fraction of particles that reflect and Re is the fraction of energy that is reflected. Note the precipitous drop in both Rn and Re when some roughness is added, especially when the incident particle strikes the surface at a grazing incidence (75 from the normal). Initially, roughness reduces reflection as expected. The gradual rise in reflection for very rough surfaces is attributed to there being less of a chance for an upward-moving atom to be recaptured due to the lower average density of the material near the surface. Planar TRIM is akin to the D = 2.00 case for normal incidence. Some interesting comparisons [4] are shown in Figure 1b. Here, D is fixed at 2.30 and planar TRIM is compared to fractal TRIM (FTRIM) for three different incident energies as a function of incident angle. Specular reflection tendencies are clearly seen with TRIM but not in FTRIM. At 50 eV, the calculation was repeated using both generator A and generator B (see Figure 1) to show that the results did not depend on the generator, just on the dimension. Finally, a comparison is made with a molecular dynamic simulation at 10 eV. The similarity of those results shows that FTRIM can be used with some confidence even at low energies. Comparisons of predicted reflection to experiment are not possible because reflection measurements have not been done in this energy range. The reflected particles come off neutral and are very difficult to detect. A better comparison to experiment can be made when sputtering is considered.

Figure 2a shows the FTRIM prediction [6] for physical sputtering of 300 eV H on C and normal incidence and at 60 incidence. Two experimental points [7] are also shown where the fractal

Figure 1. (a) Rn and Re, particle and energy reflection coefficients, versus fractal dimension D for normal incidence (α = 0) and grazing incidence (α = 75) for three different surfaces. H is incident on Ni at 50 eV. The error bars are the size of the data points. Note the large drop-off of R at the grazing incidence when D is greater than 2.00. (b) Reflection coefficients for 10, 50, and 100 eV H on Ni as a function of the incident angle (with respect to normal, w.R.T.) for a fractal Ni surface with dimension 2.30. Planar TRIM results and a molecular dynamics calculation using the embedded atom method (EAM) are also shown. Note that planar TRIM predicts reflection at the grazing incidence to be two to three times more likely than the fractal TRIM results. Statistical errors in the fractal and planar TRIM reflection coefficients are generally less than 5%.

3. Sputtering from plasma-material interactions

One of the fundamental interactions between plasmas and material surfaces is physical sputtering or ion-induced desorption. The plasma edge magnetic field lines in a magnetic fusion device such as a tokamak directs energetic charged particles to gyro-orbit and bombards surfaces at both incident angle distributions and energy distributions that are linked with the operational regime of the fusion device. Therefore, the average incident angle will be close to 45 with respect to the normal and low-incident-particle energies. Fusion device PMI can be divided between two overall types of solid-state materials: low-Z materials and high-Z materials. There is a trade-off in the selection of materials for the first wall in fusion devices. The cooling of the plasma due to eroded particles from the device wall material goes as ~Z2

Figure 2. (a) Sputtering yield of 300 eV H on C as a function of fractal dimension, D. The D of the experimental points by Haasz et al. [7] is based on the work by Avnir et al. [8]. (b) Sputtering yield of target material as a function of the fractal dimension and the angle of incidence for 100 eV C incident on a C target. The normal incidence is 0. Statistical errors in

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Therefore, low-Z materials are attractive; however, these materials tend to have low surface binding energies, which result in high-sputter yields. The sputtering yield is defined as the ratio of flux of sputtered particles over the flux of incident energetic particles. High-Z materials can sputter orders of magnitude lower than low-Z materials; however, this must be balanced against plasma cooling losses. As stated earlier in fusion devices, the material surface will

Low-Z material sputtering is relevant to plasma-surface interaction physics in fusion devices from the standpoint of minimizing fractional impurity levels in fusion plasmas [12]. Figure 3a shows experimental measurements and VFTRIM-3D simulations of sputtering yields for Li, He, and D bombardment at 45 incidence on deuterium-treated solid-phase lithium [13].

.

3.1. Solid-phase sputtering of fusion-relevant materials

the yield are generally less than 5%.

evolve where roughness can become significant [9–11].

3.1.1. Low-Z material sputtering by light incident particles

dimension of the surface is known [8] and the agreement is very good. Figure 2b shows the sputtering yield of 100 eV C on C as a function of the fractal dimension for a variety of incident angles. Initially, adding roughness increases the yield. This is due to the ability of the incident ions to knock off target atoms, which may protrude from the surface. Therefore, as expected, higher angles of incidence show an even greater rise in sputtering. The sputtering goes down for a very high roughness because the sputtered atoms are recaptured by overhanging features. Planar TRIM results are also shown. Note that the effective surface roughness for planar TRIM is only 2.00 at the normal incidence. The algorithm described earlier picks the location of the initial collision partner. If that partner would be above the surface, it is not used. The set of initial collision partner locations has a nonuniform depth distribution if the incident angle is not perpendicular to the surface. An equivalent roughness to the fractal surfaces can then be assigned. FTRIM predicts less sputtering than TRIM at higher angles of incidence and more sputtering at normal incidence. This result is significant, in that the realistic surfaces that evolve due to plasma-induced erosion and re-deposition in a fusion device with enhanced roughness will likely impact the amount of net erosion and reflected energy of fuel particles that can influence the operational regimes in these devices.

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Figure 2. (a) Sputtering yield of 300 eV H on C as a function of fractal dimension, D. The D of the experimental points by Haasz et al. [7] is based on the work by Avnir et al. [8]. (b) Sputtering yield of target material as a function of the fractal dimension and the angle of incidence for 100 eV C incident on a C target. The normal incidence is 0. Statistical errors in the yield are generally less than 5%.
