Fusion Energy Research Program

Department of Applied Mechanics and Engineering Sciences

University of California, San Diego

9500 Gilman Dr., La Jolla, CA 92093-0417

Fig. 1 The moving-belt PFC concept with ex-situ inline belt regeneration

systems for tritium recovery, heat removal and getter coatings [3].

In our recent work [3], as shown in Fig. 1, the use of moving-belt plasma-facing components (MB-PFCs) with ex-situ belt regeneration systems for continuous impurity gettering, heat removal and tritium recovery has been proposed. In order to minimize MHD effects and induced radioactivity, semi-conductor materials such as SiC-fiber fabrics are considered for the belt. These fibers are woven without binder, so that the resultant fabrics remain flexible. To compensate for the gas leak through the belt openings, the regeneration systems may be housed in a low vacuum enclosure. Importantly, MB-PFCs can be applied for all types of magnetic fusion devices whether or not in the full toroidal configuration.

The MB-PFC system performance has been evaluated in case studies under selected reactor relevant conditions, similar to those listed in Table 1. It is found that the belt erosion rate is diluted over the total belt area and is independent of moving speed. Non-saturable impurity gettering is possible under zero-erosion conditions. Heat removal can be carried out continuously either by radiative cooling or contact conductance. High-efficiency tritium recovery can be maintained for long-term (~ 100 years) operation, mitigating the impact on environmental safety.

Proposed in this report is modular application of MB-PFCs, meaning that a toroidal fusion device is installed with two or more MB-PFC modules, operating under the optimized conditions for their respective functions such as particle control and heat removal. This modular approach will avoid over-expectations like one configuration for all functions, the traditional PFC technology dilemma.

(1)

where G_{MB-e} is the erosion rate of
a moving belt, G_{e} is the erosion
rate of a standing surface component, l_{p} is the plasma
interaction length and L is the total belt length. The erosion rate is "diluted"
over the moving surface by a factor of (l_{p}/L) and independent of
belt speed.

Also, it has been demonstrated that unlimited lifetime MB-PFCs can be achieved by coating the belt with gettering materials such as Li, Be, and B at the same rate as they may be eroded during plasma exposure. The coatings deposition rate is given by the following relation:

(2)

where G_{MB-d. }is the deposition rate on a moving belt,
G_{d} is the deposition rate on a standing belt, l_{d}
is the length of the coating section, f(q) is the correction factor for
the viewing angle, q, and n is the trapping coefficient. Notice that the
aerial dilution factor, (l_{d}/L), appears in eq. (2), too.

Under the conditions listed in Table 1, TRIM.SP [4] calculations indicate
that C, O-impurities will be trapped at the efficiency of 100% by Li, Be, B
getters as long as the surface implanted layer is unsaturated. The effective
impurity deposition flux on a moving belt is estimated from eq. (2), setting
f(q)=1, n =1, and l_{d} = l_{p}. Here, we define the degree of saturation in getter coatings as follows:

(3)

where h_{ }is the degree of saturation, v is the belt speed,
G_{in} is the incoming particle flux, R is the implantation range, d_{a} is the atomic spacing, and N_{s} is the monolayer atomic density. The factors, (l_{p}/v) and (R/d_{a}), will thus
give the plasma exposure time and the number of monolayers in the range,
respectively. We assume that C, O-impurities will be gettered 100% (i.e., n
=1) as long as h __<__ h_{max-i.}= 0.5, above which
gettering is prevented due to the formation of compounds such as
Li_{2}O and/or B_{4}C. For simplicity, the maximum saturation
is assumed not to vary with temperature.

(4)

where G_{loss }is the D, T-particle loss rate, V is the total
plasma volume, n_{c }is the averaged plasma density, and t_{p
}is the global particle confinement time. To remove these particles, the
pumping system must meet the condition:

(5)

where S_{p} is the pumping speed, and P is the neutral pressure.
From the conditions in Table 1, one finds that G_{loss }= 5 x 10^{22} DT
particles/s, i.e., 1.5 x 10^{3} Torr l s. Although
it depends on the operational scenario, the edge neutral pressure is assumed
to be of the order of 10^{-3} Torr. This leads to the requirement
that S_{p} = 1.5 x 10^{6} l/s, which is extremely difficult
to be maintained for steady-state operation. In the case of ITER [1], a large
number of cryo pumps are designed to operate in an alternating mode: one
group in operation and the other under regeneration.

As such, steady-state particle removal is a key issue affecting the operational scenario. Generally, the pumping speed is restricted by gas conductance. Many existing fusion devices are equipped with large turbo molecular pumps and/or cryo pumps but in severely limited conductance configurations for protecting the inlet structure from high energy particle bombardment. On the other hand, it is well known that the first wall materials such as graphite often provide more pumping effects than actual pumps. This is because the first wall has a larger surface area and can tolerate direct bombardment of high energy plasma particles. By nature, however, these wall pumping effects are saturable and need to be regenerated.

The possibility of using MB-PFCs is thus evaluated next as a pump to remove
fuel particles at steady-state. Here, we assume that the degrees of saturation
in getter-coatings as to hydrogenic species and impurities are independent of
each other. Hydrogenic species are assumed to be trapped 100% as long as [eta]
__<__ h_{max-f. }= 0.4, the
data widely accepted for graphite [8]. Compared with hydride stoicheometries
such as LiH_{2}, this is a very conservative assumption. It is
important to mention that the saturation level remains unchanged up to
about 500 ^{o}C but decreases exponentially as temperature
increases above this point.

Total plasma volume, V | 1000 m^{3} |

Averaged plasma density, n_{c} | 10^{20} m^{-3} |

Global particle confinement time, t_{p} | 2 s |

Divertor footprint total area, A_{div.} | 5 m^{2} |

Edge neutral pressure, P | 10^{-3 }Torr |

Impurity-to-fuel plasma flux ratio | 0.01 |

Particle bombarding energy, E | 100 eV |

Averaged plasma heat flux, <q_{p}> | 1 MW/m^{2} |

Belt length, L | 20 m |

Plasma interaction length, l_{p} | 0.5 m |

Belt width, w | 1 m |

Belt speed, v | 2 m/s |

Belt thickness, t_{b} | 5 mm |

Belt density, r | 2.2 g/cm^{3} |

Belt temperature during exposure | 500°C (Module-I) |

1000°C (Module-II) | |

Belt surface emissivity, e | 0.8 |

Thermal conductivity (perp),
k_{1} | 5 W/m-K |

Thermal conductivity (//), k_{2} | 50 W/m-K |

Heat capacity, C_{p} | 0.710 J/g-K |

Thermal diffusivity, a | 0.032^{ }cm^{2}/s |

Stefan-Boltzman constant, s |
5.7x10^{-12}/sW/cm^{2}-K^{4} |

Under the conditions listed in Table 1: E = 100 eV, G_{f }= 1 x
10^{18 }D,T/cm^{2}/s and G_{ i}= 1 x 10^{18
}C,O/cm^{2}/s, it is required for MB-PFCs to be able to pump these
incoming particles that l_{p}/v < 0.34 for DT-particles and
l_{p}/v < 4.2 for C, O-impurities, using the diagram in Fig. 2. As
such, the requirement for DT-fuel particle pumping generally covers that for
impurity gettering. For example, the case study condition in Table 1:
l_{p}/v = 0.25 meets both the requirements. It is thus possible to
operate one module for two purposes.

However, modular application allows us to operate two MB-PFCs: one for impurities and the other for DT-fuel pumping under two different conditions. This capability is particularly important if a specific gettering material and/or specific temperature are required. For example, helium gettering requires nickel coatings [7] which may not be the best for DT-fuel particle pumping.

The throughput speed of the MB-PFC module in this case study, having the
plasma exposure size of 50 cm x 100 cm, is 1.5 x 10^{2 }Torr l/s for
DT-particles. Only ten of these modules can meet the requirement for ITER: 1.5
x 10^{3 }Torr l/s. Here, the belt temperature must be maintained lower
than 500 °C for effective particle control. This will be shown to
be possible in the next section.

Fig. 2 MB-PFC operational space diagram as to l_{p}/v, plotted
against particle fluxes for different l_{p}/L. Two sets of curves are
illustrated: the subscripts of i and f indicate impurity and fuel,
respectively.

The need to remove heat under vacuum conditions raises special concerns. Previously, we examined three possible mechanisms for heat removal in a vacuum or low-pressure heat exchanger: contact conductance, thermal radiation, and impinging liquid jets. Radiation heat transfer possesses clear operational advantages but is compatible only with temperatures above 800 - 1000°C. Operation in this range allows not only effective heat removal, but also the possibility of energy conversion with efficiency of 50% or more. Below 800°C, contact conductance has been shown to easily transfer the required heat loads even at low temperature [3].

In this work the limits of heat removal from a moving belt divertor have been
quantified in both the exposure zone and heat exchanger. The maximum heat flux
and total energy removed by the belt depends on the maximum allowable
temperature as well as the maximum allowable belt speed. In order to avoid the
belt materials erosion due to radiation-enhanced sublimation, we have
restricted the maximum surface temperature to 1000°C. In this regime,
radiation from the exposed belt surface to the first wall (~0.1
MW/m^{2}) can be neglected since it is much less than the incident heat
flux. A belt temperature much higher than 1000°C would not offer
substantial improvement, and may complicate material selection in the heat
exchanger.

The maximum belt speed depends on the belt drive system, which uses vacuum rollers for direction and speed control. In order to minimize the forces on the tensioning system and prevent excessive belt stretching and erosion, a limit of 2 m/s is imposed. This is a soft limit, which can be further refined through experimentation.

(6)

(7)

Here l_{p} is the heated length (plasma-exposed length), *f* is
the peaking factor, and *x* is measured with respect to the center of the
Gaussian. This heat flux was used as a boundary condition on the energy
equation expressed in a coordinate system moving with the belt speed:

(8)

Equation 8 neglects parallel conduction along the belt direction of position,
which is valid if a/v l_{p} <1. Even with a significantly
enhanced parallel belt conductivity of 50 W/m-K, this ratio is still of the
order of 3 x 10^{-5}.

Figure 3 shows an example of the non-dimensional temperature along the exposed
belt surface *vs.* non-dimensional time, t^{*}=
(t_{b}^{2}/a) t, for f = 2 and l = 5 cm, with
T^{*} defined by:

(9)

Fig. 3. Surface temperature with peaking factor = 2

Figure 4 shows the maximum surface temperature as a function of local peaking
for l = 5 cm. The maximum surface temperature occurs at the exit until
the peaking exceeds ~1. For low values of peaking, the maximum surface
temperature actually drops because heat is allowed to diffuse more deeply in
the belt before reaching the exit. Above a peaking factor of 2, the local heat
flux dominates, and the maximum temperature reaches an asymptotic value of T^{*}~ 0.4 when the heat flux is a pure Gaussian. For <q> = 2
MW/m^{2}, this asymptotic value corresponds with a surface temperature
~ 800°C higher than the inlet temperature. More moderate values of
peaking in the range of 2 - 4 would give 400 - 500°C temperature rise,
which could be reduced most easily by increasing the belt velocity.

Fig. 4. Maximum surface temperature vs. local peaking.

Fig. 5. Radiation heat exchanger schematic design

A counter-flow heat exchanger was analyzed for these conditions, including thermal resistance in the coolant walls and film. The governing equations are energy balance in the belt and coolant:

(10)

where subscripts "b", "s", and "h" refer to the belt, coolant channel surface and helium coolant, respectively. The temperature difference between the coolant channel surface and bulk coolant are determined from:

(11)

Results are shown in Figure 6 for a He outlet temperature of 700°C,
chosen to allow a high-temperature He Brayton cycle with thermal
conversion efficiency > 45%.

Fig. 6. Belt and He temperatures in heat exchanger.

(12)

A contact heat transfer scheme probably will require coolant flow through rotating seals, which is a complication but appears practical.

Fig. 7 An example of modular application of MB-PFCs.

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on Tokamak Operations",

* J. Nucl. Mater.* **162-164**(1989)151-161.

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